%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA127-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:45 PM UTC 2026
% Result : Unsatisfiable 0.75s 0.91s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA127-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.32 % Computer : n002.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 22:32:03 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.75/0.91 % SZS status Unsatisfiable
% 0.75/0.91 % SZS output start Proof
% 0.75/0.91 tff(b_type, type, (
% 0.75/0.91 b: ( $i * $i ) > $o)).
% 0.75/0.91 tff(s_type, type, (
% 0.75/0.91 s: $i > $i)).
% 0.75/0.91 tff(elem_1_type, type, (
% 0.75/0.91 elem_1: $i)).
% 0.75/0.91 tff(z_type, type, (
% 0.75/0.91 z: $i)).
% 0.75/0.91 tff(r_type, type, (
% 0.75/0.91 r: ( $i * $i ) > $o)).
% 0.75/0.91 tff(inj_0_type, type, (
% 0.75/0.91 inj_0: $i > $i)).
% 0.75/0.91 tff(1,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 0.75/0.91 tff(2,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.91 tff(3,plain,
% 0.75/0.91 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(4,plain,
% 0.75/0.91 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(5,plain,
% 0.75/0.91 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(6,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.75/0.91 tff(7,plain,
% 0.75/0.91 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.75/0.91 tff(8,plain,(
% 0.75/0.91 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.75/0.91 inference(skolemize,[status(sab)],[7])).
% 0.75/0.91 tff(9,plain,
% 0.75/0.91 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.75/0.91 tff(10,plain,
% 0.75/0.91 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.75/0.91 tff(11,plain,
% 0.75/0.91 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(12,plain,
% 0.75/0.91 (inj_0(s(s(z))) = s(z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.75/0.91 tff(13,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 0.75/0.91 tff(14,plain,
% 0.75/0.91 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[13])).
% 0.75/0.91 tff(15,plain,
% 0.75/0.91 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.75/0.91 inference(symmetry,[status(thm)],[14])).
% 0.75/0.91 tff(16,plain,
% 0.75/0.91 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(17,plain,
% 0.75/0.91 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.75/0.91 tff(18,plain,
% 0.75/0.91 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.75/0.91 inference(symmetry,[status(thm)],[17])).
% 0.75/0.91 tff(19,plain,
% 0.75/0.91 (s(elem!1) = s(z)),
% 0.75/0.91 inference(transitivity,[status(thm)],[18, 15, 12])).
% 0.75/0.91 tff(20,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1, 19])).
% 0.75/0.91 tff(21,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(22,plain,
% 0.75/0.91 (~(s(s(z)) = s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.75/0.91 tff(23,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.75/0.91 tff(24,assumption,(~r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.91 tff(25,plain,
% 0.75/0.91 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(26,plain,
% 0.75/0.91 (inj_0(s(z)) = z),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[25, 10])).
% 0.75/0.91 tff(27,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 0.75/0.92 tff(28,plain,
% 0.75/0.92 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[27])).
% 0.75/0.92 tff(29,plain,
% 0.75/0.92 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.75/0.92 inference(symmetry,[status(thm)],[28])).
% 0.75/0.92 tff(30,plain,
% 0.75/0.92 (s(elem!1) = z),
% 0.75/0.92 inference(transitivity,[status(thm)],[18, 29, 26])).
% 0.75/0.92 tff(31,plain,
% 0.75/0.92 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(32,plain,
% 0.75/0.92 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[31])).
% 0.75/0.92 tff(33,plain,
% 0.75/0.92 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(34,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.75/0.92 tff(35,plain,
% 0.75/0.92 (![X: $i] : (~(s(X) = z))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.75/0.92 tff(36,plain,(
% 0.75/0.92 ![X: $i] : (~(s(X) = z))),
% 0.75/0.92 inference(skolemize,[status(sab)],[35])).
% 0.75/0.92 tff(37,plain,
% 0.75/0.92 (![X: $i] : (~(s(X) = z))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.75/0.92 tff(38,plain,
% 0.75/0.92 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(39,plain,
% 0.75/0.92 (~(s(elem!1) = z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.75/0.92 tff(40,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[39, 30])).
% 0.75/0.92 tff(41,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(42,plain,
% 0.75/0.92 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(43,plain,
% 0.75/0.92 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[42])).
% 0.75/0.92 tff(44,plain,
% 0.75/0.92 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(45,plain,
% 0.75/0.92 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(46,plain,
% 0.75/0.92 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[45])).
% 0.75/0.92 tff(47,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.75/0.92 tff(48,plain,
% 0.75/0.92 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.75/0.92 tff(49,plain,
% 0.75/0.92 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.75/0.92 tff(50,plain,(
% 0.75/0.92 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(skolemize,[status(sab)],[49])).
% 0.75/0.92 tff(51,plain,
% 0.75/0.92 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.75/0.92 tff(52,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(53,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(54,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.75/0.92 tff(55,plain,
% 0.75/0.92 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.75/0.92 tff(56,plain,
% 0.75/0.92 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[55, 41])).
% 0.75/0.92 tff(57,plain,
% 0.75/0.92 (b(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[56, 24])).
% 0.75/0.92 tff(58,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 0.75/0.92 tff(59,plain,
% 0.75/0.92 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[58])).
% 0.75/0.92 tff(60,plain,
% 0.75/0.92 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[59])).
% 0.75/0.92 tff(61,plain,
% 0.75/0.92 ((~r(s(z), s(s(elem!1)))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[60])).
% 0.75/0.92 tff(62,plain,
% 0.75/0.92 (~r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[24, 61])).
% 0.75/0.92 tff(63,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(64,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 0.75/0.92 tff(65,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 0.75/0.92 tff(66,plain,
% 0.75/0.92 (s(z) = s(s(z))),
% 0.75/0.92 inference(symmetry,[status(thm)],[65])).
% 0.75/0.92 tff(67,plain,
% 0.75/0.92 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[66])).
% 0.75/0.92 tff(68,plain,
% 0.75/0.92 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.75/0.92 inference(symmetry,[status(thm)],[67])).
% 0.75/0.92 tff(69,plain,
% 0.75/0.92 (s(z) = inj_0(s(s(z)))),
% 0.75/0.92 inference(symmetry,[status(thm)],[12])).
% 0.75/0.92 tff(70,plain,
% 0.75/0.92 (s(z) = z),
% 0.75/0.92 inference(transitivity,[status(thm)],[69, 68, 26])).
% 0.75/0.92 tff(71,plain,
% 0.75/0.92 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(72,plain,
% 0.75/0.92 (~(s(z) = z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[71, 37])).
% 0.75/0.92 tff(73,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[72, 70])).
% 0.75/0.92 tff(74,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(75,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(76,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(77,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.75/0.92 tff(78,plain,
% 0.75/0.92 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[77, 51])).
% 0.75/0.92 tff(79,plain,
% 0.75/0.92 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[78, 74])).
% 0.75/0.92 tff(80,plain,
% 0.75/0.92 (r(s(s(z)), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[79, 64])).
% 0.75/0.92 tff(81,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(82,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.75/0.92 tff(83,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(84,plain,
% 0.75/0.92 (s(s(s(elem!1))) = s(z)),
% 0.75/0.92 inference(symmetry,[status(thm)],[83])).
% 0.75/0.92 tff(85,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 0.75/0.92 tff(86,plain,
% 0.75/0.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[85])).
% 0.75/0.92 tff(87,plain,
% 0.75/0.92 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(88,plain,
% 0.75/0.92 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[87, 10])).
% 0.75/0.92 tff(89,plain,
% 0.75/0.92 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[88])).
% 0.75/0.92 tff(90,plain,
% 0.75/0.92 (s(s(elem!1)) = z),
% 0.75/0.92 inference(transitivity,[status(thm)],[89, 86, 26])).
% 0.75/0.92 tff(91,plain,
% 0.75/0.92 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(92,plain,
% 0.75/0.92 (~(s(s(elem!1)) = z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[91, 37])).
% 0.75/0.92 tff(93,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[92, 90])).
% 0.75/0.92 tff(94,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(95,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[94, 84])).
% 0.75/0.92 tff(96,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(97,plain,
% 0.75/0.92 (((~![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)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(98,plain,
% 0.75/0.92 ((~![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)))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(99,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.75/0.92 tff(100,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[99, 51, 81, 63, 96])).
% 0.75/0.92 tff(101,plain,(r(s(z), s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(102,plain,
% 0.75/0.92 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[101, 81])).
% 0.75/0.92 tff(103,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 0.75/0.92 tff(104,plain,
% 0.75/0.92 (s(z) = s(s(elem!1))),
% 0.75/0.92 inference(symmetry,[status(thm)],[103])).
% 0.75/0.92 tff(105,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[41, 104])).
% 0.75/0.92 tff(106,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(107,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.75/0.92 tff(108,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(109,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(110,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.75/0.92 tff(111,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[110, 51, 107, 82, 106])).
% 0.75/0.92 tff(112,plain,(r(s(s(elem!1)), s(z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(113,plain,
% 0.75/0.92 (r(s(s(elem!1)), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[112, 82])).
% 0.75/0.92 tff(114,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(115,plain,
% 0.75/0.92 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(116,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[115])).
% 0.75/0.92 tff(117,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(118,plain,
% 0.75/0.92 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(119,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[118])).
% 0.75/0.92 tff(120,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.75/0.92 tff(121,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.75/0.92 tff(122,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.75/0.92 tff(123,plain,(
% 0.75/0.92 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(skolemize,[status(sab)],[122])).
% 0.75/0.92 tff(124,plain,
% 0.75/0.92 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.75/0.92 tff(125,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(126,plain,
% 0.75/0.92 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(127,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[126])).
% 0.75/0.92 tff(128,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(transitivity,[status(thm)],[127, 125])).
% 0.75/0.92 tff(129,plain,
% 0.75/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(130,plain,
% 0.75/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.75/0.92 tff(131,plain,
% 0.75/0.92 (~r(s(s(z)), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[130, 124, 80, 113])).
% 0.75/0.92 tff(132,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(133,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(134,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.75/0.92 tff(135,plain,
% 0.75/0.92 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[134, 51])).
% 0.75/0.92 tff(136,plain,
% 0.75/0.92 (b(s(s(z)), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[135, 131, 114])).
% 0.75/0.92 tff(137,plain,
% 0.75/0.92 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(138,plain,
% 0.75/0.92 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[137, 10])).
% 0.75/0.92 tff(139,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 0.75/0.92 tff(140,plain,
% 0.75/0.92 (s(s(z)) = s(s(s(z)))),
% 0.75/0.92 inference(symmetry,[status(thm)],[139])).
% 0.75/0.92 tff(141,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.75/0.92 tff(142,plain,
% 0.75/0.92 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[141])).
% 0.75/0.92 tff(143,plain,
% 0.75/0.92 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 0.75/0.92 inference(symmetry,[status(thm)],[142])).
% 0.75/0.92 tff(144,plain,
% 0.75/0.92 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[138])).
% 0.75/0.92 tff(145,plain,
% 0.75/0.92 (s(s(z)) = s(z)),
% 0.75/0.92 inference(transitivity,[status(thm)],[144, 143, 12])).
% 0.75/0.92 tff(146,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[74, 145])).
% 0.75/0.92 tff(147,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(148,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[147, 140])).
% 0.75/0.92 tff(149,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(150,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(151,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 0.75/0.92 tff(152,plain,
% 0.75/0.92 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[151])).
% 0.75/0.92 tff(153,plain,
% 0.75/0.92 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(154,plain,
% 0.75/0.92 (inj_0(s(elem!1)) = elem!1),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[153, 10])).
% 0.75/0.92 tff(155,plain,
% 0.75/0.92 (elem!1 = inj_0(s(elem!1))),
% 0.75/0.92 inference(symmetry,[status(thm)],[154])).
% 0.75/0.92 tff(156,plain,
% 0.75/0.92 (elem!1 = s(s(elem!1))),
% 0.75/0.92 inference(transitivity,[status(thm)],[155, 152, 17, 151])).
% 0.75/0.92 tff(157,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[150, 156])).
% 0.75/0.92 tff(158,plain,((~(s(elem!1) = s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(159,plain,
% 0.75/0.92 (~(s(elem!1) = s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[158, 150])).
% 0.75/0.92 tff(160,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(161,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(162,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.75/0.92 tff(163,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 0.75/0.92 tff(164,plain,
% 0.75/0.92 (elem!1 = s(s(elem!1))),
% 0.75/0.92 inference(symmetry,[status(thm)],[163])).
% 0.75/0.92 tff(165,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[150, 164])).
% 0.75/0.92 tff(166,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(167,plain,
% 0.75/0.92 (~(s(s(elem!1)) = elem!1)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[166, 150])).
% 0.75/0.92 tff(168,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(169,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 0.75/0.92 tff(170,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(171,plain,
% 0.75/0.92 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(172,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[171])).
% 0.75/0.92 tff(173,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.92 inference(transitivity,[status(thm)],[172, 170])).
% 0.75/0.92 tff(174,plain,
% 0.75/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(175,plain,
% 0.75/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.75/0.92 tff(176,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[175, 124, 169, 168, 161])).
% 0.75/0.92 tff(177,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(178,plain,
% 0.75/0.92 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[177, 161, 80])).
% 0.75/0.92 tff(179,assumption,(~b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(180,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.92 tff(181,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(182,plain,
% 0.75/0.92 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[181])).
% 0.75/0.92 tff(183,plain,
% 0.75/0.92 (s(z) = s(s(elem!1))),
% 0.75/0.92 inference(transitivity,[status(thm)],[69, 182, 88])).
% 0.75/0.92 tff(184,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[41, 183])).
% 0.75/0.92 tff(185,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(186,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(187,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(188,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.75/0.92 tff(189,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[188, 51, 185, 180, 179])).
% 0.75/0.92 tff(190,plain,(r(s(s(z)), s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(191,plain,
% 0.75/0.92 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[190, 178])).
% 0.75/0.92 tff(192,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.92 tff(193,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(194,plain,
% 0.75/0.92 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(195,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[194])).
% 0.75/0.92 tff(196,plain,
% 0.75/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.75/0.92 inference(transitivity,[status(thm)],[195, 193])).
% 0.75/0.93 tff(197,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(198,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.75/0.93 tff(199,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[198, 124, 169, 160, 192])).
% 0.75/0.93 tff(200,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(201,plain,
% 0.75/0.93 (~r(s(s(z)), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[200, 160, 80])).
% 0.75/0.93 tff(202,plain,
% 0.75/0.93 (b(s(s(z)), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[135, 201, 114])).
% 0.75/0.93 tff(203,plain,
% 0.75/0.93 (s(s(elem!1)) = s(s(s(elem!1)))),
% 0.75/0.93 inference(symmetry,[status(thm)],[58])).
% 0.75/0.93 tff(204,plain,
% 0.75/0.93 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[203])).
% 0.75/0.93 tff(205,plain,
% 0.75/0.93 (s(elem!1) = s(s(elem!1))),
% 0.75/0.93 inference(transitivity,[status(thm)],[18, 204, 88])).
% 0.75/0.93 tff(206,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 0.75/0.93 tff(207,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.75/0.93 tff(208,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(209,plain,
% 0.75/0.93 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[208, 159])).
% 0.75/0.93 tff(210,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.93 tff(211,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(212,plain,
% 0.75/0.93 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(213,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[212])).
% 0.75/0.93 tff(214,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[213, 211])).
% 0.75/0.93 tff(215,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(216,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.75/0.93 tff(217,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[216, 124, 160, 210, 161])).
% 0.75/0.93 tff(218,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(219,plain,
% 0.75/0.93 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[218, 160, 161])).
% 0.75/0.93 tff(220,plain,
% 0.75/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(221,plain,
% 0.75/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(222,plain,
% 0.75/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.75/0.93 tff(223,plain,
% 0.75/0.93 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[222, 51])).
% 0.75/0.93 tff(224,plain,
% 0.75/0.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[223, 219, 209])).
% 0.75/0.93 tff(225,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.93 tff(226,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.93 tff(227,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.93 tff(228,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(229,plain,
% 0.75/0.93 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.75/0.93 inference(bind,[status(th)],[])).
% 0.75/0.93 tff(230,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(quant_intro,[status(thm)],[229])).
% 0.75/0.93 tff(231,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(232,plain,
% 0.75/0.93 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.75/0.93 inference(bind,[status(th)],[])).
% 0.75/0.93 tff(233,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(quant_intro,[status(thm)],[232])).
% 0.75/0.93 tff(234,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.75/0.93 tff(235,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.75/0.93 tff(236,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.75/0.93 tff(237,plain,(
% 0.75/0.93 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(skolemize,[status(sab)],[236])).
% 0.75/0.93 tff(238,plain,
% 0.75/0.93 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.75/0.93 tff(239,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(240,plain,
% 0.75/0.93 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(241,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[240])).
% 0.75/0.93 tff(242,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[241, 239])).
% 0.75/0.93 tff(243,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(244,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.75/0.93 tff(245,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[244, 238, 228, 227, 226, 225])).
% 0.75/0.93 tff(246,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(247,plain,
% 0.75/0.93 (~b(s(s(elem!1)), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[246, 224, 202, 191])).
% 0.75/0.93 tff(248,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 0.75/0.93 tff(249,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(250,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(251,plain,
% 0.75/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(252,plain,
% 0.75/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(253,plain,
% 0.75/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.75/0.93 tff(254,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[253, 51, 250, 249, 248])).
% 0.75/0.93 tff(255,plain,(r(s(s(elem!1)), elem!1) | b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(256,plain,
% 0.75/0.93 (r(s(s(elem!1)), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[255, 247, 167])).
% 0.75/0.93 tff(257,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(258,plain,
% 0.75/0.93 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(259,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[258])).
% 0.75/0.93 tff(260,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[259, 257])).
% 0.75/0.93 tff(261,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(262,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.75/0.93 tff(263,plain,
% 0.75/0.93 ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[262, 124])).
% 0.75/0.93 tff(264,plain,
% 0.75/0.93 (~r(elem!1, s(z))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[263, 256, 162])).
% 0.75/0.93 tff(265,plain,
% 0.75/0.93 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[177, 80, 161])).
% 0.75/0.93 tff(266,plain,
% 0.75/0.93 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[190, 265])).
% 0.75/0.93 tff(267,plain,
% 0.75/0.93 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 0.75/0.93 inference(commutativity,[status(thm)],[])).
% 0.75/0.93 tff(268,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 0.75/0.93 tff(269,plain,
% 0.75/0.93 (s(elem!1) = s(s(elem!1))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.75/0.93 tff(270,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[206, 269])).
% 0.75/0.93 tff(271,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(272,plain,
% 0.75/0.93 (~(s(s(elem!1)) = s(elem!1))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[271, 159])).
% 0.75/0.93 tff(273,plain,
% 0.75/0.93 (~b(s(s(elem!1)), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[246, 202, 224, 266])).
% 0.75/0.93 tff(274,plain,
% 0.75/0.93 (r(s(s(elem!1)), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[255, 273, 167])).
% 0.75/0.93 tff(275,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 0.75/0.93 tff(276,assumption,(elem!1 = s(z)), introduced(assumption)).
% 0.75/0.93 tff(277,plain,
% 0.75/0.93 (s(elem!1) = s(s(z))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[276])).
% 0.75/0.93 tff(278,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 0.75/0.93 tff(279,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.75/0.93 tff(280,plain,((~(elem!1 = s(z))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(281,plain,
% 0.75/0.93 (s(elem!1) = s(s(z))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[280, 276])).
% 0.75/0.93 tff(282,plain,
% 0.75/0.93 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[281])).
% 0.75/0.93 tff(283,plain,
% 0.75/0.93 (b(s(s(z)), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 0.75/0.93 inference(symmetry,[status(thm)],[282])).
% 0.75/0.93 tff(284,plain,
% 0.75/0.93 (b(s(elem!1), s(s(elem!1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[227, 283])).
% 0.75/0.93 tff(285,plain,
% 0.75/0.93 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[281])).
% 0.75/0.93 tff(286,plain,
% 0.75/0.93 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.93 inference(symmetry,[status(thm)],[285])).
% 0.75/0.93 tff(287,plain,
% 0.75/0.93 (b(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[225, 286])).
% 0.75/0.93 tff(288,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.93 tff(289,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.75/0.93 tff(290,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.93 tff(291,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(292,plain,
% 0.75/0.93 (((~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(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(293,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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))))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[292])).
% 0.75/0.93 tff(294,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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)))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[293, 291])).
% 0.75/0.93 tff(295,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(296,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.75/0.93 tff(297,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[296, 238, 290, 289, 288, 226])).
% 0.75/0.93 tff(298,plain,((~b(s(s(elem!1)), 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))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(299,plain,
% 0.75/0.93 (~b(s(s(elem!1)), s(elem!1))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[298, 287, 226, 284])).
% 0.75/0.93 tff(300,plain,
% 0.75/0.93 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[276])).
% 0.75/0.93 tff(301,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(302,plain,
% 0.75/0.93 (r(s(s(elem!1)), s(z))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.75/0.93 tff(303,plain,
% 0.75/0.93 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[281])).
% 0.75/0.93 tff(304,plain,
% 0.75/0.93 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 0.75/0.93 inference(symmetry,[status(thm)],[303])).
% 0.75/0.93 tff(305,plain,
% 0.75/0.93 (r(s(elem!1), s(z))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[169, 304])).
% 0.75/0.93 tff(306,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 0.75/0.93 tff(307,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.75/0.93 tff(308,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(309,plain,
% 0.75/0.93 (((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(310,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[309])).
% 0.75/0.93 tff(311,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[310, 308])).
% 0.75/0.93 tff(312,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(313,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.75/0.93 tff(314,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[313, 124, 307, 306, 162])).
% 0.75/0.93 tff(315,plain,((~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(316,plain,
% 0.75/0.93 (~r(s(s(elem!1)), s(elem!1))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[315, 305, 302])).
% 0.75/0.93 tff(317,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.75/0.93 tff(318,assumption,(~r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.75/0.93 tff(319,plain,
% 0.75/0.93 (((~![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)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(320,plain,
% 0.75/0.93 ((~![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)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(321,plain,
% 0.75/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.75/0.93 tff(322,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[321, 51, 318, 317, 275])).
% 0.75/0.93 tff(323,plain,(b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(324,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[323, 316, 299, 275])).
% 0.75/0.93 tff(325,plain,((~(elem!1 = s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(326,plain,
% 0.75/0.93 (~(elem!1 = s(z))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[325, 224, 272, 80, 202, 266, 274])).
% 0.75/0.93 tff(327,plain,
% 0.75/0.93 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 0.75/0.93 inference(commutativity,[status(thm)],[])).
% 0.75/0.93 tff(328,assumption,(s(z) = elem!1), introduced(assumption)).
% 0.75/0.93 tff(329,plain,
% 0.75/0.93 (elem!1 = s(z)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.75/0.93 tff(330,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 0.75/0.93 tff(331,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[330, 329])).
% 0.75/0.93 tff(332,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(333,plain,
% 0.75/0.93 (~(s(z) = elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[332, 326])).
% 0.75/0.93 tff(334,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(335,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(336,plain,
% 0.75/0.93 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(337,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[336])).
% 0.75/0.93 tff(338,plain,
% 0.75/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[337, 335])).
% 0.75/0.93 tff(339,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(340,plain,
% 0.75/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.75/0.93 tff(341,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[340, 124, 301, 160, 334])).
% 0.75/0.93 tff(342,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(343,plain,
% 0.75/0.93 (~r(s(z), elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[342, 274, 160])).
% 0.75/0.94 tff(344,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 0.75/0.94 tff(345,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 0.75/0.94 tff(346,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 0.75/0.94 tff(347,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(348,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(349,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.75/0.94 tff(350,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[349, 51, 346, 345, 344])).
% 0.75/0.94 tff(351,plain,(b(s(z), elem!1) | r(s(z), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(352,plain,
% 0.75/0.94 (b(s(z), elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[351, 343, 333])).
% 0.75/0.94 tff(353,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 0.75/0.94 tff(354,plain,
% 0.75/0.94 (s(s(elem!1)) = s(s(z))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[353])).
% 0.75/0.94 tff(355,plain,
% 0.75/0.94 (s(s(z)) = s(s(elem!1))),
% 0.75/0.94 inference(symmetry,[status(thm)],[354])).
% 0.75/0.94 tff(356,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[114, 355])).
% 0.75/0.94 tff(357,plain,((~(s(elem!1) = s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(358,plain,
% 0.75/0.94 (~(s(elem!1) = s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[357, 114])).
% 0.75/0.94 tff(359,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 0.75/0.94 tff(360,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(361,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(362,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.75/0.94 tff(363,plain,
% 0.75/0.94 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[362, 51])).
% 0.75/0.94 tff(364,plain,
% 0.75/0.94 (b(elem!1, s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[363, 326, 359])).
% 0.75/0.94 tff(365,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 0.75/0.94 tff(366,plain,
% 0.75/0.94 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[365])).
% 0.75/0.94 tff(367,plain,
% 0.75/0.94 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 0.75/0.94 inference(symmetry,[status(thm)],[366])).
% 0.75/0.94 tff(368,plain,
% 0.75/0.94 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[367])).
% 0.75/0.94 tff(369,plain,
% 0.75/0.94 (~b(elem!1, s(z))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[64, 368])).
% 0.75/0.94 tff(370,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 0.75/0.94 tff(371,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[370, 369])).
% 0.75/0.94 tff(372,plain,((~(elem!1 = s(s(z)))) | (~b(elem!1, s(z))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(373,plain,
% 0.75/0.94 (~(elem!1 = s(s(z)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[372, 364, 64])).
% 0.75/0.94 tff(374,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 0.75/0.94 tff(375,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 0.75/0.94 tff(376,plain,
% 0.75/0.94 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[375])).
% 0.75/0.94 tff(377,plain,
% 0.75/0.94 (elem!1 = s(z)),
% 0.75/0.94 inference(transitivity,[status(thm)],[155, 376, 12])).
% 0.75/0.94 tff(378,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[330, 377])).
% 0.75/0.94 tff(379,plain,((~(s(elem!1) = s(s(z)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(380,plain,
% 0.75/0.94 (~(s(elem!1) = s(s(z)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[379, 326])).
% 0.75/0.94 tff(381,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 0.75/0.94 tff(382,plain,
% 0.75/0.94 (s(elem!1) = elem!1),
% 0.75/0.94 inference(symmetry,[status(thm)],[381])).
% 0.75/0.94 tff(383,plain,
% 0.75/0.94 (s(s(elem!1)) = s(elem!1)),
% 0.75/0.94 inference(monotonicity,[status(thm)],[382])).
% 0.75/0.94 tff(384,plain,
% 0.75/0.94 (s(elem!1) = s(s(elem!1))),
% 0.75/0.94 inference(symmetry,[status(thm)],[383])).
% 0.75/0.94 tff(385,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[206, 384])).
% 0.75/0.94 tff(386,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(387,plain,
% 0.75/0.94 (~(elem!1 = s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[386, 159])).
% 0.75/0.94 tff(388,plain,
% 0.75/0.94 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.75/0.94 inference(commutativity,[status(thm)],[])).
% 0.75/0.94 tff(389,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 0.75/0.94 tff(390,plain,
% 0.75/0.94 (elem!1 = s(elem!1)),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.75/0.94 tff(391,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(392,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[391, 390])).
% 0.75/0.94 tff(393,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(394,plain,
% 0.75/0.94 (~(s(elem!1) = elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[393, 387])).
% 0.75/0.94 tff(395,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.75/0.94 tff(396,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(397,plain,
% 0.75/0.94 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(398,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[397])).
% 0.75/0.94 tff(399,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.94 inference(transitivity,[status(thm)],[398, 396])).
% 0.75/0.94 tff(400,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(401,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.75/0.94 tff(402,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[401, 124, 395, 301, 307])).
% 0.75/0.94 tff(403,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(404,plain,
% 0.75/0.94 (~r(s(elem!1), elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[403, 307, 301])).
% 0.75/0.94 tff(405,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(406,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(407,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.75/0.94 tff(408,plain,
% 0.75/0.94 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[407, 51])).
% 0.75/0.94 tff(409,plain,
% 0.75/0.94 (b(s(elem!1), elem!1)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[408, 404, 394])).
% 0.75/0.94 tff(410,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.94 tff(411,plain,
% 0.75/0.94 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[410])).
% 0.75/0.94 tff(412,plain,
% 0.75/0.94 (elem!1 = s(s(elem!1))),
% 0.75/0.94 inference(transitivity,[status(thm)],[155, 411, 88])).
% 0.75/0.94 tff(413,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[150, 412])).
% 0.75/0.94 tff(414,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(415,plain,
% 0.75/0.94 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[414, 150])).
% 0.75/0.94 tff(416,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 0.75/0.94 tff(417,plain,
% 0.75/0.94 (s(elem!1) = s(s(s(elem!1)))),
% 0.75/0.94 inference(symmetry,[status(thm)],[416])).
% 0.75/0.94 tff(418,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.94 tff(419,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[418, 417])).
% 0.75/0.94 tff(420,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(421,plain,
% 0.75/0.94 (~(s(s(s(elem!1))) = s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[420, 415])).
% 0.75/0.94 tff(422,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 0.75/0.94 tff(423,plain,
% 0.75/0.94 (s(elem!1) = s(z)),
% 0.75/0.94 inference(symmetry,[status(thm)],[422])).
% 0.75/0.94 tff(424,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1, 423])).
% 0.75/0.94 tff(425,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(426,plain,
% 0.75/0.94 (~(s(z) = s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[425, 1])).
% 0.75/0.94 tff(427,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 0.75/0.94 tff(428,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(429,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(430,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.75/0.94 tff(431,plain,
% 0.75/0.94 (~b(s(z), s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[430, 238, 409, 370, 427])).
% 0.75/0.94 tff(432,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(433,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(434,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(435,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(436,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(437,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.75/0.94 tff(438,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[437, 51, 434, 433, 432])).
% 0.75/0.94 tff(439,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(440,plain,
% 0.75/0.94 (r(s(z), s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[439, 431, 426])).
% 0.75/0.94 tff(441,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(442,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(443,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(444,plain,
% 0.75/0.94 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(445,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[444])).
% 0.75/0.94 tff(446,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.94 inference(transitivity,[status(thm)],[445, 443])).
% 0.75/0.94 tff(447,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(448,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.75/0.94 tff(449,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[448, 124, 442, 161, 441])).
% 0.75/0.94 tff(450,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(451,plain,
% 0.75/0.94 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[450, 440, 161])).
% 0.75/0.94 tff(452,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(453,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(454,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(455,plain,
% 0.75/0.94 (((~![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)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(456,plain,
% 0.75/0.94 ((~![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)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(457,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.75/0.94 tff(458,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[457, 51, 454, 453, 452])).
% 0.75/0.94 tff(459,plain,(r(s(s(s(elem!1))), s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(460,plain,
% 0.75/0.94 (b(s(s(s(elem!1))), s(elem!1))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[459, 451, 421])).
% 0.75/0.94 tff(461,plain,
% 0.75/0.94 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[177, 169, 161])).
% 0.75/0.94 tff(462,plain,
% 0.75/0.94 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[190, 461])).
% 0.75/0.94 tff(463,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(464,plain,
% 0.75/0.94 (((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(465,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[464])).
% 0.75/0.94 tff(466,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 0.75/0.94 inference(transitivity,[status(thm)],[465, 463])).
% 0.75/0.94 tff(467,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(468,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[467, 466])).
% 0.75/0.94 tff(469,plain,
% 0.75/0.94 (~b(s(elem!1), s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[468, 238, 409, 370, 427])).
% 0.75/0.94 tff(470,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(471,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(472,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.75/0.94 tff(473,plain,
% 0.75/0.94 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[472, 51])).
% 0.75/0.94 tff(474,plain,
% 0.75/0.94 (r(s(elem!1), s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[473, 469, 1])).
% 0.75/0.94 tff(475,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 0.75/0.94 tff(476,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(477,plain,
% 0.75/0.94 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(478,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[477])).
% 0.75/0.94 tff(479,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.94 inference(transitivity,[status(thm)],[478, 476])).
% 0.75/0.94 tff(480,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(481,plain,
% 0.75/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.75/0.94 tff(482,plain,
% 0.75/0.94 ($false),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[481, 124, 169, 475, 306])).
% 0.75/0.94 tff(483,plain,((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(484,plain,
% 0.75/0.94 (~r(s(elem!1), s(s(z)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[483, 474, 169])).
% 0.75/0.94 tff(485,plain,
% 0.75/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(486,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(487,plain,
% 0.75/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.75/0.94 tff(488,plain,
% 0.75/0.94 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[487, 51])).
% 0.75/0.94 tff(489,plain,
% 0.75/0.94 (b(s(elem!1), s(s(z)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[488, 484, 278])).
% 0.75/0.94 tff(490,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 0.75/0.94 tff(491,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.75/0.94 tff(492,plain,
% 0.75/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(493,plain,
% 0.75/0.95 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(494,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[493])).
% 0.75/0.95 tff(495,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[494, 492])).
% 0.75/0.95 tff(496,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(497,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.75/0.95 tff(498,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[497, 238, 491, 290, 490, 225])).
% 0.75/0.95 tff(499,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(500,plain,
% 0.75/0.95 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[499, 489, 462, 460])).
% 0.75/0.95 tff(501,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(502,plain,
% 0.75/0.95 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[501])).
% 0.75/0.95 tff(503,plain,
% 0.75/0.95 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 0.75/0.95 inference(symmetry,[status(thm)],[502])).
% 0.75/0.95 tff(504,plain,
% 0.75/0.95 ((~b(s(elem!1), s(s(s(elem!1))))) <=> (~b(s(elem!1), elem!1))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[503])).
% 0.75/0.95 tff(505,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.95 tff(506,plain,
% 0.75/0.95 (~b(s(elem!1), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.75/0.95 tff(507,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 0.75/0.95 tff(508,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[507, 506])).
% 0.75/0.95 tff(509,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | b(s(elem!1), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(510,plain,
% 0.75/0.95 (~(elem!1 = s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[509, 500, 409])).
% 0.75/0.95 tff(511,plain,
% 0.75/0.95 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.95 inference(commutativity,[status(thm)],[])).
% 0.75/0.95 tff(512,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 0.75/0.95 tff(513,plain,
% 0.75/0.95 (elem!1 = s(s(s(elem!1)))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.75/0.95 tff(514,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.95 tff(515,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[514, 513])).
% 0.75/0.95 tff(516,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(517,plain,
% 0.75/0.95 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[516, 510])).
% 0.75/0.95 tff(518,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(519,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(520,plain,
% 0.75/0.95 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(521,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[520])).
% 0.75/0.95 tff(522,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[521, 519])).
% 0.75/0.95 tff(523,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(524,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.75/0.95 tff(525,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[524, 124, 518, 160, 306])).
% 0.75/0.95 tff(526,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(527,plain,
% 0.75/0.95 (~r(s(elem!1), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[526, 474, 160])).
% 0.75/0.95 tff(528,assumption,(~b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(529,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(530,plain,
% 0.75/0.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(531,plain,
% 0.75/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(532,plain,
% 0.75/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.75/0.95 tff(533,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[532, 51, 529, 206, 528])).
% 0.75/0.95 tff(534,plain,(r(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(535,plain,
% 0.75/0.95 (b(s(elem!1), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[534, 527, 159])).
% 0.75/0.95 tff(536,plain,
% 0.75/0.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(537,plain,
% 0.75/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(538,plain,
% 0.75/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.75/0.95 tff(539,plain,
% 0.75/0.95 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[538, 51])).
% 0.75/0.95 tff(540,plain,
% 0.75/0.95 (r(s(elem!1), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[539, 500, 415])).
% 0.75/0.95 tff(541,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 0.75/0.95 tff(542,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.95 tff(543,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.95 tff(544,plain,
% 0.75/0.95 (r(s(z), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[56, 2])).
% 0.75/0.95 tff(545,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(546,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.95 tff(547,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(548,plain,
% 0.75/0.95 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(549,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[548])).
% 0.75/0.95 tff(550,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[549, 547])).
% 0.75/0.95 tff(551,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(552,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[551, 550])).
% 0.75/0.95 tff(553,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[552, 238, 543, 226, 370, 546])).
% 0.75/0.95 tff(554,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(555,plain,
% 0.75/0.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[554, 546, 370, 543])).
% 0.75/0.95 tff(556,plain,
% 0.75/0.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[223, 555, 545])).
% 0.75/0.95 tff(557,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(558,plain,
% 0.75/0.95 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~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))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(559,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[558])).
% 0.75/0.95 tff(560,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[559, 557])).
% 0.75/0.95 tff(561,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(562,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[561, 560])).
% 0.75/0.95 tff(563,plain,
% 0.75/0.95 (~r(s(s(s(elem!1))), s(z))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[562, 124, 160, 556])).
% 0.75/0.95 tff(564,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.75/0.95 tff(565,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(566,plain,
% 0.75/0.95 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(567,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[566])).
% 0.75/0.95 tff(568,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[567, 565])).
% 0.75/0.95 tff(569,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(570,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.75/0.95 tff(571,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[570, 238, 543, 370, 564, 546])).
% 0.75/0.95 tff(572,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(573,plain,
% 0.75/0.95 (~b(s(s(s(elem!1))), s(z))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[572, 546, 370, 543])).
% 0.75/0.95 tff(574,plain,
% 0.75/0.95 (((~![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)))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(575,plain,
% 0.75/0.95 ((~![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)))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(576,plain,
% 0.75/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.75/0.95 tff(577,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[576, 51, 573, 94, 563])).
% 0.75/0.95 tff(578,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(579,plain,
% 0.75/0.95 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[578, 544, 209, 370, 543])).
% 0.75/0.95 tff(580,plain,
% 0.75/0.95 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[101, 579])).
% 0.75/0.95 tff(581,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(582,plain,
% 0.75/0.95 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(583,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[582])).
% 0.75/0.95 tff(584,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[583, 581])).
% 0.75/0.95 tff(585,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(586,plain,
% 0.75/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.75/0.95 tff(587,plain,
% 0.75/0.95 (~r(s(z), s(elem!1))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[586, 124, 542, 580])).
% 0.75/0.95 tff(588,plain,
% 0.75/0.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[218, 580, 544])).
% 0.75/0.95 tff(589,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[223, 588, 209])).
% 0.75/0.95 tff(590,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 0.75/0.95 tff(591,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.75/0.95 tff(592,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, 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))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(593,plain,
% 0.75/0.95 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(594,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[593])).
% 0.75/0.95 tff(595,plain,
% 0.75/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.96 inference(transitivity,[status(thm)],[594, 592])).
% 0.75/0.96 tff(596,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(597,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.75/0.96 tff(598,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[597, 124, 590, 591, 307])).
% 0.75/0.96 tff(599,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(600,plain,
% 0.75/0.96 (~r(elem!1, s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[599, 307, 590])).
% 0.75/0.96 tff(601,plain,
% 0.75/0.96 (b(s(s(elem!1)), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[255, 167, 250])).
% 0.75/0.96 tff(602,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.75/0.96 tff(603,plain,
% 0.75/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(604,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(605,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.75/0.96 tff(606,plain,
% 0.75/0.96 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[605, 51])).
% 0.75/0.96 tff(607,plain,
% 0.75/0.96 (b(elem!1, s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[606, 150, 602])).
% 0.75/0.96 tff(608,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(609,plain,
% 0.75/0.96 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(610,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[609])).
% 0.75/0.96 tff(611,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.96 inference(transitivity,[status(thm)],[610, 608])).
% 0.75/0.96 tff(612,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(613,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.75/0.96 tff(614,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[613, 238, 607, 543, 601, 226])).
% 0.75/0.96 tff(615,plain,((elem!1 = s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(616,plain,
% 0.75/0.96 (r(s(s(elem!1)), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[615, 600, 150, 226, 543])).
% 0.75/0.96 tff(617,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(618,plain,
% 0.75/0.96 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(619,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[618])).
% 0.75/0.96 tff(620,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.75/0.96 inference(transitivity,[status(thm)],[619, 617])).
% 0.75/0.96 tff(621,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(622,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.75/0.96 tff(623,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[622, 124, 590, 616, 307])).
% 0.75/0.96 tff(624,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(625,plain,
% 0.75/0.96 (~r(elem!1, s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[624, 589, 150, 307, 543])).
% 0.75/0.96 tff(626,plain,
% 0.75/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(627,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(628,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[627, 626])).
% 0.75/0.96 tff(629,plain,
% 0.75/0.96 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[628, 51])).
% 0.75/0.96 tff(630,plain,
% 0.75/0.96 (b(elem!1, s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[629, 625, 387])).
% 0.75/0.96 tff(631,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 0.75/0.96 tff(632,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 0.75/0.96 tff(633,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(634,plain,
% 0.75/0.96 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(635,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[634])).
% 0.75/0.96 tff(636,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[635, 633])).
% 0.75/0.96 tff(637,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(638,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.75/0.96 tff(639,plain,
% 0.75/0.96 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[638, 238])).
% 0.75/0.96 tff(640,plain,
% 0.75/0.96 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[639, 288, 631, 491])).
% 0.75/0.96 tff(641,plain,
% 0.75/0.96 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.96 inference(symmetry,[status(thm)],[511])).
% 0.75/0.96 tff(642,plain,
% 0.75/0.96 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[641])).
% 0.75/0.96 tff(643,plain,
% 0.75/0.96 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[514, 642])).
% 0.75/0.96 tff(644,plain,
% 0.75/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(645,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(646,plain,
% 0.75/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.75/0.96 tff(647,plain,
% 0.75/0.96 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[646, 51])).
% 0.75/0.96 tff(648,plain,
% 0.75/0.96 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[647, 643, 640])).
% 0.75/0.96 tff(649,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.75/0.96 tff(650,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(651,plain,
% 0.75/0.96 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(652,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[651])).
% 0.75/0.96 tff(653,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[652, 650])).
% 0.75/0.96 tff(654,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(655,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.75/0.96 tff(656,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[655, 124, 395, 542, 649])).
% 0.75/0.96 tff(657,plain,((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(658,plain,
% 0.75/0.96 (~r(s(elem!1), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[657, 648, 542])).
% 0.75/0.96 tff(659,plain,
% 0.75/0.96 (b(s(elem!1), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[408, 658, 632])).
% 0.75/0.96 tff(660,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 0.75/0.96 tff(661,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(662,plain,
% 0.75/0.96 (((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(663,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[662])).
% 0.75/0.96 tff(664,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 0.75/0.96 inference(transitivity,[status(thm)],[663, 661])).
% 0.75/0.96 tff(665,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(666,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.75/0.96 tff(667,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[666, 238, 631, 507, 370, 660])).
% 0.75/0.96 tff(668,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(669,plain,
% 0.75/0.96 (~b(s(z), s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[668, 659, 370, 631])).
% 0.75/0.96 tff(670,plain,
% 0.75/0.96 (s(z) = s(elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[439, 669, 434])).
% 0.75/0.96 tff(671,plain,
% 0.75/0.96 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[670])).
% 0.75/0.96 tff(672,plain,
% 0.75/0.96 (b(s(elem!1), s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.75/0.96 inference(symmetry,[status(thm)],[671])).
% 0.75/0.96 tff(673,plain,
% 0.75/0.96 (b(s(z), s(s(elem!1)))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[288, 672])).
% 0.75/0.96 tff(674,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[2, 673])).
% 0.75/0.96 tff(675,plain,((~b(s(elem!1), s(s(elem!1)))) | b(s(z), s(s(elem!1))) | r(s(z), s(elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(elem!1), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(676,plain,
% 0.75/0.96 (~b(s(elem!1), s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[675, 2, 587, 370, 630, 394, 542, 514, 491])).
% 0.75/0.96 tff(677,plain,
% 0.75/0.96 (r(s(elem!1), s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[534, 676, 159])).
% 0.75/0.96 tff(678,plain,
% 0.75/0.96 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[177, 580, 169])).
% 0.75/0.96 tff(679,plain,
% 0.75/0.96 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[190, 678])).
% 0.75/0.96 tff(680,plain,
% 0.75/0.96 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(681,plain,
% 0.75/0.96 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[680, 10])).
% 0.75/0.96 tff(682,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.96 tff(683,plain,
% 0.75/0.96 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 0.75/0.96 inference(symmetry,[status(thm)],[682])).
% 0.75/0.96 tff(684,plain,
% 0.75/0.96 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[683])).
% 0.75/0.96 tff(685,plain,
% 0.75/0.96 (s(s(elem!1)) = s(s(s(elem!1)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[89, 684, 681])).
% 0.75/0.96 tff(686,plain,
% 0.75/0.96 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[685])).
% 0.75/0.96 tff(687,plain,
% 0.75/0.96 (s(elem!1) = s(s(s(elem!1)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[18, 686, 684, 681])).
% 0.75/0.96 tff(688,plain,
% 0.75/0.96 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[687])).
% 0.75/0.96 tff(689,plain,
% 0.75/0.96 (elem!1 = s(s(elem!1))),
% 0.75/0.96 inference(transitivity,[status(thm)],[155, 688, 88])).
% 0.75/0.96 tff(690,plain,
% 0.75/0.96 ($false),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[150, 689])).
% 0.75/0.96 tff(691,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.96 tff(692,plain,
% 0.75/0.96 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[691, 150])).
% 0.75/0.96 tff(693,plain,
% 0.75/0.96 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.75/0.96 inference(commutativity,[status(thm)],[])).
% 0.75/0.96 tff(694,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(695,plain,
% 0.75/0.96 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(696,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[695])).
% 0.75/0.96 tff(697,plain,
% 0.75/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[696, 694])).
% 0.75/0.96 tff(698,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
% 0.75/0.96 tff(699,plain,
% 0.75/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 0.75/0.96 inference(modus_ponens,[status(thm)],[698, 697])).
% 0.75/0.96 tff(700,plain,
% 0.75/0.96 ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[699, 124])).
% 0.75/0.96 tff(701,plain,
% 0.75/0.96 (~r(s(elem!1), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[700, 518, 301])).
% 0.75/0.96 tff(702,plain,
% 0.75/0.96 (b(s(elem!1), elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[408, 701, 632])).
% 0.75/0.96 tff(703,plain,
% 0.75/0.96 (~b(s(z), s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[668, 702, 370, 631])).
% 0.75/0.96 tff(704,plain,
% 0.75/0.96 (s(z) = s(elem!1)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[439, 703, 434])).
% 0.75/0.96 tff(705,plain,
% 0.75/0.96 (s(elem!1) = s(z)),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[425, 704])).
% 0.75/0.96 tff(706,plain,
% 0.75/0.96 (s(s(z)) = s(s(elem!1))),
% 0.75/0.96 inference(unit_resolution,[status(thm)],[357, 705])).
% 0.75/0.96 tff(707,plain,
% 0.75/0.96 (s(s(elem!1)) = s(s(z))),
% 0.75/0.96 inference(symmetry,[status(thm)],[706])).
% 0.75/0.96 tff(708,plain,
% 0.75/0.96 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[707])).
% 0.75/0.96 tff(709,plain,
% 0.75/0.96 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.75/0.96 inference(transitivity,[status(thm)],[708, 693])).
% 0.75/0.96 tff(710,plain,
% 0.75/0.96 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.75/0.96 inference(symmetry,[status(thm)],[709])).
% 0.75/0.96 tff(711,plain,
% 0.75/0.96 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[710])).
% 0.75/0.96 tff(712,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 0.75/0.96 tff(713,plain,
% 0.75/0.96 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 0.75/0.96 inference(monotonicity,[status(thm)],[712])).
% 0.75/0.96 tff(714,plain,
% 0.75/0.96 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(715,plain,
% 0.75/0.97 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[714, 10])).
% 0.75/0.97 tff(716,plain,
% 0.75/0.97 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[715])).
% 0.75/0.97 tff(717,plain,
% 0.75/0.97 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[712])).
% 0.75/0.97 tff(718,plain,
% 0.75/0.97 (s(s(s(s(s(z))))) = s(z)),
% 0.75/0.97 inference(transitivity,[status(thm)],[717, 716, 713, 12])).
% 0.75/0.97 tff(719,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 0.75/0.97 tff(720,plain,
% 0.75/0.97 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[719])).
% 0.75/0.97 tff(721,plain,
% 0.75/0.97 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(722,plain,
% 0.75/0.97 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[721, 10])).
% 0.75/0.97 tff(723,plain,
% 0.75/0.97 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[722])).
% 0.75/0.97 tff(724,plain,
% 0.75/0.97 (s(s(s(s(z)))) = z),
% 0.75/0.97 inference(transitivity,[status(thm)],[723, 720, 26])).
% 0.75/0.97 tff(725,plain,
% 0.75/0.97 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(726,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[725, 37])).
% 0.75/0.97 tff(727,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[726, 724])).
% 0.75/0.97 tff(728,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(729,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[728, 718])).
% 0.75/0.97 tff(730,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(731,plain,
% 0.75/0.97 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[730, 711])).
% 0.75/0.97 tff(732,plain,
% 0.75/0.97 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[706])).
% 0.75/0.97 tff(733,plain,
% 0.75/0.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.97 inference(symmetry,[status(thm)],[732])).
% 0.75/0.97 tff(734,plain,
% 0.75/0.97 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[733])).
% 0.75/0.97 tff(735,plain,
% 0.75/0.97 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[734])).
% 0.75/0.97 tff(736,plain,
% 0.75/0.97 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[707, 735])).
% 0.75/0.97 tff(737,plain,
% 0.75/0.97 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[736])).
% 0.75/0.97 tff(738,plain,
% 0.75/0.97 ((~r(s(s(z)), s(s(s(s(elem!1)))))) <=> (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[737])).
% 0.75/0.97 tff(739,plain,
% 0.75/0.97 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[706])).
% 0.75/0.97 tff(740,plain,
% 0.75/0.97 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[225, 739])).
% 0.75/0.97 tff(741,plain,
% 0.75/0.97 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[13])).
% 0.75/0.97 tff(742,plain,
% 0.75/0.97 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 0.75/0.97 inference(symmetry,[status(thm)],[741])).
% 0.75/0.97 tff(743,plain,
% 0.75/0.97 ((~b(elem!1, s(s(elem!1)))) <=> (~b(elem!1, s(s(z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[742])).
% 0.75/0.97 tff(744,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.97 tff(745,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(746,plain,
% 0.75/0.97 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(747,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[746])).
% 0.75/0.97 tff(748,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[747, 745])).
% 0.75/0.97 tff(749,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(750,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.75/0.97 tff(751,plain,
% 0.75/0.97 (~b(elem!1, s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[750, 238, 543, 226, 744])).
% 0.75/0.97 tff(752,plain,
% 0.75/0.97 (~b(elem!1, s(s(z)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[751, 743])).
% 0.75/0.97 tff(753,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 0.75/0.97 tff(754,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[753, 752])).
% 0.75/0.97 tff(755,plain,((~b(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(756,plain,
% 0.75/0.97 (~b(elem!1, s(s(z)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[755, 706, 543, 226, 740])).
% 0.75/0.97 tff(757,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 0.75/0.97 tff(758,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 0.75/0.97 tff(759,plain,
% 0.75/0.97 (((~![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))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(760,plain,
% 0.75/0.97 ((~![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))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(761,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.75/0.97 tff(762,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[761, 51, 541, 758, 757])).
% 0.75/0.97 tff(763,plain,(b(elem!1, s(s(z))) | (elem!1 = s(s(z))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(764,plain,
% 0.75/0.97 (r(elem!1, s(s(z)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[763, 756, 541])).
% 0.75/0.97 tff(765,plain,
% 0.75/0.97 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[734])).
% 0.75/0.97 tff(766,plain,
% 0.75/0.97 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[765])).
% 0.75/0.97 tff(767,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(commutativity,[status(thm)],[])).
% 0.75/0.97 tff(768,plain,
% 0.75/0.97 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[704])).
% 0.75/0.97 tff(769,plain,
% 0.75/0.97 (z = inj_0(s(z))),
% 0.75/0.97 inference(symmetry,[status(thm)],[26])).
% 0.75/0.97 tff(770,plain,
% 0.75/0.97 (z = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[769, 768, 154])).
% 0.75/0.97 tff(771,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[770])).
% 0.75/0.97 tff(772,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[771, 767])).
% 0.75/0.97 tff(773,plain,
% 0.75/0.97 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[772])).
% 0.75/0.97 tff(774,plain,
% 0.75/0.97 (~(elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[726, 773])).
% 0.75/0.97 tff(775,plain,
% 0.75/0.97 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[734])).
% 0.75/0.97 tff(776,plain,
% 0.75/0.97 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[775])).
% 0.75/0.97 tff(777,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.97 tff(778,plain,
% 0.75/0.97 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[734])).
% 0.75/0.97 tff(779,plain,
% 0.75/0.97 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[778])).
% 0.75/0.97 tff(780,plain,
% 0.75/0.97 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[779])).
% 0.75/0.97 tff(781,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.75/0.97 tff(782,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(783,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(784,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[783, 782])).
% 0.75/0.97 tff(785,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[784, 238, 631, 507, 491, 781])).
% 0.75/0.97 tff(786,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(787,plain,
% 0.75/0.97 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[786, 702, 631, 491])).
% 0.75/0.97 tff(788,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[647, 787, 643])).
% 0.75/0.97 tff(789,plain,
% 0.75/0.97 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(symmetry,[status(thm)],[767])).
% 0.75/0.97 tff(790,plain,
% 0.75/0.97 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[789])).
% 0.75/0.97 tff(791,plain,
% 0.75/0.97 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[422])).
% 0.75/0.97 tff(792,plain,
% 0.75/0.97 (z = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[769, 791, 154])).
% 0.75/0.97 tff(793,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[792])).
% 0.75/0.97 tff(794,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[793, 767])).
% 0.75/0.97 tff(795,plain,
% 0.75/0.97 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[794])).
% 0.75/0.97 tff(796,plain,
% 0.75/0.97 (~(elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[726, 795])).
% 0.75/0.97 tff(797,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[796, 790])).
% 0.75/0.97 tff(798,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.75/0.97 inference(commutativity,[status(thm)],[])).
% 0.75/0.97 tff(799,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[423])).
% 0.75/0.97 tff(800,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[799, 798])).
% 0.75/0.97 tff(801,plain,
% 0.75/0.97 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 0.75/0.97 inference(symmetry,[status(thm)],[800])).
% 0.75/0.97 tff(802,plain,
% 0.75/0.97 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[801])).
% 0.75/0.97 tff(803,plain,
% 0.75/0.97 (s(elem!1) = s(z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[425, 422])).
% 0.75/0.97 tff(804,plain,
% 0.75/0.97 (s(s(z)) = s(s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[357, 353])).
% 0.75/0.97 tff(805,plain,
% 0.75/0.97 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[804])).
% 0.75/0.97 tff(806,plain,
% 0.75/0.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.97 inference(symmetry,[status(thm)],[805])).
% 0.75/0.97 tff(807,plain,
% 0.75/0.97 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[806])).
% 0.75/0.97 tff(808,plain,
% 0.75/0.97 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(z))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[807, 353])).
% 0.75/0.97 tff(809,plain,
% 0.75/0.97 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(z) = s(s(s(s(z)))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[808, 798])).
% 0.75/0.97 tff(810,plain,
% 0.75/0.97 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 0.75/0.97 inference(symmetry,[status(thm)],[809])).
% 0.75/0.97 tff(811,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 0.75/0.97 tff(812,plain,
% 0.75/0.97 (s(s(s(s(elem!1)))) = s(elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[811, 810])).
% 0.75/0.97 tff(813,plain,
% 0.75/0.97 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[353])).
% 0.75/0.97 tff(814,plain,
% 0.75/0.97 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.97 inference(symmetry,[status(thm)],[813])).
% 0.75/0.97 tff(815,plain,
% 0.75/0.97 (z = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[769, 814, 154])).
% 0.75/0.97 tff(816,plain,
% 0.75/0.97 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[815])).
% 0.75/0.97 tff(817,plain,
% 0.75/0.97 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[816, 511])).
% 0.75/0.97 tff(818,plain,
% 0.75/0.97 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.97 inference(transitivity,[status(thm)],[817, 641])).
% 0.75/0.97 tff(819,plain,
% 0.75/0.97 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[818])).
% 0.75/0.97 tff(820,plain,
% 0.75/0.97 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(821,plain,
% 0.75/0.97 (~(s(s(s(elem!1))) = z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[820, 37])).
% 0.75/0.97 tff(822,plain,
% 0.75/0.97 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[821, 819])).
% 0.75/0.97 tff(823,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 0.75/0.97 tff(824,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 0.75/0.97 tff(825,plain,
% 0.75/0.97 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[824])).
% 0.75/0.97 tff(826,plain,
% 0.75/0.97 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[681])).
% 0.75/0.97 tff(827,plain,
% 0.75/0.97 (s(s(s(elem!1))) = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[826, 825, 154])).
% 0.75/0.97 tff(828,plain,
% 0.75/0.97 (b(s(s(s(elem!1))), elem!1) <=> b(elem!1, elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[827])).
% 0.75/0.97 tff(829,plain,
% 0.75/0.97 (b(elem!1, elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(symmetry,[status(thm)],[828])).
% 0.75/0.97 tff(830,plain,
% 0.75/0.97 ((~b(elem!1, elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[829])).
% 0.75/0.97 tff(831,plain,
% 0.75/0.97 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 0.75/0.97 inference(bind,[status(th)],[])).
% 0.75/0.97 tff(832,plain,
% 0.75/0.97 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.75/0.97 inference(quant_intro,[status(thm)],[831])).
% 0.75/0.97 tff(833,plain,
% 0.75/0.97 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(834,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 0.75/0.97 tff(835,plain,
% 0.75/0.97 (![X: $i] : (~b(X, X))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.75/0.97 tff(836,plain,(
% 0.75/0.97 ![X: $i] : (~b(X, X))),
% 0.75/0.97 inference(skolemize,[status(sab)],[835])).
% 0.75/0.97 tff(837,plain,
% 0.75/0.97 (![X: $i] : (~b(X, X))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[836, 832])).
% 0.75/0.97 tff(838,plain,
% 0.75/0.97 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(839,plain,
% 0.75/0.97 (~b(elem!1, elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[838, 837])).
% 0.75/0.97 tff(840,plain,
% 0.75/0.97 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[839, 830])).
% 0.75/0.97 tff(841,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), elem!1) <=> r(elem!1, elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[827])).
% 0.75/0.97 tff(842,plain,
% 0.75/0.97 (r(elem!1, elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(symmetry,[status(thm)],[841])).
% 0.75/0.97 tff(843,plain,
% 0.75/0.97 ((~r(elem!1, elem!1)) <=> (~r(s(s(s(elem!1))), elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[842])).
% 0.75/0.97 tff(844,plain,
% 0.75/0.97 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 0.75/0.97 inference(bind,[status(th)],[])).
% 0.75/0.97 tff(845,plain,
% 0.75/0.97 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 0.75/0.97 inference(quant_intro,[status(thm)],[844])).
% 0.75/0.97 tff(846,plain,
% 0.75/0.97 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(847,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 0.75/0.97 tff(848,plain,
% 0.75/0.97 (![X: $i] : (~r(X, X))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.75/0.97 tff(849,plain,(
% 0.75/0.97 ![X: $i] : (~r(X, X))),
% 0.75/0.97 inference(skolemize,[status(sab)],[848])).
% 0.75/0.97 tff(850,plain,
% 0.75/0.97 (![X: $i] : (~r(X, X))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[849, 845])).
% 0.75/0.97 tff(851,plain,
% 0.75/0.97 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(852,plain,
% 0.75/0.97 (~r(elem!1, elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[851, 850])).
% 0.75/0.97 tff(853,plain,
% 0.75/0.97 (~r(s(s(s(elem!1))), elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[852, 843])).
% 0.75/0.97 tff(854,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[647, 853, 840, 823])).
% 0.75/0.97 tff(855,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(856,plain,
% 0.75/0.97 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[855, 822])).
% 0.75/0.97 tff(857,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[856, 812])).
% 0.75/0.97 tff(858,plain,((~(s(z) = s(s(s(s(z)))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(859,plain,
% 0.75/0.97 (~(s(z) = s(s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[858, 803])).
% 0.75/0.97 tff(860,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[859, 802])).
% 0.75/0.97 tff(861,assumption,(r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.97 tff(862,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(863,plain,
% 0.75/0.97 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(864,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[863])).
% 0.75/0.97 tff(865,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[864, 862])).
% 0.75/0.97 tff(866,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(867,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.75/0.97 tff(868,plain,
% 0.75/0.97 (~r(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[867, 124, 518, 542, 861])).
% 0.75/0.97 tff(869,plain,
% 0.75/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(870,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(871,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.75/0.97 tff(872,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[871, 51, 868])).
% 0.75/0.97 tff(873,plain,
% 0.75/0.97 (b(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[872, 860])).
% 0.75/0.97 tff(874,plain,
% 0.75/0.97 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[423])).
% 0.75/0.97 tff(875,plain,
% 0.75/0.97 (b(s(z), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[874])).
% 0.75/0.97 tff(876,plain,
% 0.75/0.97 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[423])).
% 0.75/0.97 tff(877,plain,
% 0.75/0.97 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[876])).
% 0.75/0.97 tff(878,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(879,plain,
% 0.75/0.97 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(880,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[879])).
% 0.75/0.97 tff(881,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[880, 878])).
% 0.75/0.97 tff(882,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(883,plain,
% 0.75/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[882, 881])).
% 0.75/0.97 tff(884,plain,
% 0.75/0.97 (~r(s(elem!1), s(s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[883, 124, 542, 861])).
% 0.75/0.97 tff(885,plain,
% 0.75/0.97 (~r(s(z), s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[884, 877])).
% 0.75/0.97 tff(886,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.97 tff(887,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.97 tff(888,assumption,(~(s(z) = s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.97 tff(889,plain,
% 0.75/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(890,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(891,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.75/0.97 tff(892,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[891, 51, 888, 887, 886])).
% 0.75/0.97 tff(893,plain,(b(s(z), s(s(s(s(z))))) | (s(z) = s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(894,plain,
% 0.75/0.97 (b(s(z), s(s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[893, 885, 859])).
% 0.75/0.97 tff(895,plain,
% 0.75/0.97 (b(s(elem!1), s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[894, 875])).
% 0.75/0.97 tff(896,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(897,plain,
% 0.75/0.97 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(898,plain,
% 0.75/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[897])).
% 0.75/0.98 tff(899,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.98 inference(transitivity,[status(thm)],[898, 896])).
% 0.75/0.98 tff(900,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(901,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[900, 899])).
% 0.75/0.98 tff(902,plain,
% 0.75/0.98 (~b(s(s(s(s(z)))), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[901, 238, 631, 895, 873])).
% 0.75/0.98 tff(903,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(904,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(905,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.75/0.98 tff(906,plain,
% 0.75/0.98 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[905, 51, 902])).
% 0.75/0.98 tff(907,plain,
% 0.75/0.98 (r(s(s(s(s(z)))), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[906, 797])).
% 0.75/0.98 tff(908,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(909,plain,
% 0.75/0.98 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(910,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[909])).
% 0.75/0.98 tff(911,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.98 inference(transitivity,[status(thm)],[910, 908])).
% 0.75/0.98 tff(912,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(913,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[912, 911])).
% 0.75/0.98 tff(914,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[913, 124, 649, 861, 907])).
% 0.75/0.98 tff(915,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(916,plain,
% 0.75/0.98 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[915, 788, 631, 704, 518, 542])).
% 0.75/0.98 tff(917,plain,
% 0.75/0.98 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[916, 780])).
% 0.75/0.98 tff(918,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(919,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(920,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.75/0.98 tff(921,plain,
% 0.75/0.98 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[920, 51])).
% 0.75/0.98 tff(922,plain,
% 0.75/0.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[921, 917, 777])).
% 0.75/0.98 tff(923,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(924,plain,
% 0.75/0.98 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(925,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[924])).
% 0.75/0.98 tff(926,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[925, 923])).
% 0.75/0.98 tff(927,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(928,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[927, 926])).
% 0.75/0.98 tff(929,plain,
% 0.75/0.98 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[928, 238])).
% 0.75/0.98 tff(930,plain,
% 0.75/0.98 (~b(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[929, 922, 543, 491])).
% 0.75/0.98 tff(931,plain,
% 0.75/0.98 (~b(elem!1, s(s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[930, 776])).
% 0.75/0.98 tff(932,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(933,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(934,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[933, 932])).
% 0.75/0.98 tff(935,plain,
% 0.75/0.98 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[934, 51])).
% 0.75/0.98 tff(936,plain,
% 0.75/0.98 (r(elem!1, s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[935, 931, 774])).
% 0.75/0.98 tff(937,plain,
% 0.75/0.98 (r(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[936, 766])).
% 0.75/0.98 tff(938,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.75/0.98 tff(939,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 0.75/0.98 tff(940,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.75/0.98 tff(941,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(942,plain,
% 0.75/0.98 (((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(943,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[942])).
% 0.75/0.98 tff(944,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[943, 941])).
% 0.75/0.98 tff(945,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(946,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.75/0.98 tff(947,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[946, 124, 940, 939, 938])).
% 0.75/0.98 tff(948,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(949,plain,
% 0.75/0.98 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[948, 937, 764])).
% 0.75/0.98 tff(950,plain,
% 0.75/0.98 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[949, 738])).
% 0.75/0.98 tff(951,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[733])).
% 0.75/0.98 tff(952,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(symmetry,[status(thm)],[951])).
% 0.75/0.98 tff(953,plain,
% 0.75/0.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[734, 733])).
% 0.75/0.98 tff(954,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[922, 953])).
% 0.75/0.98 tff(955,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[954, 952])).
% 0.75/0.98 tff(956,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(957,plain,
% 0.75/0.98 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(958,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[957])).
% 0.75/0.98 tff(959,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[958, 956])).
% 0.75/0.98 tff(960,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(961,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[960, 959])).
% 0.75/0.98 tff(962,plain,
% 0.75/0.98 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[961, 238, 226, 740, 955])).
% 0.75/0.98 tff(963,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(964,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(965,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.75/0.98 tff(966,plain,
% 0.75/0.98 ((s(s(elem!1)) = s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[965, 51, 962])).
% 0.75/0.98 tff(967,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[966, 950, 731])).
% 0.75/0.98 tff(968,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (elem!1 = s(s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | r(s(z), s(elem!1)) | (~b(elem!1, s(z))) | (s(elem!1) = elem!1) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(969,plain,
% 0.75/0.98 (~r(s(s(elem!1)), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[968, 677, 543, 491, 692, 630, 542, 541, 514, 679, 587, 370, 394, 589])).
% 0.75/0.98 tff(970,plain,
% 0.75/0.98 (r(elem!1, s(s(elem!1)))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[615, 969, 150, 589, 543])).
% 0.75/0.98 tff(971,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(972,plain,
% 0.75/0.98 (((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(973,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[972])).
% 0.75/0.98 tff(974,plain,
% 0.75/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.98 inference(transitivity,[status(thm)],[973, 971])).
% 0.75/0.98 tff(975,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(976,plain,
% 0.75/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.75/0.98 tff(977,plain,
% 0.75/0.98 (~r(s(elem!1), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[976, 124, 970, 677])).
% 0.75/0.98 tff(978,plain,
% 0.75/0.98 (b(s(elem!1), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[408, 977, 394])).
% 0.75/0.98 tff(979,plain,
% 0.75/0.98 (~b(s(z), s(elem!1))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[668, 978, 370, 630])).
% 0.75/0.98 tff(980,plain,
% 0.75/0.98 (s(z) = s(elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[439, 979, 587])).
% 0.75/0.98 tff(981,plain,
% 0.75/0.98 (s(elem!1) = s(z)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[425, 980])).
% 0.75/0.98 tff(982,plain,
% 0.75/0.98 (s(s(z)) = s(s(elem!1))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[357, 981])).
% 0.75/0.98 tff(983,plain,
% 0.75/0.98 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[982])).
% 0.75/0.98 tff(984,plain,
% 0.75/0.98 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.98 inference(symmetry,[status(thm)],[983])).
% 0.75/0.98 tff(985,plain,
% 0.75/0.98 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[984])).
% 0.75/0.98 tff(986,plain,
% 0.75/0.98 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.75/0.98 inference(symmetry,[status(thm)],[985])).
% 0.75/0.98 tff(987,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[984])).
% 0.75/0.98 tff(988,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(symmetry,[status(thm)],[987])).
% 0.75/0.98 tff(989,plain,
% 0.75/0.98 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[984])).
% 0.75/0.98 tff(990,plain,
% 0.75/0.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[989, 984])).
% 0.75/0.98 tff(991,plain,
% 0.75/0.98 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[989])).
% 0.75/0.98 tff(992,plain,
% 0.75/0.98 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(symmetry,[status(thm)],[991])).
% 0.75/0.98 tff(993,plain,
% 0.75/0.98 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[992])).
% 0.75/0.98 tff(994,plain,
% 0.75/0.98 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[786, 978, 630, 491])).
% 0.75/0.98 tff(995,plain,
% 0.75/0.98 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[647, 994, 643])).
% 0.75/0.98 tff(996,plain,
% 0.75/0.98 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[915, 995, 630, 677, 980, 542])).
% 0.75/0.98 tff(997,plain,
% 0.75/0.98 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[996, 993])).
% 0.75/0.98 tff(998,plain,
% 0.75/0.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[921, 997, 692])).
% 0.75/0.98 tff(999,plain,
% 0.75/0.98 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[998, 990])).
% 0.75/0.99 tff(1000,plain,
% 0.75/0.99 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[999, 988])).
% 0.75/0.99 tff(1001,plain,
% 0.75/0.99 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[980])).
% 0.75/0.99 tff(1002,plain,
% 0.75/0.99 (z = elem!1),
% 0.75/0.99 inference(transitivity,[status(thm)],[769, 1001, 154])).
% 0.75/0.99 tff(1003,plain,
% 0.75/0.99 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1002])).
% 0.75/0.99 tff(1004,plain,
% 0.75/0.99 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1003])).
% 0.75/0.99 tff(1005,plain,
% 0.75/0.99 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1006,plain,
% 0.75/0.99 (~(s(s(s(s(s(z))))) = z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1005, 37])).
% 0.75/0.99 tff(1007,plain,
% 0.75/0.99 (~(s(s(s(s(s(z))))) = elem!1)),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1006, 1004])).
% 0.75/0.99 tff(1008,plain,
% 0.75/0.99 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 0.75/0.99 inference(commutativity,[status(thm)],[])).
% 0.75/0.99 tff(1009,plain,
% 0.75/0.99 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1008])).
% 0.75/0.99 tff(1010,plain,
% 0.75/0.99 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[989, 984])).
% 0.75/0.99 tff(1011,plain,
% 0.75/0.99 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1010])).
% 0.75/0.99 tff(1012,plain,
% 0.75/0.99 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[692, 1011])).
% 0.75/0.99 tff(1013,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 0.75/0.99 tff(1014,plain,
% 0.75/0.99 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1013])).
% 0.75/0.99 tff(1015,plain,
% 0.75/0.99 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1014])).
% 0.75/0.99 tff(1016,plain,
% 0.75/0.99 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1015])).
% 0.75/0.99 tff(1017,plain,
% 0.75/0.99 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.75/0.99 inference(transitivity,[status(thm)],[723, 1016, 715])).
% 0.75/0.99 tff(1018,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 0.75/0.99 tff(1019,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1018, 1017])).
% 0.75/0.99 tff(1020,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(1021,plain,
% 0.75/0.99 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1020, 1012])).
% 0.75/0.99 tff(1022,plain,
% 0.75/0.99 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1021, 1009])).
% 0.75/0.99 tff(1023,plain,
% 0.75/0.99 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1002])).
% 0.75/0.99 tff(1024,plain,
% 0.75/0.99 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[1023, 767])).
% 0.75/0.99 tff(1025,plain,
% 0.75/0.99 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1024])).
% 0.75/0.99 tff(1026,plain,
% 0.75/0.99 (~(elem!1 = s(s(s(s(z)))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[726, 1025])).
% 0.75/0.99 tff(1027,plain,
% 0.75/0.99 (~(s(s(s(s(z)))) = elem!1)),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1026, 790])).
% 0.75/0.99 tff(1028,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1029,plain,
% 0.75/0.99 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1030,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1029])).
% 0.75/0.99 tff(1031,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(transitivity,[status(thm)],[1030, 1028])).
% 0.75/0.99 tff(1032,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1033,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 0.75/0.99 tff(1034,plain,
% 0.75/0.99 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1033, 238, 543, 589])).
% 0.75/0.99 tff(1035,plain,
% 0.75/0.99 (~b(s(s(s(s(z)))), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1034, 1000])).
% 0.75/0.99 tff(1036,plain,
% 0.75/0.99 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[905, 51, 1035])).
% 0.75/0.99 tff(1037,plain,
% 0.75/0.99 (r(s(s(s(s(z)))), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1036, 1027])).
% 0.75/0.99 tff(1038,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.75/0.99 tff(1039,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 0.75/0.99 tff(1040,assumption,(b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.99 tff(1041,assumption,(b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.99 tff(1042,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1043,plain,
% 0.75/0.99 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1044,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1043])).
% 0.75/0.99 tff(1045,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[1044, 1042])).
% 0.75/0.99 tff(1046,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1047,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.75/0.99 tff(1048,plain,
% 0.75/0.99 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1047, 238, 226, 1041, 1040])).
% 0.75/0.99 tff(1049,plain,
% 0.75/0.99 (((~![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)))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1050,plain,
% 0.75/0.99 ((~![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)))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1051,plain,
% 0.75/0.99 ((~![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))))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 0.75/0.99 tff(1052,plain,
% 0.75/0.99 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1051, 51, 1048, 1039])).
% 0.75/0.99 tff(1053,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 0.75/0.99 tff(1054,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1055,plain,
% 0.75/0.99 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1056,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1055])).
% 0.75/0.99 tff(1057,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.75/0.99 tff(1058,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1059,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.75/0.99 tff(1060,plain,
% 0.75/0.99 (~b(s(s(s(s(s(z))))), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1059, 238, 543, 226, 1040])).
% 0.75/0.99 tff(1061,plain,
% 0.75/0.99 (((~![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))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1062,plain,
% 0.75/0.99 ((~![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))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1063,plain,
% 0.75/0.99 ((~![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)),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 0.75/0.99 tff(1064,plain,
% 0.75/0.99 ((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)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1063, 51])).
% 0.75/0.99 tff(1065,plain,
% 0.75/0.99 (r(s(s(s(s(s(z))))), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1064, 1060, 1053])).
% 0.75/0.99 tff(1066,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1067,plain,
% 0.75/0.99 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1068,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1067])).
% 0.75/0.99 tff(1069,plain,
% 0.75/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.75/0.99 inference(transitivity,[status(thm)],[1068, 1066])).
% 0.75/0.99 tff(1070,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(1071,plain,
% 0.75/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.75/0.99 tff(1072,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1071, 124, 1065, 1052, 1038])).
% 0.75/0.99 tff(1073,plain,((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), elem!1)) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(1074,plain,
% 0.75/0.99 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1073, 1037, 1022, 1007, 589, 1000, 543])).
% 0.75/0.99 tff(1075,plain,
% 0.75/0.99 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[13])).
% 0.75/0.99 tff(1076,plain,
% 0.75/0.99 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1075])).
% 0.75/0.99 tff(1077,plain,
% 0.75/0.99 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1076])).
% 0.75/0.99 tff(1078,plain,
% 0.75/0.99 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1077])).
% 0.75/0.99 tff(1079,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 0.75/0.99 tff(1080,plain,
% 0.75/0.99 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.75/0.99 tff(1081,assumption,(~b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/0.99 tff(1082,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1081, 1080])).
% 0.75/0.99 tff(1083,plain,(b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(1084,plain,
% 0.75/0.99 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1083, 1074, 982])).
% 0.75/0.99 tff(1085,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 0.75/0.99 tff(1086,plain,
% 0.75/0.99 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1085])).
% 0.75/0.99 tff(1087,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.99 tff(1088,plain,
% 0.75/0.99 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 0.75/0.99 inference(symmetry,[status(thm)],[1087])).
% 0.75/0.99 tff(1089,plain,
% 0.75/0.99 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[1088])).
% 0.75/0.99 tff(1090,plain,
% 0.75/0.99 (s(s(s(s(z)))) = s(s(z))),
% 0.75/0.99 inference(transitivity,[status(thm)],[723, 1089, 138])).
% 0.75/0.99 tff(1091,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[730, 1090])).
% 0.75/0.99 tff(1092,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(1093,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1092, 1086])).
% 0.75/0.99 tff(1094,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(1095,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 0.75/0.99 tff(1096,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 0.75/0.99 tff(1097,plain,
% 0.75/0.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(1098,plain,
% 0.75/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1099,plain,
% 0.75/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.75/1.00 tff(1100,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1099, 51, 1096, 1095, 1094])).
% 0.75/1.00 tff(1101,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1102,plain,
% 0.75/1.00 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1101, 1084])).
% 0.75/1.00 tff(1103,plain,
% 0.75/1.00 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1102, 986])).
% 0.75/1.00 tff(1104,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1105,plain,
% 0.75/1.00 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1106,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1105])).
% 0.75/1.00 tff(1107,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1106, 1104])).
% 0.75/1.00 tff(1108,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1109,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 0.75/1.00 tff(1110,plain,
% 0.75/1.00 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1109, 124, 677, 542, 1103])).
% 0.75/1.00 tff(1111,plain,
% 0.75/1.00 (s(elem!1) = s(z)),
% 0.75/1.00 inference(symmetry,[status(thm)],[980])).
% 0.75/1.00 tff(1112,plain,
% 0.75/1.00 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1111])).
% 0.75/1.00 tff(1113,plain,
% 0.75/1.00 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 0.75/1.00 inference(symmetry,[status(thm)],[1112])).
% 0.75/1.00 tff(1114,plain,
% 0.75/1.00 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1113])).
% 0.75/1.00 tff(1115,plain,
% 0.75/1.00 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[728, 1114])).
% 0.75/1.00 tff(1116,plain,
% 0.75/1.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1117,plain,
% 0.75/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1118,plain,
% 0.75/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 0.75/1.00 tff(1119,plain,
% 0.75/1.00 (b(s(s(s(s(s(z))))), s(elem!1))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1118, 51, 1115, 1110])).
% 0.75/1.00 tff(1120,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1121,plain,
% 0.75/1.00 (((~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))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1122,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1121])).
% 0.75/1.00 tff(1123,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1122, 1120])).
% 0.75/1.00 tff(1124,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1125,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 0.75/1.00 tff(1126,plain,
% 0.75/1.00 (~b(s(s(s(s(s(z))))), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1125, 238, 630, 978, 1119])).
% 0.75/1.00 tff(1127,plain,
% 0.75/1.00 (r(s(s(s(s(s(z))))), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1064, 1126, 1007])).
% 0.75/1.00 tff(1128,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1129,plain,
% 0.75/1.00 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1130,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1129])).
% 0.75/1.00 tff(1131,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.75/1.00 tff(1132,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1133,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.75/1.00 tff(1134,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1133, 124, 995, 1127, 1103])).
% 0.75/1.00 tff(1135,plain,(b(s(z), s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1136,plain,
% 0.75/1.00 (b(s(z), s(s(elem!1)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1135, 491, 543, 542, 370, 514, 150, 541, 307, 169])).
% 0.75/1.00 tff(1137,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.75/1.00 tff(1138,plain,
% 0.75/1.00 (~r(s(s(elem!1)), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[622, 124, 590, 307])).
% 0.75/1.00 tff(1139,plain,
% 0.75/1.00 (b(s(s(elem!1)), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[255, 1138, 167])).
% 0.75/1.00 tff(1140,plain,
% 0.75/1.00 (~r(elem!1, s(s(elem!1)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[599, 590, 307])).
% 0.75/1.00 tff(1141,plain,
% 0.75/1.00 (b(elem!1, s(s(elem!1)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[606, 1140, 150])).
% 0.75/1.00 tff(1142,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1143,plain,
% 0.75/1.00 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1144,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1143])).
% 0.75/1.00 tff(1145,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1144, 1142])).
% 0.75/1.00 tff(1146,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(z))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1147,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 0.75/1.00 tff(1148,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1147, 238, 1141, 1139, 1137, 370])).
% 0.75/1.00 tff(1149,plain,((~r(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1150,plain,
% 0.75/1.00 (~r(elem!1, s(elem!1))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1149, 1136, 370, 307, 150])).
% 0.75/1.00 tff(1151,plain,
% 0.75/1.00 (b(elem!1, s(elem!1))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[629, 1150, 387])).
% 0.75/1.00 tff(1152,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 0.75/1.00 tff(1153,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1154,plain,
% 0.75/1.00 (((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1155,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1154])).
% 0.75/1.00 tff(1156,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1155, 1153])).
% 0.75/1.00 tff(1157,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1158,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.75/1.00 tff(1159,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1158, 238, 631, 1137, 370, 1152])).
% 0.75/1.00 tff(1160,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1161,plain,
% 0.75/1.00 (~b(s(elem!1), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1160, 1151, 370, 1136])).
% 0.75/1.00 tff(1162,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1163,plain,
% 0.75/1.00 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1164,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1163])).
% 0.75/1.00 tff(1165,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1164, 1162])).
% 0.75/1.00 tff(1166,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1167,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.75/1.00 tff(1168,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1167, 124, 518, 542, 210])).
% 0.75/1.00 tff(1169,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1170,plain,
% 0.75/1.00 (~r(s(elem!1), s(s(elem!1)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1169, 210, 542])).
% 0.75/1.00 tff(1171,plain,
% 0.75/1.00 (b(s(elem!1), s(s(elem!1)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[534, 1170, 159])).
% 0.75/1.00 tff(1172,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[639, 1171, 631, 491])).
% 0.75/1.00 tff(1173,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[647, 1172, 823])).
% 0.75/1.00 tff(1174,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[647, 640, 823])).
% 0.75/1.00 tff(1175,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1176,plain,
% 0.75/1.00 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1177,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[1176])).
% 0.75/1.00 tff(1178,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[1177, 1175])).
% 0.75/1.00 tff(1179,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(1180,plain,
% 0.75/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 0.75/1.00 tff(1181,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1180, 124, 301, 210, 649])).
% 0.75/1.00 tff(1182,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(1183,plain,
% 0.75/1.00 (~r(s(s(elem!1)), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1182, 1174, 210])).
% 0.75/1.00 tff(1184,plain,
% 0.75/1.00 (b(s(s(elem!1)), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[255, 1183, 248])).
% 0.75/1.00 tff(1185,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.75/1.00 tff(1186,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1187,plain,
% 0.75/1.00 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(1188,plain,
% 0.75/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1187])).
% 0.75/1.01 tff(1189,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.75/1.01 tff(1190,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1191,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.75/1.01 tff(1192,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1191, 238, 631, 1185, 1184, 288])).
% 0.75/1.01 tff(1193,plain,((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1194,plain,
% 0.75/1.01 (~b(elem!1, s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1193, 1171, 631, 167, 210, 823, 491])).
% 0.75/1.01 tff(1195,plain,
% 0.75/1.01 (r(elem!1, s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[606, 1194, 150])).
% 0.75/1.01 tff(1196,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1197,plain,
% 0.75/1.01 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1198,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1197])).
% 0.75/1.01 tff(1199,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1198, 1196])).
% 0.75/1.01 tff(1200,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1201,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.75/1.01 tff(1202,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1201, 124, 1195, 210, 1173])).
% 0.75/1.01 tff(1203,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1204,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1203, 643, 150, 1151, 491, 542])).
% 0.75/1.01 tff(1205,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[223, 1204, 209])).
% 0.75/1.01 tff(1206,plain,
% 0.75/1.01 (~b(s(z), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[554, 1205, 370, 543])).
% 0.75/1.01 tff(1207,plain,
% 0.75/1.01 (r(s(z), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[101, 1206])).
% 0.75/1.01 tff(1208,plain,
% 0.75/1.01 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[177, 1207, 169])).
% 0.75/1.01 tff(1209,plain,
% 0.75/1.01 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[190, 1208])).
% 0.75/1.01 tff(1210,plain,
% 0.75/1.01 (~b(s(elem!1), s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[639, 781, 631, 491])).
% 0.75/1.01 tff(1211,plain,
% 0.75/1.01 (r(s(elem!1), s(s(elem!1)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[534, 1210, 206])).
% 0.75/1.01 tff(1212,plain,
% 0.75/1.01 (~(elem!1 = s(elem!1))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[386, 206])).
% 0.75/1.01 tff(1213,plain,
% 0.75/1.01 (~(s(elem!1) = elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[393, 1212])).
% 0.75/1.01 tff(1214,plain,
% 0.75/1.01 (~b(s(elem!1), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[786, 781, 631, 491])).
% 0.75/1.01 tff(1215,plain,
% 0.75/1.01 (r(s(elem!1), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[408, 1214, 1213])).
% 0.75/1.01 tff(1216,plain,
% 0.75/1.01 (~r(s(s(elem!1)), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[700, 1215, 1211])).
% 0.75/1.01 tff(1217,plain,
% 0.75/1.01 (b(s(s(elem!1)), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[255, 1216, 248])).
% 0.75/1.01 tff(1218,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1219,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1220,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.75/1.01 tff(1221,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1220, 238, 631, 1217, 781, 226])).
% 0.75/1.01 tff(1222,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1223,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1222, 1151, 1205, 167, 159, 491])).
% 0.75/1.01 tff(1224,plain,
% 0.75/1.01 (r(s(s(s(elem!1))), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[647, 1223, 643])).
% 0.75/1.01 tff(1225,plain,
% 0.75/1.01 (~r(s(elem!1), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[657, 1224, 542])).
% 0.75/1.01 tff(1226,plain,
% 0.75/1.01 (b(s(elem!1), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[408, 1225, 394])).
% 0.75/1.01 tff(1227,plain,
% 0.75/1.01 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 0.75/1.01 inference(commutativity,[status(thm)],[])).
% 0.75/1.01 tff(1228,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 0.75/1.01 tff(1229,plain,
% 0.75/1.01 (elem!1 = s(s(z))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.75/1.01 tff(1230,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[541, 1229])).
% 0.75/1.01 tff(1231,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1232,plain,
% 0.75/1.01 (~(s(s(z)) = elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1231, 541])).
% 0.75/1.01 tff(1233,plain,
% 0.75/1.01 (~r(s(elem!1), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[483, 306, 169])).
% 0.75/1.01 tff(1234,plain,
% 0.75/1.01 (b(s(elem!1), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[488, 1233, 278])).
% 0.75/1.01 tff(1235,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 0.75/1.01 tff(1236,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1237,plain,
% 0.75/1.01 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1238,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1237])).
% 0.75/1.01 tff(1239,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1238, 1236])).
% 0.75/1.01 tff(1240,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1241,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1240, 1239])).
% 0.75/1.01 tff(1242,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1241, 238, 491, 490, 225, 1235])).
% 0.75/1.01 tff(1243,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1244,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1243, 1234, 491, 225])).
% 0.75/1.01 tff(1245,plain,
% 0.75/1.01 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 0.75/1.01 inference(commutativity,[status(thm)],[])).
% 0.75/1.01 tff(1246,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 0.75/1.01 tff(1247,plain,
% 0.75/1.01 (s(elem!1) = s(s(z))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 0.75/1.01 tff(1248,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[278, 1247])).
% 0.75/1.01 tff(1249,plain,((~(s(s(z)) = s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1250,plain,
% 0.75/1.01 (~(s(s(z)) = s(elem!1))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1249, 278])).
% 0.75/1.01 tff(1251,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1252,plain,
% 0.75/1.01 (((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1253,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z)))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1252])).
% 0.75/1.01 tff(1254,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.75/1.01 tff(1255,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(elem!1))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1256,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(z)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.75/1.01 tff(1257,plain,
% 0.75/1.01 (~r(s(s(z)), s(elem!1))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1256, 124, 169, 306])).
% 0.75/1.01 tff(1258,plain,
% 0.75/1.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1259,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1260,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.75/1.01 tff(1261,plain,
% 0.75/1.01 (b(s(s(z)), s(elem!1))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1260, 51, 1257, 1250])).
% 0.75/1.01 tff(1262,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1263,plain,
% 0.75/1.01 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1264,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1263])).
% 0.75/1.01 tff(1265,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.75/1.01 tff(1266,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1267,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.75/1.01 tff(1268,plain,
% 0.75/1.01 (~b(s(s(z)), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1267, 238, 631, 507, 1261])).
% 0.75/1.01 tff(1269,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 0.75/1.01 tff(1270,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 0.75/1.01 tff(1271,plain,
% 0.75/1.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1272,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1273,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.75/1.01 tff(1274,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1273, 51, 374, 1270, 1269])).
% 0.75/1.01 tff(1275,plain,(b(s(s(z)), elem!1) | (s(s(z)) = elem!1) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1276,plain,
% 0.75/1.01 (r(s(s(z)), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1275, 1268, 374])).
% 0.75/1.01 tff(1277,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1278,plain,
% 0.75/1.01 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1279,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1278])).
% 0.75/1.01 tff(1280,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.75/1.01 inference(transitivity,[status(thm)],[1279, 1277])).
% 0.75/1.01 tff(1281,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1282,plain,
% 0.75/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.75/1.01 tff(1283,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1282, 124, 649, 1276])).
% 0.75/1.01 tff(1284,plain,
% 0.75/1.01 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 0.75/1.01 inference(commutativity,[status(thm)],[])).
% 0.75/1.01 tff(1285,plain,
% 0.75/1.01 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 0.75/1.01 inference(symmetry,[status(thm)],[1284])).
% 0.75/1.01 tff(1286,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 0.75/1.01 tff(1287,plain,
% 0.75/1.01 (s(s(z)) = s(s(s(elem!1)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1286, 1285])).
% 0.75/1.01 tff(1288,assumption,(~(s(s(z)) = s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.01 tff(1289,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1288, 1287])).
% 0.75/1.01 tff(1290,plain,((~(s(s(s(elem!1))) = s(s(z)))) | (s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1291,plain,
% 0.75/1.01 (~(s(s(s(elem!1))) = s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1290, 185])).
% 0.75/1.01 tff(1292,plain,
% 0.75/1.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(1293,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(1294,plain,
% 0.75/1.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.75/1.01 tff(1295,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1294, 51, 1291, 1283, 1244])).
% 0.75/1.01 tff(1296,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(1297,plain,
% 0.75/1.01 (~r(s(elem!1), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1296, 1224, 1232, 1151, 1226, 169, 491, 1209, 278])).
% 0.75/1.01 tff(1298,plain,
% 0.75/1.01 (s(elem!1) = s(z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[473, 1297, 1161])).
% 0.75/1.01 tff(1299,plain,
% 0.75/1.01 (s(s(z)) = s(s(elem!1))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[357, 1298])).
% 0.75/1.01 tff(1300,plain,
% 0.75/1.01 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1299])).
% 0.75/1.01 tff(1301,plain,
% 0.75/1.01 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1209, 1300])).
% 0.75/1.01 tff(1302,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[1298])).
% 0.75/1.01 tff(1303,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[491, 1302])).
% 0.75/1.01 tff(1304,plain,
% 0.75/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1305,plain,
% 0.75/1.02 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1306,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1305])).
% 0.75/1.02 tff(1307,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1306, 1304])).
% 0.75/1.02 tff(1308,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1309,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1308, 1307])).
% 0.75/1.02 tff(1310,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1309, 238, 1136, 1205, 1303, 1301])).
% 0.75/1.02 tff(1311,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1312,plain,
% 0.75/1.02 (~b(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1311, 540, 278, 370, 460, 169, 150, 307, 510, 541])).
% 0.75/1.02 tff(1313,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.02 tff(1314,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.02 tff(1315,plain,
% 0.75/1.02 (((~![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)))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1316,plain,
% 0.75/1.02 ((~![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)))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1317,plain,
% 0.75/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 0.75/1.02 tff(1318,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1317, 51, 1314, 514, 1313])).
% 0.75/1.02 tff(1319,plain,(r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1320,plain,
% 0.75/1.02 (r(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1319, 510, 1312])).
% 0.75/1.02 tff(1321,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.02 tff(1322,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1323,plain,
% 0.75/1.02 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1324,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1323])).
% 0.75/1.02 tff(1325,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1324, 1322])).
% 0.75/1.02 tff(1326,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1327,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 0.75/1.02 tff(1328,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1327, 124, 590, 1321, 542])).
% 0.75/1.02 tff(1329,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1330,plain,
% 0.75/1.02 (~r(elem!1, s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1329, 1320, 540])).
% 0.75/1.02 tff(1331,plain,
% 0.75/1.02 (b(elem!1, s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[629, 1330, 387])).
% 0.75/1.02 tff(1332,plain,
% 0.75/1.02 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[639, 1331, 535, 460])).
% 0.75/1.02 tff(1333,plain,
% 0.75/1.02 (~r(s(s(s(elem!1))), elem!1)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1296, 1331, 374, 409, 474, 460, 169, 462, 278])).
% 0.75/1.02 tff(1334,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[647, 1333, 1332, 517])).
% 0.75/1.02 tff(1335,plain,((~r(s(s(elem!1)), s(elem!1))) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(s(z))) | (~b(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (elem!1 = s(s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1336,plain,
% 0.75/1.02 (~r(s(s(elem!1)), s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1335, 380, 80, 374, 364, 150, 373, 161, 160, 358, 352, 274])).
% 0.75/1.02 tff(1337,plain,
% 0.75/1.02 (b(s(s(elem!1)), s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[323, 1336, 272])).
% 0.75/1.02 tff(1338,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1339,plain,
% 0.75/1.02 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1340,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1339])).
% 0.75/1.02 tff(1341,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1340, 1338])).
% 0.75/1.02 tff(1342,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1343,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.75/1.02 tff(1344,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1343, 238, 1337, 202, 224, 266])).
% 0.75/1.02 tff(1345,plain,((~r(s(z), s(s(elem!1)))) | (s(s(z)) = elem!1) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(z)) | r(elem!1, s(z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1346,plain,
% 0.75/1.02 (s(s(z)) = elem!1),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1345, 264, 64, 114, 161, 150, 160])).
% 0.75/1.02 tff(1347,plain,
% 0.75/1.02 (~(elem!1 = s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[325, 256, 80, 191, 272, 202, 224])).
% 0.75/1.02 tff(1348,plain,
% 0.75/1.02 (b(elem!1, s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[363, 264, 1347])).
% 0.75/1.02 tff(1349,plain,
% 0.75/1.02 (~(elem!1 = s(s(z)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[372, 1348, 64])).
% 0.75/1.02 tff(1350,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1231, 1349, 1346])).
% 0.75/1.02 tff(1351,plain,((~r(s(z), s(s(elem!1)))) | b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1352,plain,
% 0.75/1.02 (~r(s(z), s(s(elem!1)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1351, 150, 113, 102, 114, 64])).
% 0.75/1.02 tff(1353,plain,
% 0.75/1.02 (b(s(z), s(s(elem!1)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[56, 1352])).
% 0.75/1.02 tff(1354,plain,
% 0.75/1.02 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[276])).
% 0.75/1.02 tff(1355,plain,
% 0.75/1.02 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(symmetry,[status(thm)],[1354])).
% 0.75/1.02 tff(1356,plain,
% 0.75/1.02 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1355])).
% 0.75/1.02 tff(1357,plain,
% 0.75/1.02 (~b(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[81, 1356])).
% 0.75/1.02 tff(1358,plain,
% 0.75/1.02 (s(z) = elem!1),
% 0.75/1.02 inference(symmetry,[status(thm)],[276])).
% 0.75/1.02 tff(1359,plain,
% 0.75/1.02 (s(z) = s(s(s(elem!1)))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1358, 501])).
% 0.75/1.02 tff(1360,plain,
% 0.75/1.02 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1359])).
% 0.75/1.02 tff(1361,plain,
% 0.75/1.02 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.75/1.02 inference(symmetry,[status(thm)],[1360])).
% 0.75/1.02 tff(1362,plain,
% 0.75/1.02 (s(s(elem!1)) = z),
% 0.75/1.02 inference(transitivity,[status(thm)],[89, 1361, 26])).
% 0.75/1.02 tff(1363,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[92, 1362])).
% 0.75/1.02 tff(1364,plain,((~(elem!1 = s(z))) | (~(elem!1 = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1365,plain,
% 0.75/1.02 (~(elem!1 = s(s(s(elem!1))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1364, 276])).
% 0.75/1.02 tff(1366,plain,
% 0.75/1.02 (b(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1319, 1365, 1313])).
% 0.75/1.02 tff(1367,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1366, 1357])).
% 0.75/1.02 tff(1368,plain,((~(elem!1 = s(z))) | b(s(z), s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1369,plain,
% 0.75/1.02 (r(elem!1, s(s(s(elem!1))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1368, 276, 81])).
% 0.75/1.02 tff(1370,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 0.75/1.02 tff(1371,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1372,plain,
% 0.75/1.02 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1373,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1372])).
% 0.75/1.02 tff(1374,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1373, 1371])).
% 0.75/1.02 tff(1375,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1376,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.75/1.02 tff(1377,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1376, 124, 1321, 1370, 161])).
% 0.75/1.02 tff(1378,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1379,plain,
% 0.75/1.02 (~r(elem!1, s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1378, 1369, 161])).
% 0.75/1.02 tff(1380,assumption,(~(s(s(s(s(s(z))))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.02 tff(1381,plain,
% 0.75/1.02 (s(s(s(z))) = s(elem!1)),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1228])).
% 0.75/1.02 tff(1382,plain,
% 0.75/1.02 (s(s(s(s(z)))) = s(s(elem!1))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1381])).
% 0.75/1.02 tff(1383,plain,
% 0.75/1.02 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1382])).
% 0.75/1.02 tff(1384,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1380, 1383])).
% 0.75/1.02 tff(1385,plain,((~(s(s(z)) = elem!1)) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1386,plain,
% 0.75/1.02 (~(s(s(z)) = elem!1)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1385, 1380])).
% 0.75/1.02 tff(1387,plain,
% 0.75/1.02 (~(s(z) = s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[425, 358])).
% 0.75/1.02 tff(1388,plain,
% 0.75/1.02 (~r(s(z), s(s(elem!1)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1345, 64, 150, 161, 1386, 359, 114])).
% 0.75/1.02 tff(1389,plain,
% 0.75/1.02 (b(s(z), s(s(elem!1)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[56, 1388])).
% 0.75/1.02 tff(1390,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1391,plain,
% 0.75/1.02 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(1392,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[1391])).
% 0.75/1.02 tff(1393,plain,
% 0.75/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.02 inference(transitivity,[status(thm)],[1392, 1390])).
% 0.75/1.02 tff(1394,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(1395,plain,
% 0.75/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 0.75/1.02 tff(1396,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1395, 124, 307, 210, 442])).
% 0.75/1.02 tff(1397,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(1398,plain,
% 0.75/1.02 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1397, 307, 210])).
% 0.75/1.02 tff(1399,plain,
% 0.75/1.02 (b(s(s(s(elem!1))), s(elem!1))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[459, 1398, 421])).
% 0.75/1.02 tff(1400,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 0.75/1.02 tff(1401,plain,
% 0.75/1.02 (elem!1 = s(z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[363, 1400, 359])).
% 0.75/1.02 tff(1402,plain,
% 0.88/1.02 (s(elem!1) = s(s(z))),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[280, 1401])).
% 0.88/1.02 tff(1403,plain,
% 0.88/1.02 (s(s(elem!1)) = s(s(s(z)))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1402])).
% 0.88/1.02 tff(1404,plain,
% 0.88/1.02 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1403])).
% 0.88/1.02 tff(1405,plain,
% 0.88/1.02 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1404])).
% 0.88/1.02 tff(1406,plain,
% 0.88/1.02 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.02 inference(symmetry,[status(thm)],[1405])).
% 0.88/1.02 tff(1407,plain,
% 0.88/1.02 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1406])).
% 0.88/1.02 tff(1408,plain,
% 0.88/1.02 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1403])).
% 0.88/1.02 tff(1409,plain,
% 0.88/1.02 (b(s(z), s(s(s(z))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[1137, 1408])).
% 0.88/1.02 tff(1410,plain,
% 0.88/1.02 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1401])).
% 0.88/1.02 tff(1411,plain,
% 0.88/1.02 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 0.88/1.02 inference(symmetry,[status(thm)],[1410])).
% 0.88/1.02 tff(1412,plain,
% 0.88/1.02 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1402])).
% 0.88/1.02 tff(1413,plain,
% 0.88/1.02 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 0.88/1.02 inference(symmetry,[status(thm)],[1412])).
% 0.88/1.02 tff(1414,plain,
% 0.88/1.02 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 0.88/1.02 inference(transitivity,[status(thm)],[1413, 1411])).
% 0.88/1.02 tff(1415,plain,
% 0.88/1.02 (r(s(elem!1), elem!1)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[80, 1414])).
% 0.88/1.02 tff(1416,plain,
% 0.88/1.02 (~r(s(s(elem!1)), elem!1)),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[403, 1415, 307])).
% 0.88/1.02 tff(1417,plain,
% 0.88/1.02 (b(s(s(elem!1)), elem!1)),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[255, 1416, 248])).
% 0.88/1.02 tff(1418,plain,
% 0.88/1.02 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[276])).
% 0.88/1.02 tff(1419,plain,
% 0.88/1.02 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.88/1.02 inference(symmetry,[status(thm)],[1418])).
% 0.88/1.02 tff(1420,plain,
% 0.88/1.02 (s(s(elem!1)) = s(s(s(z)))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[281])).
% 0.88/1.02 tff(1421,plain,
% 0.88/1.02 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1420])).
% 0.88/1.02 tff(1422,plain,
% 0.88/1.02 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.88/1.02 inference(symmetry,[status(thm)],[1421])).
% 0.88/1.02 tff(1423,plain,
% 0.88/1.02 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.88/1.02 inference(transitivity,[status(thm)],[1422, 1419])).
% 0.88/1.02 tff(1424,plain,
% 0.88/1.02 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1423])).
% 0.88/1.02 tff(1425,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.88/1.02 tff(1426,plain,
% 0.88/1.02 (~b(s(s(elem!1)), elem!1)),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 0.88/1.02 tff(1427,plain,
% 0.88/1.02 ($false),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[228, 1426])).
% 0.88/1.02 tff(1428,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(elem!1)), elem!1)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.02 tff(1429,plain,
% 0.88/1.02 (b(s(s(s(z))), s(z))),
% 0.88/1.02 inference(unit_resolution,[status(thm)],[1428, 1417, 1401])).
% 0.88/1.02 tff(1430,plain,
% 0.88/1.02 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1404, 1403])).
% 0.88/1.02 tff(1431,plain,
% 0.88/1.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[210, 1430])).
% 0.88/1.02 tff(1432,plain,
% 0.88/1.02 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1404])).
% 0.88/1.02 tff(1433,plain,
% 0.88/1.02 (b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.02 inference(modus_ponens,[status(thm)],[266, 1432])).
% 0.88/1.02 tff(1434,plain,
% 0.88/1.02 (s(s(z)) = s(elem!1)),
% 0.88/1.02 inference(symmetry,[status(thm)],[375])).
% 0.88/1.02 tff(1435,plain,
% 0.88/1.02 (s(s(elem!1)) = s(s(s(z)))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[375])).
% 0.88/1.02 tff(1436,plain,
% 0.88/1.02 (s(s(s(z))) = s(s(elem!1))),
% 0.88/1.02 inference(symmetry,[status(thm)],[1435])).
% 0.88/1.02 tff(1437,plain,
% 0.88/1.02 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.88/1.02 inference(monotonicity,[status(thm)],[1436, 1434])).
% 0.88/1.03 tff(1438,plain,
% 0.88/1.03 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 0.88/1.03 inference(symmetry,[status(thm)],[1437])).
% 0.88/1.03 tff(1439,plain,
% 0.88/1.03 (r(s(s(s(z))), s(s(z)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[307, 1438])).
% 0.88/1.03 tff(1440,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.88/1.03 tff(1441,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1440, 1439])).
% 0.88/1.03 tff(1442,plain,(r(s(s(s(z))), s(s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1443,plain,
% 0.88/1.03 (r(s(s(s(z))), s(s(z)))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1442, 1402, 307])).
% 0.88/1.03 tff(1444,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.88/1.03 tff(1445,plain,
% 0.88/1.03 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(1446,plain,
% 0.88/1.03 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 0.88/1.03 inference(symmetry,[status(thm)],[1445])).
% 0.88/1.03 tff(1447,plain,
% 0.88/1.03 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1446])).
% 0.88/1.03 tff(1448,plain,
% 0.88/1.03 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1449,plain,
% 0.88/1.03 (~(s(s(z)) = z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1448, 37])).
% 0.88/1.03 tff(1450,plain,
% 0.88/1.03 (~(z = s(s(z)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1449, 1447])).
% 0.88/1.03 tff(1451,plain,
% 0.88/1.03 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(1452,plain,
% 0.88/1.03 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 0.88/1.03 inference(symmetry,[status(thm)],[1451])).
% 0.88/1.03 tff(1453,plain,
% 0.88/1.03 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1452])).
% 0.88/1.03 tff(1454,plain,
% 0.88/1.03 (~(z = s(s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[726, 1453])).
% 0.88/1.03 tff(1455,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.88/1.03 tff(1456,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.88/1.03 tff(1457,assumption,(b(z, s(z))), introduced(assumption)).
% 0.88/1.03 tff(1458,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1459,plain,
% 0.88/1.03 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1460,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1459])).
% 0.88/1.03 tff(1461,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.88/1.03 tff(1462,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1463,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.88/1.03 tff(1464,plain,
% 0.88/1.03 (~b(z, s(s(s(z))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1463, 238, 1457, 1456, 1455])).
% 0.88/1.03 tff(1465,plain,
% 0.88/1.03 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 0.88/1.03 inference(commutativity,[status(thm)],[])).
% 0.88/1.03 tff(1466,plain,
% 0.88/1.03 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 0.88/1.03 inference(symmetry,[status(thm)],[1465])).
% 0.88/1.03 tff(1467,plain,
% 0.88/1.03 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1466])).
% 0.88/1.03 tff(1468,plain,
% 0.88/1.03 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1469,plain,
% 0.88/1.03 (~(s(s(s(z))) = z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1468, 37])).
% 0.88/1.03 tff(1470,plain,
% 0.88/1.03 (~(z = s(s(s(z))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1469, 1467])).
% 0.88/1.03 tff(1471,plain,
% 0.88/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1472,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1473,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.88/1.03 tff(1474,plain,
% 0.88/1.03 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1473, 51])).
% 0.88/1.03 tff(1475,plain,
% 0.88/1.03 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1474, 1470])).
% 0.88/1.03 tff(1476,plain,
% 0.88/1.03 (r(z, s(s(s(z))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1475, 1464])).
% 0.88/1.03 tff(1477,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.88/1.03 tff(1478,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1479,plain,
% 0.88/1.03 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1480,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1479])).
% 0.88/1.03 tff(1481,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1480, 1478])).
% 0.88/1.03 tff(1482,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1483,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.88/1.03 tff(1484,plain,
% 0.88/1.03 (~r(z, s(s(s(s(z)))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1483, 124, 1477, 1476])).
% 0.88/1.03 tff(1485,plain,
% 0.88/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1486,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1487,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 0.88/1.03 tff(1488,plain,
% 0.88/1.03 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1487, 51, 1484])).
% 0.88/1.03 tff(1489,plain,
% 0.88/1.03 (b(z, s(s(s(s(z)))))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1488, 1454])).
% 0.88/1.03 tff(1490,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1491,plain,
% 0.88/1.03 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1492,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1491])).
% 0.88/1.03 tff(1493,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1492, 1490])).
% 0.88/1.03 tff(1494,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1495,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 0.88/1.03 tff(1496,plain,
% 0.88/1.03 (~r(s(s(s(s(z)))), z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1495, 124, 1477, 1476])).
% 0.88/1.03 tff(1497,plain,
% 0.88/1.03 (((~![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))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1498,plain,
% 0.88/1.03 ((~![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))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1499,plain,
% 0.88/1.03 ((~![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)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 0.88/1.03 tff(1500,plain,
% 0.88/1.03 (b(s(s(s(s(z)))), z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1499, 51, 726, 1496])).
% 0.88/1.03 tff(1501,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.03 tff(1502,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1503,plain,
% 0.88/1.03 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1504,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1503])).
% 0.88/1.03 tff(1505,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1504, 1502])).
% 0.88/1.03 tff(1506,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1507,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 0.88/1.03 tff(1508,plain,
% 0.88/1.03 (~b(z, s(s(z)))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1507, 238, 1501, 1500, 1489])).
% 0.88/1.03 tff(1509,plain,
% 0.88/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1510,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1511,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 0.88/1.03 tff(1512,plain,
% 0.88/1.03 ((z = s(s(z))) | r(z, s(s(z)))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1511, 51, 1508])).
% 0.88/1.03 tff(1513,plain,
% 0.88/1.03 (r(z, s(s(z)))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1512, 1450])).
% 0.88/1.03 tff(1514,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1515,plain,
% 0.88/1.03 (((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1516,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1515])).
% 0.88/1.03 tff(1517,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1516, 1514])).
% 0.88/1.03 tff(1518,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1519,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 0.88/1.03 tff(1520,plain,
% 0.88/1.03 (~b(s(s(s(z))), z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1519, 238, 1457, 1456, 1455])).
% 0.88/1.03 tff(1521,plain,
% 0.88/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1522,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1523,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.88/1.03 tff(1524,plain,
% 0.88/1.03 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1523, 51, 1469])).
% 0.88/1.03 tff(1525,plain,
% 0.88/1.03 (r(s(s(s(z))), z)),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1524, 1520])).
% 0.88/1.03 tff(1526,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1527,plain,
% 0.88/1.03 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1528,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1527])).
% 0.88/1.03 tff(1529,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1528, 1526])).
% 0.88/1.03 tff(1530,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1531,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z))))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 0.88/1.03 tff(1532,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1531, 124, 1525, 1513, 1444])).
% 0.88/1.03 tff(1533,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1534,plain,
% 0.88/1.03 (~b(z, s(z))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1533, 1443, 1433, 1431, 1429, 1409])).
% 0.88/1.03 tff(1535,assumption,(z = s(z)), introduced(assumption)).
% 0.88/1.03 tff(1536,plain,
% 0.88/1.03 (s(z) = z),
% 0.88/1.03 inference(symmetry,[status(thm)],[1535])).
% 0.88/1.03 tff(1537,plain,
% 0.88/1.03 ($false),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[72, 1536])).
% 0.88/1.03 tff(1538,plain,(~(z = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.03 tff(1539,plain,
% 0.88/1.03 (((~![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)))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1540,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1541,plain,
% 0.88/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.88/1.03 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 0.88/1.03 tff(1542,plain,
% 0.88/1.03 (b(z, s(z)) | r(z, s(z))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1541, 51, 1538])).
% 0.88/1.03 tff(1543,plain,
% 0.88/1.03 (r(z, s(z))),
% 0.88/1.03 inference(unit_resolution,[status(thm)],[1542, 1534])).
% 0.88/1.03 tff(1544,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.88/1.03 tff(1545,assumption,(r(z, s(z))), introduced(assumption)).
% 0.88/1.03 tff(1546,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.88/1.03 tff(1547,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1548,plain,
% 0.88/1.03 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.03 inference(rewrite,[status(thm)],[])).
% 0.88/1.03 tff(1549,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 0.88/1.03 inference(monotonicity,[status(thm)],[1548])).
% 0.88/1.03 tff(1550,plain,
% 0.88/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.03 inference(transitivity,[status(thm)],[1549, 1547])).
% 0.88/1.03 tff(1551,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.03 inference(quant_inst,[status(thm)],[])).
% 0.88/1.03 tff(1552,plain,
% 0.88/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 0.88/1.04 tff(1553,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1552, 124, 169, 1546, 1544])).
% 0.88/1.04 tff(1554,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1555,plain,
% 0.88/1.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1554, 1544, 169])).
% 0.88/1.04 tff(1556,assumption,(~(s(s(s(s(z)))) = s(s(z)))), introduced(assumption)).
% 0.88/1.04 tff(1557,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.88/1.04 tff(1558,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.88/1.04 tff(1559,plain,
% 0.88/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1560,plain,
% 0.88/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1561,plain,
% 0.88/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 0.88/1.04 tff(1562,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1561, 51, 1558, 1557, 1556])).
% 0.88/1.04 tff(1563,plain,(b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1564,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1563, 730])).
% 0.88/1.04 tff(1565,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1564, 1555])).
% 0.88/1.04 tff(1566,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1567,plain,
% 0.88/1.04 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1568,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1567])).
% 0.88/1.04 tff(1569,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1568, 1566])).
% 0.88/1.04 tff(1570,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1571,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 0.88/1.04 tff(1572,plain,
% 0.88/1.04 (~r(z, s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1571, 124, 1544, 1545])).
% 0.88/1.04 tff(1573,plain,
% 0.88/1.04 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1487, 51, 1572])).
% 0.88/1.04 tff(1574,plain,
% 0.88/1.04 (b(z, s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1573, 1454])).
% 0.88/1.04 tff(1575,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.88/1.04 tff(1576,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1577,plain,
% 0.88/1.04 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1578,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1577])).
% 0.88/1.04 tff(1579,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1578, 1576])).
% 0.88/1.04 tff(1580,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1581,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 0.88/1.04 tff(1582,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1581, 124, 169, 1545, 1575])).
% 0.88/1.04 tff(1583,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1584,plain,
% 0.88/1.04 (~r(z, s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1583, 1545, 169])).
% 0.88/1.04 tff(1585,plain,
% 0.88/1.04 ((z = s(s(z))) | b(z, s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1511, 51, 1584])).
% 0.88/1.04 tff(1586,plain,
% 0.88/1.04 (b(z, s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1585, 1450])).
% 0.88/1.04 tff(1587,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.88/1.04 tff(1588,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1589,plain,
% 0.88/1.04 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1590,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1589])).
% 0.88/1.04 tff(1591,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1590, 1588])).
% 0.88/1.04 tff(1592,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1593,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 0.88/1.04 tff(1594,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1593, 238, 1587, 1501, 1586, 1574])).
% 0.88/1.04 tff(1595,plain,((~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1596,plain,
% 0.88/1.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1595, 1565, 169, 1545, 1544])).
% 0.88/1.04 tff(1597,plain,
% 0.88/1.04 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.88/1.04 inference(symmetry,[status(thm)],[693])).
% 0.88/1.04 tff(1598,plain,
% 0.88/1.04 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1597])).
% 0.88/1.04 tff(1599,plain,
% 0.88/1.04 (~(s(s(z)) = s(s(s(s(z)))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[730, 1598])).
% 0.88/1.04 tff(1600,plain,
% 0.88/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1601,plain,
% 0.88/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1602,plain,
% 0.88/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 0.88/1.04 tff(1603,plain,
% 0.88/1.04 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1602, 51])).
% 0.88/1.04 tff(1604,plain,
% 0.88/1.04 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1603, 1599])).
% 0.88/1.04 tff(1605,plain,
% 0.88/1.04 (r(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1604, 1596])).
% 0.88/1.04 tff(1606,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1607,plain,
% 0.88/1.04 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1608,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1607])).
% 0.88/1.04 tff(1609,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1608, 1606])).
% 0.88/1.04 tff(1610,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1611,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 0.88/1.04 tff(1612,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1611, 124, 169, 1544, 1605])).
% 0.88/1.04 tff(1613,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1614,plain,
% 0.88/1.04 (~r(s(s(s(s(z)))), s(z))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1613, 1543, 80])).
% 0.88/1.04 tff(1615,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 0.88/1.04 tff(1616,plain,
% 0.88/1.04 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1615])).
% 0.88/1.04 tff(1617,plain,
% 0.88/1.04 (s(s(s(z))) = z),
% 0.88/1.04 inference(transitivity,[status(thm)],[716, 1616, 26])).
% 0.88/1.04 tff(1618,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1469, 1617])).
% 0.88/1.04 tff(1619,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1620,plain,
% 0.88/1.04 (((~![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)))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1621,plain,
% 0.88/1.04 ((~![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)))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1622,plain,
% 0.88/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 0.88/1.04 tff(1623,plain,
% 0.88/1.04 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1622, 51])).
% 0.88/1.04 tff(1624,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1623, 1619])).
% 0.88/1.04 tff(1625,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(z))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1624, 1614])).
% 0.88/1.04 tff(1626,plain,
% 0.88/1.04 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1435])).
% 0.88/1.04 tff(1627,plain,
% 0.88/1.04 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1626, 375])).
% 0.88/1.04 tff(1628,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.88/1.04 inference(symmetry,[status(thm)],[1627])).
% 0.88/1.04 tff(1629,plain,
% 0.88/1.04 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1628])).
% 0.88/1.04 tff(1630,plain,
% 0.88/1.04 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[1557, 1629])).
% 0.88/1.04 tff(1631,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[491, 1630])).
% 0.88/1.04 tff(1632,plain,(b(s(s(s(s(z)))), s(s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1633,plain,
% 0.88/1.04 (b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1632, 1402, 491])).
% 0.88/1.04 tff(1634,plain,
% 0.88/1.04 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1404])).
% 0.88/1.04 tff(1635,plain,
% 0.88/1.04 (r(s(z), s(s(s(s(z)))))),
% 0.88/1.04 inference(modus_ponens,[status(thm)],[161, 1634])).
% 0.88/1.04 tff(1636,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.04 tff(1637,plain,
% 0.88/1.04 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1636])).
% 0.88/1.04 tff(1638,plain,
% 0.88/1.04 (s(z) = s(s(s(s(z))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[69, 1637, 722])).
% 0.88/1.04 tff(1639,plain,
% 0.88/1.04 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1638])).
% 0.88/1.04 tff(1640,plain,
% 0.88/1.04 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.88/1.04 inference(symmetry,[status(thm)],[1639])).
% 0.88/1.04 tff(1641,plain,
% 0.88/1.04 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1636])).
% 0.88/1.04 tff(1642,plain,
% 0.88/1.04 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 0.88/1.04 inference(symmetry,[status(thm)],[1641])).
% 0.88/1.04 tff(1643,plain,
% 0.88/1.04 (s(s(s(s(s(s(z)))))) = z),
% 0.88/1.04 inference(transitivity,[status(thm)],[1642, 716, 1640, 26])).
% 0.88/1.04 tff(1644,plain,
% 0.88/1.04 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1645,plain,
% 0.88/1.04 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1644, 37])).
% 0.88/1.04 tff(1646,plain,
% 0.88/1.04 ($false),
% 0.88/1.04 inference(unit_resolution,[status(thm)],[1645, 1643])).
% 0.88/1.04 tff(1647,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.04 tff(1648,plain,
% 0.88/1.04 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1626])).
% 0.88/1.04 tff(1649,plain,
% 0.88/1.04 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1648, 1626])).
% 0.88/1.04 tff(1650,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.04 tff(1651,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.04 tff(1652,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.04 tff(1653,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1654,plain,
% 0.88/1.04 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.88/1.04 inference(rewrite,[status(thm)],[])).
% 0.88/1.04 tff(1655,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.88/1.04 inference(monotonicity,[status(thm)],[1654])).
% 0.88/1.04 tff(1656,plain,
% 0.88/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.88/1.04 inference(transitivity,[status(thm)],[1655, 1653])).
% 0.88/1.04 tff(1657,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.04 inference(quant_inst,[status(thm)],[])).
% 0.88/1.04 tff(1658,plain,
% 0.88/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 0.88/1.05 tff(1659,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1658, 124, 1651, 1652, 1650])).
% 0.88/1.05 tff(1660,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1661,plain,
% 0.88/1.05 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1660, 1651, 1650])).
% 0.88/1.05 tff(1662,plain,
% 0.88/1.05 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.88/1.05 inference(symmetry,[status(thm)],[1626])).
% 0.88/1.05 tff(1663,plain,
% 0.88/1.05 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 0.88/1.05 inference(symmetry,[status(thm)],[1648])).
% 0.88/1.05 tff(1664,plain,
% 0.88/1.05 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1663, 1662])).
% 0.88/1.05 tff(1665,plain,
% 0.88/1.05 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.05 inference(symmetry,[status(thm)],[1664])).
% 0.88/1.05 tff(1666,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 0.88/1.05 tff(1667,plain,
% 0.88/1.05 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.88/1.05 tff(1668,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.05 tff(1669,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1668, 1667])).
% 0.88/1.05 tff(1670,plain,(r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1671,plain,
% 0.88/1.05 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1670, 1661, 375])).
% 0.88/1.05 tff(1672,plain,
% 0.88/1.05 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[921, 1671, 777])).
% 0.88/1.05 tff(1673,plain,
% 0.88/1.05 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1672, 1649])).
% 0.88/1.05 tff(1674,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1675,plain,
% 0.88/1.05 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1676,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1675])).
% 0.88/1.05 tff(1677,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1676, 1674])).
% 0.88/1.05 tff(1678,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1679,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 0.88/1.05 tff(1680,plain,
% 0.88/1.05 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1679, 238, 1587, 1501, 1673])).
% 0.88/1.05 tff(1681,assumption,(~(s(s(z)) = s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1682,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1683,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1684,plain,
% 0.88/1.05 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1685,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1684])).
% 0.88/1.05 tff(1686,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1685, 1683])).
% 0.88/1.05 tff(1687,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1688,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 0.88/1.05 tff(1689,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1688, 124, 169, 1651, 1682])).
% 0.88/1.05 tff(1690,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1691,plain,
% 0.88/1.05 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1690, 1651, 169])).
% 0.88/1.05 tff(1692,plain,
% 0.88/1.05 (((~![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)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1693,plain,
% 0.88/1.05 ((~![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)))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1694,plain,
% 0.88/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 0.88/1.05 tff(1695,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1694, 51, 1691, 1681, 1680])).
% 0.88/1.05 tff(1696,plain,((~r(s(z), s(s(s(s(s(z))))))) | (s(s(z)) = s(s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1697,plain,
% 0.88/1.05 ((~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1696, 1647])).
% 0.88/1.05 tff(1698,plain,
% 0.88/1.05 (~r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1697, 1635, 80, 1402, 1633, 1433, 777])).
% 0.88/1.05 tff(1699,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1700,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.05 tff(1701,plain,
% 0.88/1.05 (s(s(s(s(s(z))))) = s(z)),
% 0.88/1.05 inference(symmetry,[status(thm)],[1700])).
% 0.88/1.05 tff(1702,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[728, 1701])).
% 0.88/1.05 tff(1703,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1704,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1705,plain,
% 0.88/1.05 (((~![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)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1706,plain,
% 0.88/1.05 ((~![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)))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1707,plain,
% 0.88/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.88/1.05 tff(1708,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1707, 51, 1704, 1703, 1699])).
% 0.88/1.05 tff(1709,plain,(b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1710,plain,
% 0.88/1.05 (b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1709, 1698])).
% 0.88/1.05 tff(1711,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.88/1.05 tff(1712,plain,
% 0.88/1.05 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 0.88/1.05 inference(commutativity,[status(thm)],[])).
% 0.88/1.05 tff(1713,plain,
% 0.88/1.05 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 0.88/1.05 inference(symmetry,[status(thm)],[1712])).
% 0.88/1.05 tff(1714,plain,
% 0.88/1.05 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1713])).
% 0.88/1.05 tff(1715,plain,
% 0.88/1.05 (~(z = s(s(s(s(s(z))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1006, 1714])).
% 0.88/1.05 tff(1716,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1717,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 0.88/1.05 tff(1718,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1719,plain,
% 0.88/1.05 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1720,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1719])).
% 0.88/1.05 tff(1721,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1720, 1718])).
% 0.88/1.05 tff(1722,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1723,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.88/1.05 tff(1724,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1723, 124, 169, 1717, 1711])).
% 0.88/1.05 tff(1725,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1726,plain,
% 0.88/1.05 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1725, 1711, 169])).
% 0.88/1.05 tff(1727,plain,
% 0.88/1.05 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 0.88/1.05 inference(commutativity,[status(thm)],[])).
% 0.88/1.05 tff(1728,plain,
% 0.88/1.05 ((~(s(s(z)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(z))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1727])).
% 0.88/1.05 tff(1729,plain,
% 0.88/1.05 (~(s(s(s(s(s(z))))) = s(s(z)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1647, 1728])).
% 0.88/1.05 tff(1730,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 0.88/1.05 tff(1731,assumption,(~(s(s(s(s(s(z))))) = s(s(z)))), introduced(assumption)).
% 0.88/1.05 tff(1732,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 0.88/1.05 tff(1733,plain,
% 0.88/1.05 (((~![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))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1734,plain,
% 0.88/1.05 ((~![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))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1735,plain,
% 0.88/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 0.88/1.05 tff(1736,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1735, 51, 1732, 1731, 1730])).
% 0.88/1.05 tff(1737,plain,(b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))) | (s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1738,plain,
% 0.88/1.05 (b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1737, 1729])).
% 0.88/1.05 tff(1739,plain,
% 0.88/1.05 (b(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1738, 1726])).
% 0.88/1.05 tff(1740,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1741,plain,
% 0.88/1.05 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(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))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1742,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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)))))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1741])).
% 0.88/1.05 tff(1743,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1742, 1740])).
% 0.88/1.05 tff(1744,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1745,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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)))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 0.88/1.05 tff(1746,plain,
% 0.88/1.05 (~b(z, s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1745, 238, 1739, 1586, 1716])).
% 0.88/1.05 tff(1747,plain,
% 0.88/1.05 (((~![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)))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1748,plain,
% 0.88/1.05 ((~![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)))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1749,plain,
% 0.88/1.05 ((~![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))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 0.88/1.05 tff(1750,plain,
% 0.88/1.05 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1749, 51, 1746])).
% 0.88/1.05 tff(1751,plain,
% 0.88/1.05 (r(z, s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1750, 1715])).
% 0.88/1.05 tff(1752,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1753,plain,
% 0.88/1.05 (((~r(s(s(s(s(s(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(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1754,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1753])).
% 0.88/1.05 tff(1755,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1754, 1752])).
% 0.88/1.05 tff(1756,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1757,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 0.88/1.05 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 0.88/1.05 tff(1758,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1757, 124, 1711, 1545, 1751])).
% 0.88/1.05 tff(1759,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1760,plain,
% 0.88/1.05 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1759, 1711, 169, 1545])).
% 0.88/1.05 tff(1761,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1762,assumption,(~r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.05 tff(1763,plain,
% 0.88/1.05 ($false),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1694, 51, 1762, 1647, 1761])).
% 0.88/1.05 tff(1764,plain,(b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.05 tff(1765,plain,
% 0.88/1.05 (r(s(s(z)), s(s(s(s(s(z))))))),
% 0.88/1.05 inference(unit_resolution,[status(thm)],[1764, 1760])).
% 0.88/1.05 tff(1766,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1767,plain,
% 0.88/1.05 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(rewrite,[status(thm)],[])).
% 0.88/1.05 tff(1768,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 0.88/1.05 inference(monotonicity,[status(thm)],[1767])).
% 0.88/1.05 tff(1769,plain,
% 0.88/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(transitivity,[status(thm)],[1768, 1766])).
% 0.88/1.05 tff(1770,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 0.88/1.05 inference(quant_inst,[status(thm)],[])).
% 0.88/1.05 tff(1771,plain,
% 0.88/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 0.88/1.06 tff(1772,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1771, 124, 169, 1765, 1711])).
% 0.88/1.06 tff(1773,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1774,plain,
% 0.88/1.06 (~r(s(s(s(s(s(z))))), s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1773, 1543, 80])).
% 0.88/1.06 tff(1775,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1776,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1777,plain,
% 0.88/1.06 (((~![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)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1778,plain,
% 0.88/1.06 ((~![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)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1779,plain,
% 0.88/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.88/1.06 tff(1780,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1779, 51, 1776, 728, 1775])).
% 0.88/1.06 tff(1781,plain,(b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1782,plain,
% 0.88/1.06 (b(s(s(s(s(s(z))))), s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1781, 1774])).
% 0.88/1.06 tff(1783,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1784,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1785,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.88/1.06 tff(1786,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.06 tff(1787,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1788,plain,
% 0.88/1.06 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1789,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1788])).
% 0.88/1.06 tff(1790,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1789, 1787])).
% 0.88/1.06 tff(1791,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1792,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.88/1.06 tff(1793,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1792, 238, 1786, 1785, 1784, 1783])).
% 0.88/1.06 tff(1794,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1795,plain,
% 0.88/1.06 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1794, 1782, 1710, 1625])).
% 0.88/1.06 tff(1796,plain,
% 0.88/1.06 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1795, 1407])).
% 0.88/1.06 tff(1797,plain,
% 0.88/1.06 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1358])).
% 0.88/1.06 tff(1798,plain,
% 0.88/1.06 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 0.88/1.06 inference(symmetry,[status(thm)],[1797])).
% 0.88/1.06 tff(1799,plain,
% 0.88/1.06 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1798])).
% 0.88/1.06 tff(1800,plain,
% 0.88/1.06 (~b(s(z), elem!1)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[839, 1799])).
% 0.88/1.06 tff(1801,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[427, 1800])).
% 0.88/1.06 tff(1802,plain,((~(elem!1 = s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1803,plain,
% 0.88/1.06 (~b(s(z), elem!1)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1802, 1401])).
% 0.88/1.06 tff(1804,plain,
% 0.88/1.06 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1402])).
% 0.88/1.06 tff(1805,plain,
% 0.88/1.06 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 0.88/1.06 inference(symmetry,[status(thm)],[1804])).
% 0.88/1.06 tff(1806,plain,
% 0.88/1.06 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), s(z)))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1805])).
% 0.88/1.06 tff(1807,plain,
% 0.88/1.06 (~b(s(elem!1), s(z))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[64, 1806])).
% 0.88/1.06 tff(1808,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1809,assumption,(~r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.88/1.06 tff(1810,plain,
% 0.88/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1811,plain,
% 0.88/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1812,plain,
% 0.88/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 0.88/1.06 tff(1813,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1812, 51, 1081, 1809, 1380])).
% 0.88/1.06 tff(1814,plain,(b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1815,plain,
% 0.88/1.06 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1814, 1380, 1081])).
% 0.88/1.06 tff(1816,plain,
% 0.88/1.06 (r(s(elem!1), s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[473, 358, 1808])).
% 0.88/1.06 tff(1817,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.88/1.06 tff(1818,assumption,(r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.88/1.06 tff(1819,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1820,plain,
% 0.88/1.06 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1821,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1820])).
% 0.88/1.06 tff(1822,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1821, 1819])).
% 0.88/1.06 tff(1823,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1824,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1823, 1822])).
% 0.88/1.06 tff(1825,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1824, 124, 1711, 161, 1818])).
% 0.88/1.06 tff(1826,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1827,plain,
% 0.88/1.06 (~r(s(s(s(s(s(z))))), s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1826, 161, 1818])).
% 0.88/1.06 tff(1828,plain,
% 0.88/1.06 (b(s(s(s(s(s(z))))), s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1781, 1827])).
% 0.88/1.06 tff(1829,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1830,plain,
% 0.88/1.06 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1831,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1830])).
% 0.88/1.06 tff(1832,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1831, 1829])).
% 0.88/1.06 tff(1833,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1834,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 0.88/1.06 tff(1835,plain,
% 0.88/1.06 (~r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1834, 124, 161, 1818])).
% 0.88/1.06 tff(1836,plain,
% 0.88/1.06 (b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1709, 1835])).
% 0.88/1.06 tff(1837,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1838,plain,
% 0.88/1.06 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1839,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1838])).
% 0.88/1.06 tff(1840,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1839, 1837])).
% 0.88/1.06 tff(1841,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1842,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1841, 1840])).
% 0.88/1.06 tff(1843,plain,
% 0.88/1.06 (~b(s(s(s(s(s(z))))), z)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1842, 238, 1457, 1785, 1783])).
% 0.88/1.06 tff(1844,plain,
% 0.88/1.06 (((~![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))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1845,plain,
% 0.88/1.06 ((~![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))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1846,plain,
% 0.88/1.06 ((~![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)),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 0.88/1.06 tff(1847,plain,
% 0.88/1.06 (r(s(s(s(s(s(z))))), z)),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 1843])).
% 0.88/1.06 tff(1848,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1849,plain,
% 0.88/1.06 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1850,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1849])).
% 0.88/1.06 tff(1851,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1850, 1848])).
% 0.88/1.06 tff(1852,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1853,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.88/1.06 tff(1854,plain,
% 0.88/1.06 (~b(z, s(s(z)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1853, 238, 1817, 1457, 1785])).
% 0.88/1.06 tff(1855,plain,
% 0.88/1.06 ((z = s(s(z))) | r(z, s(s(z)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1511, 51, 1854])).
% 0.88/1.06 tff(1856,plain,
% 0.88/1.06 (r(z, s(s(z)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1855, 1450])).
% 0.88/1.06 tff(1857,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1858,plain,
% 0.88/1.06 (((~b(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(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(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1859,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1858])).
% 0.88/1.06 tff(1860,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1859, 1857])).
% 0.88/1.06 tff(1861,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1862,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 0.88/1.06 tff(1863,plain,
% 0.88/1.06 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1862, 238, 1817, 1785, 1783])).
% 0.88/1.06 tff(1864,plain,
% 0.88/1.06 (r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1738, 1863])).
% 0.88/1.06 tff(1865,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1866,plain,
% 0.88/1.06 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(rewrite,[status(thm)],[])).
% 0.88/1.06 tff(1867,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))))),
% 0.88/1.06 inference(monotonicity,[status(thm)],[1866])).
% 0.88/1.06 tff(1868,plain,
% 0.88/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(transitivity,[status(thm)],[1867, 1865])).
% 0.88/1.06 tff(1869,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.06 inference(quant_inst,[status(thm)],[])).
% 0.88/1.06 tff(1870,plain,
% 0.88/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z))),
% 0.88/1.06 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.88/1.06 tff(1871,plain,
% 0.88/1.06 ($false),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1870, 124, 1864, 1856, 1847])).
% 0.88/1.06 tff(1872,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.06 tff(1873,plain,
% 0.88/1.06 (~b(z, s(z))),
% 0.88/1.06 inference(unit_resolution,[status(thm)],[1872, 1836, 1828, 1817])).
% 0.88/1.06 tff(1874,plain,
% 0.88/1.07 (r(z, s(z))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1542, 1873])).
% 0.88/1.07 tff(1875,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1876,plain,
% 0.88/1.07 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1877,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1876])).
% 0.88/1.07 tff(1878,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1877, 1875])).
% 0.88/1.07 tff(1879,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1880,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1879, 1878])).
% 0.88/1.07 tff(1881,plain,
% 0.88/1.07 (~r(s(elem!1), z)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1880, 124, 306, 1874])).
% 0.88/1.07 tff(1882,plain,
% 0.88/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1883,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1884,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 0.88/1.07 tff(1885,plain,
% 0.88/1.07 (b(s(elem!1), z)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1884, 51, 39, 1881])).
% 0.88/1.07 tff(1886,plain,
% 0.88/1.07 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1794, 1784, 1785, 1783])).
% 0.88/1.07 tff(1887,plain,
% 0.88/1.07 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1013])).
% 0.88/1.07 tff(1888,plain,
% 0.88/1.07 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1887, 1013])).
% 0.88/1.07 tff(1889,plain,
% 0.88/1.07 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1890,plain,
% 0.88/1.07 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1889, 10])).
% 0.88/1.07 tff(1891,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 0.88/1.07 tff(1892,plain,
% 0.88/1.07 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1891])).
% 0.88/1.07 tff(1893,plain,
% 0.88/1.07 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.88/1.07 inference(symmetry,[status(thm)],[1892])).
% 0.88/1.07 tff(1894,plain,
% 0.88/1.07 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 0.88/1.07 inference(transitivity,[status(thm)],[716, 1893, 1890])).
% 0.88/1.07 tff(1895,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1092, 1894])).
% 0.88/1.07 tff(1896,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1897,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1896, 1888])).
% 0.88/1.07 tff(1898,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1899,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.88/1.07 tff(1900,plain,
% 0.88/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1901,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1902,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 0.88/1.07 tff(1903,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1902, 51, 1668, 1899, 1898])).
% 0.88/1.07 tff(1904,plain,(r(s(s(s(s(s(z))))), s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1905,plain,
% 0.88/1.07 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1904, 1886])).
% 0.88/1.07 tff(1906,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 0.88/1.07 tff(1907,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1862, 238, 1817, 1906, 1785, 1783])).
% 0.88/1.07 tff(1908,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1909,plain,
% 0.88/1.07 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1908, 1817, 1785, 1783])).
% 0.88/1.07 tff(1910,plain,
% 0.88/1.07 (r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1738, 1909])).
% 0.88/1.07 tff(1911,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1912,plain,
% 0.88/1.07 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1913,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1912])).
% 0.88/1.07 tff(1914,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1913, 1911])).
% 0.88/1.07 tff(1915,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1916,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 0.88/1.07 tff(1917,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1916, 238, 1817, 1587, 1785, 1784])).
% 0.88/1.07 tff(1918,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1919,plain,
% 0.88/1.07 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1918, 1817, 1784, 1785])).
% 0.88/1.07 tff(1920,plain,
% 0.88/1.07 (r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1564, 1919])).
% 0.88/1.07 tff(1921,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1922,plain,
% 0.88/1.07 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1923,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1922])).
% 0.88/1.07 tff(1924,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1923, 1921])).
% 0.88/1.07 tff(1925,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1926,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 0.88/1.07 tff(1927,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1926, 124, 1546, 1717, 1652])).
% 0.88/1.07 tff(1928,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1929,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1928, 1920, 1910, 1905])).
% 0.88/1.07 tff(1930,plain,((~b(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(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1931,plain,
% 0.88/1.07 (~b(s(s(s(s(z)))), s(z))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1930, 1836, 1828, 1817])).
% 0.88/1.07 tff(1932,plain,
% 0.88/1.07 (r(s(s(s(s(z)))), s(z))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1623, 1931, 1619])).
% 0.88/1.07 tff(1933,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1934,plain,
% 0.88/1.07 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1935,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1934])).
% 0.88/1.07 tff(1936,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1935, 1933])).
% 0.88/1.07 tff(1937,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1938,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 0.88/1.07 tff(1939,plain,
% 0.88/1.07 (~r(s(s(s(s(z)))), z)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1938, 124, 1932, 1874])).
% 0.88/1.07 tff(1940,plain,
% 0.88/1.07 (b(s(s(s(s(z)))), z)),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1499, 51, 726, 1939])).
% 0.88/1.07 tff(1941,plain,
% 0.88/1.07 (~r(z, s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1571, 124, 1932, 1874])).
% 0.88/1.07 tff(1942,plain,
% 0.88/1.07 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1487, 51, 1941])).
% 0.88/1.07 tff(1943,plain,
% 0.88/1.07 (b(z, s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1942, 1454])).
% 0.88/1.07 tff(1944,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1945,plain,
% 0.88/1.07 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1946,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1945])).
% 0.88/1.07 tff(1947,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1946, 1944])).
% 0.88/1.07 tff(1948,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1949,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 0.88/1.07 tff(1950,plain,
% 0.88/1.07 (~b(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1949, 238, 1943, 1940, 1885])).
% 0.88/1.07 tff(1951,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1952,plain,
% 0.88/1.07 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1953,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1952])).
% 0.88/1.07 tff(1954,plain,
% 0.88/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.88/1.07 inference(transitivity,[status(thm)],[1953, 1951])).
% 0.88/1.07 tff(1955,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1956,plain,
% 0.88/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1955, 1954])).
% 0.88/1.07 tff(1957,plain,
% 0.88/1.07 (~r(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1956, 124, 306, 1932])).
% 0.88/1.07 tff(1958,plain,
% 0.88/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 0.88/1.07 inference(rewrite,[status(thm)],[])).
% 0.88/1.07 tff(1959,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 0.88/1.07 inference(quant_inst,[status(thm)],[])).
% 0.88/1.07 tff(1960,plain,
% 0.88/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 0.88/1.07 tff(1961,plain,
% 0.88/1.07 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1960, 51, 1957])).
% 0.88/1.07 tff(1962,plain,
% 0.88/1.07 (s(elem!1) = s(s(s(s(z))))),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[1961, 1950])).
% 0.88/1.07 tff(1963,plain,
% 0.88/1.07 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1962])).
% 0.88/1.07 tff(1964,plain,
% 0.88/1.07 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.07 inference(monotonicity,[status(thm)],[1963])).
% 0.88/1.07 tff(1965,plain,
% 0.88/1.07 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(elem!1)))),
% 0.88/1.07 inference(symmetry,[status(thm)],[1964])).
% 0.88/1.07 tff(1966,plain,
% 0.88/1.07 (b(s(z), s(s(elem!1)))),
% 0.88/1.07 inference(modus_ponens,[status(thm)],[1836, 1965])).
% 0.88/1.07 tff(1967,plain,
% 0.88/1.07 ($false),
% 0.88/1.07 inference(unit_resolution,[status(thm)],[2, 1966])).
% 0.88/1.07 tff(1968,plain,((~b(s(s(z)), s(z))) | b(s(z), s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.07 tff(1969,plain,
% 0.88/1.08 (~b(s(s(z)), s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1968, 161, 306, 2, 1815])).
% 0.88/1.08 tff(1970,plain,
% 0.88/1.08 (r(s(s(z)), s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[79, 1969])).
% 0.88/1.08 tff(1971,plain,
% 0.88/1.08 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 0.88/1.08 inference(commutativity,[status(thm)],[])).
% 0.88/1.08 tff(1972,plain,
% 0.88/1.08 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 0.88/1.08 inference(symmetry,[status(thm)],[1971])).
% 0.88/1.08 tff(1973,plain,
% 0.88/1.08 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(z))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1972])).
% 0.88/1.08 tff(1974,plain,
% 0.88/1.08 (~(elem!1 = s(s(z)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[1386, 1973])).
% 0.88/1.08 tff(1975,plain,
% 0.88/1.08 (~r(s(s(s(s(s(z))))), s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1826, 161, 1815])).
% 0.88/1.08 tff(1976,plain,
% 0.88/1.08 (b(s(s(s(s(s(z))))), s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1781, 1975])).
% 0.88/1.08 tff(1977,plain,
% 0.88/1.08 (s(elem!1) = s(s(elem!1))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[386, 381])).
% 0.88/1.08 tff(1978,plain,
% 0.88/1.08 (elem!1 = s(s(elem!1))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[158, 1977])).
% 0.88/1.08 tff(1979,plain,
% 0.88/1.08 (s(s(elem!1)) = elem!1),
% 0.88/1.08 inference(symmetry,[status(thm)],[1978])).
% 0.88/1.08 tff(1980,plain,
% 0.88/1.08 (s(s(elem!1)) = s(elem!1)),
% 0.88/1.08 inference(transitivity,[status(thm)],[1979, 381])).
% 0.88/1.08 tff(1981,plain,
% 0.88/1.08 (b(s(z), s(s(elem!1))) <=> b(s(z), s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.08 tff(1982,plain,
% 0.88/1.08 (b(s(z), s(elem!1)) <=> b(s(z), s(s(elem!1)))),
% 0.88/1.08 inference(symmetry,[status(thm)],[1981])).
% 0.88/1.08 tff(1983,plain,
% 0.88/1.08 ((~b(s(z), s(elem!1))) <=> (~b(s(z), s(s(elem!1))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1982])).
% 0.88/1.08 tff(1984,plain,
% 0.88/1.08 (b(s(z), elem!1) <=> b(s(z), s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[381])).
% 0.88/1.08 tff(1985,plain,
% 0.88/1.08 ((~b(s(z), elem!1)) <=> (~b(s(z), s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1984])).
% 0.88/1.08 tff(1986,plain,
% 0.88/1.08 (~b(s(z), s(elem!1))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[345, 1985])).
% 0.88/1.08 tff(1987,plain,
% 0.88/1.08 (~b(s(z), s(s(elem!1)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[1986, 1983])).
% 0.88/1.08 tff(1988,plain,
% 0.88/1.08 (r(s(z), s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[56, 1987])).
% 0.88/1.08 tff(1989,plain,
% 0.88/1.08 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.08 tff(1990,plain,
% 0.88/1.08 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.88/1.08 inference(symmetry,[status(thm)],[1989])).
% 0.88/1.08 tff(1991,plain,
% 0.88/1.08 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.08 tff(1992,plain,
% 0.88/1.08 (s(s(elem!1)) = s(s(s(elem!1)))),
% 0.88/1.08 inference(symmetry,[status(thm)],[1991])).
% 0.88/1.08 tff(1993,plain,
% 0.88/1.08 (s(elem!1) = s(s(s(elem!1)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[382, 1978, 1992])).
% 0.88/1.08 tff(1994,plain,
% 0.88/1.08 ((elem!1 = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[381])).
% 0.88/1.08 tff(1995,plain,
% 0.88/1.08 ((~(elem!1 = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1994])).
% 0.88/1.08 tff(1996,plain,
% 0.88/1.08 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[514, 1995])).
% 0.88/1.08 tff(1997,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1996, 1993])).
% 0.88/1.08 tff(1998,plain,((~(elem!1 = s(elem!1))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(1999,plain,
% 0.88/1.08 (elem!1 = s(s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1998, 381])).
% 0.88/1.08 tff(2000,plain,
% 0.88/1.08 (s(s(s(elem!1))) = elem!1),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[501, 641])).
% 0.88/1.08 tff(2001,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[823, 2000])).
% 0.88/1.08 tff(2002,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2003,plain,
% 0.88/1.08 (s(s(s(elem!1))) = elem!1),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2002, 1999])).
% 0.88/1.08 tff(2004,plain,
% 0.88/1.08 (s(s(s(elem!1))) = s(elem!1)),
% 0.88/1.08 inference(transitivity,[status(thm)],[2003, 381])).
% 0.88/1.08 tff(2005,plain,
% 0.88/1.08 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2004])).
% 0.88/1.08 tff(2006,plain,
% 0.88/1.08 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2005, 1990])).
% 0.88/1.08 tff(2007,plain,
% 0.88/1.08 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[1818, 2006])).
% 0.88/1.08 tff(2008,assumption,(r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 0.88/1.08 tff(2009,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2010,plain,
% 0.88/1.08 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2011,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2010])).
% 0.88/1.08 tff(2012,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2011, 2009])).
% 0.88/1.08 tff(2013,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2014,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 0.88/1.08 tff(2015,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2014, 124, 160, 1651, 2008])).
% 0.88/1.08 tff(2016,plain,((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2017,plain,
% 0.88/1.08 (~r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2016, 2007, 1988])).
% 0.88/1.08 tff(2018,plain,
% 0.88/1.08 (b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1709, 2017])).
% 0.88/1.08 tff(2019,plain,
% 0.88/1.08 (r(s(s(elem!1)), s(z)) <=> r(s(elem!1), s(z))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.08 tff(2020,plain,
% 0.88/1.08 (r(s(elem!1), s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2019])).
% 0.88/1.08 tff(2021,plain,
% 0.88/1.08 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[381])).
% 0.88/1.08 tff(2022,plain,
% 0.88/1.08 (~(elem!1 = s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1364, 1999])).
% 0.88/1.08 tff(2023,plain,
% 0.88/1.08 (r(elem!1, s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[363, 2022, 1400])).
% 0.88/1.08 tff(2024,plain,
% 0.88/1.08 (r(s(elem!1), s(z))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2023, 2021])).
% 0.88/1.08 tff(2025,plain,
% 0.88/1.08 (r(s(s(elem!1)), s(z))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2024, 2020])).
% 0.88/1.08 tff(2026,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 0.88/1.08 tff(2027,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2028,plain,
% 0.88/1.08 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2029,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z)))))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2028])).
% 0.88/1.08 tff(2030,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2029, 2027])).
% 0.88/1.08 tff(2031,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2032,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(z)))))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 0.88/1.08 tff(2033,plain,
% 0.88/1.08 (~r(z, s(s(s(s(s(z))))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2032, 124, 2026, 2008])).
% 0.88/1.08 tff(2034,plain,
% 0.88/1.08 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1749, 51, 2033])).
% 0.88/1.08 tff(2035,plain,
% 0.88/1.08 (b(z, s(s(s(s(s(z))))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2034, 1715])).
% 0.88/1.08 tff(2036,plain,
% 0.88/1.08 ((z = s(z)) <=> (s(z) = z)),
% 0.88/1.08 inference(commutativity,[status(thm)],[])).
% 0.88/1.08 tff(2037,plain,
% 0.88/1.08 ((s(z) = z) <=> (z = s(z))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2036])).
% 0.88/1.08 tff(2038,plain,
% 0.88/1.08 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2037])).
% 0.88/1.08 tff(2039,plain,
% 0.88/1.08 (~(z = s(z))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[72, 2038])).
% 0.88/1.08 tff(2040,assumption,(~r(z, s(z))), introduced(assumption)).
% 0.88/1.08 tff(2041,plain,
% 0.88/1.08 ((z = s(z)) | b(z, s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1541, 51, 2040])).
% 0.88/1.08 tff(2042,plain,
% 0.88/1.08 (b(z, s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2041, 2039])).
% 0.88/1.08 tff(2043,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2044,plain,
% 0.88/1.08 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(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(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2045,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2044])).
% 0.88/1.08 tff(2046,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2045, 2043])).
% 0.88/1.08 tff(2047,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2048,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 0.88/1.08 tff(2049,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2048, 238, 2042, 2035, 1785, 1783])).
% 0.88/1.08 tff(2050,plain,(r(z, s(z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2051,plain,
% 0.88/1.08 (r(z, s(z))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2050, 2026, 1783, 1785, 2008])).
% 0.88/1.08 tff(2052,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2053,plain,
% 0.88/1.08 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2054,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2053])).
% 0.88/1.08 tff(2055,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2054, 2052])).
% 0.88/1.08 tff(2056,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2057,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 0.88/1.08 tff(2058,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2057, 124, 162, 2026, 2051])).
% 0.88/1.08 tff(2059,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2060,plain,
% 0.88/1.08 (~r(z, s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2059, 2018, 2025, 1783, 2007])).
% 0.88/1.08 tff(2061,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 0.88/1.08 tff(2062,plain,
% 0.88/1.08 (s(s(elem!1)) = z),
% 0.88/1.08 inference(symmetry,[status(thm)],[2061])).
% 0.88/1.08 tff(2063,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[92, 2062])).
% 0.88/1.08 tff(2064,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2065,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 0.88/1.08 tff(2066,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 0.88/1.08 tff(2067,plain,
% 0.88/1.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2068,plain,
% 0.88/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2069,plain,
% 0.88/1.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 0.88/1.08 tff(2070,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2069, 51, 2066, 2065, 2064])).
% 0.88/1.08 tff(2071,plain,(b(z, s(s(elem!1))) | r(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2072,plain,
% 0.88/1.08 (b(z, s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2071, 2060])).
% 0.88/1.08 tff(2073,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 0.88/1.08 tff(2074,plain,
% 0.88/1.08 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2073])).
% 0.88/1.08 tff(2075,plain,
% 0.88/1.08 ((~b(z, elem!1)) <=> (~b(z, s(s(elem!1))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2074])).
% 0.88/1.08 tff(2076,assumption,(~b(z, elem!1)), introduced(assumption)).
% 0.88/1.08 tff(2077,plain,
% 0.88/1.08 (~b(z, s(s(elem!1)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 0.88/1.08 tff(2078,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 0.88/1.08 tff(2079,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2078, 2077])).
% 0.88/1.08 tff(2080,plain,(b(z, elem!1) | (~b(z, s(s(elem!1)))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2081,plain,
% 0.88/1.08 (b(z, elem!1)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2080, 2072, 1978])).
% 0.88/1.08 tff(2082,plain,
% 0.88/1.08 (b(z, s(elem!1)) <=> b(z, elem!1)),
% 0.88/1.08 inference(monotonicity,[status(thm)],[382])).
% 0.88/1.08 tff(2083,plain,
% 0.88/1.08 (b(z, elem!1) <=> b(z, s(elem!1))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2082])).
% 0.88/1.08 tff(2084,assumption,(b(z, elem!1)), introduced(assumption)).
% 0.88/1.08 tff(2085,plain,
% 0.88/1.08 (b(z, s(elem!1))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 0.88/1.08 tff(2086,plain,
% 0.88/1.08 (b(s(elem!1), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[382])).
% 0.88/1.08 tff(2087,plain,
% 0.88/1.08 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2086])).
% 0.88/1.08 tff(2088,plain,
% 0.88/1.08 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[767])).
% 0.88/1.08 tff(2089,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 0.88/1.08 tff(2090,plain,
% 0.88/1.08 (s(s(s(s(z)))) = s(elem!1)),
% 0.88/1.08 inference(transitivity,[status(thm)],[2089, 381])).
% 0.88/1.08 tff(2091,plain,
% 0.88/1.08 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2090])).
% 0.88/1.08 tff(2092,plain,
% 0.88/1.08 (s(s(s(s(s(z))))) = s(elem!1)),
% 0.88/1.08 inference(transitivity,[status(thm)],[2091, 1979, 381])).
% 0.88/1.08 tff(2093,plain,
% 0.88/1.08 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.08 tff(2094,plain,
% 0.88/1.08 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2093])).
% 0.88/1.08 tff(2095,plain,
% 0.88/1.08 (s(elem!1) = s(s(s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2073])).
% 0.88/1.08 tff(2096,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[418, 2095])).
% 0.88/1.08 tff(2097,plain,((~(elem!1 = s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2098,plain,
% 0.88/1.08 (s(elem!1) = s(s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2097, 1978])).
% 0.88/1.08 tff(2099,assumption,(s(s(s(s(s(z))))) = s(s(elem!1))), introduced(assumption)).
% 0.88/1.08 tff(2100,plain,
% 0.88/1.08 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2099])).
% 0.88/1.08 tff(2101,plain,
% 0.88/1.08 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(z))))))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2100])).
% 0.88/1.08 tff(2102,plain,
% 0.88/1.08 (s(s(s(elem!1))) = s(elem!1)),
% 0.88/1.08 inference(symmetry,[status(thm)],[410])).
% 0.88/1.08 tff(2103,plain,
% 0.88/1.08 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2099])).
% 0.88/1.08 tff(2104,plain,
% 0.88/1.08 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2103, 2102, 18, 2101, 722])).
% 0.88/1.08 tff(2105,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1896, 2104])).
% 0.88/1.08 tff(2106,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2107,plain,
% 0.88/1.08 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2106, 2098])).
% 0.88/1.08 tff(2108,plain,
% 0.88/1.08 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2107, 2094])).
% 0.88/1.08 tff(2109,plain,
% 0.88/1.08 ($false),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2108, 2092])).
% 0.88/1.08 tff(2110,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.08 tff(2111,plain,
% 0.88/1.08 (~(s(s(s(s(z)))) = elem!1)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2110, 381])).
% 0.88/1.08 tff(2112,plain,
% 0.88/1.08 (~(elem!1 = s(s(s(s(z)))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2111, 2088])).
% 0.88/1.08 tff(2113,plain,
% 0.88/1.08 (r(s(elem!1), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[382])).
% 0.88/1.08 tff(2114,plain,
% 0.88/1.08 ((~r(s(elem!1), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2113])).
% 0.88/1.08 tff(2115,plain,
% 0.88/1.08 (~r(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[1956, 124, 306, 1544])).
% 0.88/1.08 tff(2116,plain,
% 0.88/1.08 (~r(elem!1, s(s(s(s(z)))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 0.88/1.08 tff(2117,plain,
% 0.88/1.08 (b(elem!1, s(s(s(s(z)))))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[935, 2116, 2112])).
% 0.88/1.08 tff(2118,plain,
% 0.88/1.08 (b(s(elem!1), s(s(s(s(z)))))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2117, 2087])).
% 0.88/1.08 tff(2119,plain,
% 0.88/1.08 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.88/1.08 inference(monotonicity,[status(thm)],[382])).
% 0.88/1.08 tff(2120,plain,
% 0.88/1.08 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(elem!1))),
% 0.88/1.08 inference(symmetry,[status(thm)],[2119])).
% 0.88/1.08 tff(2121,plain,
% 0.88/1.08 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), elem!1)),
% 0.88/1.08 inference(monotonicity,[status(thm)],[382])).
% 0.88/1.08 tff(2122,plain,
% 0.88/1.08 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2121])).
% 0.88/1.08 tff(2123,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2124,plain,
% 0.88/1.08 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2125,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 0.88/1.08 inference(monotonicity,[status(thm)],[2124])).
% 0.88/1.08 tff(2126,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.88/1.08 inference(transitivity,[status(thm)],[2125, 2123])).
% 0.88/1.08 tff(2127,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.88/1.08 inference(quant_inst,[status(thm)],[])).
% 0.88/1.08 tff(2128,plain,
% 0.88/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2127, 2126])).
% 0.88/1.08 tff(2129,plain,
% 0.88/1.08 (~r(s(s(s(s(z)))), s(elem!1))),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2128, 124, 306, 1544])).
% 0.88/1.08 tff(2130,plain,
% 0.88/1.08 (~r(s(s(s(s(z)))), elem!1)),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2129, 2122])).
% 0.88/1.08 tff(2131,plain,
% 0.88/1.08 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[905, 51])).
% 0.88/1.08 tff(2132,plain,
% 0.88/1.08 (b(s(s(s(s(z)))), elem!1)),
% 0.88/1.08 inference(unit_resolution,[status(thm)],[2131, 2130, 2111])).
% 0.88/1.08 tff(2133,plain,
% 0.88/1.08 (b(s(s(s(s(z)))), s(elem!1))),
% 0.88/1.08 inference(modus_ponens,[status(thm)],[2132, 2120])).
% 0.88/1.08 tff(2134,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2135,plain,
% 0.88/1.08 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))))),
% 0.88/1.08 inference(rewrite,[status(thm)],[])).
% 0.88/1.08 tff(2136,plain,
% 0.88/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1)))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2135])).
% 0.88/1.09 tff(2137,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2136, 2134])).
% 0.88/1.09 tff(2138,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2139,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2138, 2137])).
% 0.88/1.09 tff(2140,plain,
% 0.88/1.09 ((~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2139, 238, 2133, 2118])).
% 0.88/1.09 tff(2141,plain,
% 0.88/1.09 (~b(s(s(s(s(z)))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2140, 2085])).
% 0.88/1.09 tff(2142,plain,
% 0.88/1.09 (r(s(s(s(s(z)))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1499, 51, 726, 2141])).
% 0.88/1.09 tff(2143,plain,
% 0.88/1.09 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(elem!1))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.09 tff(2144,plain,
% 0.88/1.09 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = s(elem!1))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[1980])).
% 0.88/1.09 tff(2145,plain,
% 0.88/1.09 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(z)))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2144, 1245])).
% 0.88/1.09 tff(2146,plain,
% 0.88/1.09 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 0.88/1.09 inference(symmetry,[status(thm)],[2145])).
% 0.88/1.09 tff(2147,plain,
% 0.88/1.09 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2146])).
% 0.88/1.09 tff(2148,plain,
% 0.88/1.09 (~(s(elem!1) = s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[379, 2022])).
% 0.88/1.09 tff(2149,plain,
% 0.88/1.09 (~(s(s(z)) = s(s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 0.88/1.09 tff(2150,plain,
% 0.88/1.09 (~r(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[200, 169, 160])).
% 0.88/1.09 tff(2151,plain,
% 0.88/1.09 (b(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[135, 2150, 2149])).
% 0.88/1.09 tff(2152,plain,
% 0.88/1.09 (b(s(s(z)), s(elem!1))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2151, 2143])).
% 0.88/1.09 tff(2153,plain,
% 0.88/1.09 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1554, 169, 1544])).
% 0.88/1.09 tff(2154,plain,
% 0.88/1.09 (b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1564, 2153])).
% 0.88/1.09 tff(2155,plain,
% 0.88/1.09 (~r(s(elem!1), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[483, 169, 306])).
% 0.88/1.09 tff(2156,plain,
% 0.88/1.09 (b(s(elem!1), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[488, 2155, 2148])).
% 0.88/1.09 tff(2157,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2158,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2159,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 0.88/1.09 tff(2160,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2159, 238, 2156, 2154, 2152, 2133])).
% 0.88/1.09 tff(2161,plain,((~r(s(s(z)), s(z))) | (~(elem!1 = s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2162,plain,
% 0.88/1.09 (~r(s(s(z)), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2161, 1544, 381, 306, 160])).
% 0.88/1.09 tff(2163,plain,
% 0.88/1.09 (b(s(s(z)), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[79, 2162])).
% 0.88/1.09 tff(2164,plain,
% 0.88/1.09 (~b(z, s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1872, 2163, 1783, 1785])).
% 0.88/1.09 tff(2165,plain,
% 0.88/1.09 (r(z, s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1542, 2164])).
% 0.88/1.09 tff(2166,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1938, 124, 1544, 2165, 2142])).
% 0.88/1.09 tff(2167,plain,((~r(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))))))) | (~(elem!1 = s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2168,plain,
% 0.88/1.09 (~r(s(s(s(s(z)))), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2167, 2018, 1783, 381, 2024, 1988, 2081])).
% 0.88/1.09 tff(2169,plain,
% 0.88/1.09 (b(s(s(s(s(z)))), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1623, 2168, 1619])).
% 0.88/1.09 tff(2170,plain,
% 0.88/1.09 (~b(s(s(z)), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1930, 2169, 2018, 1783])).
% 0.88/1.09 tff(2171,plain,
% 0.88/1.09 (r(s(s(z)), s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[79, 2170])).
% 0.88/1.09 tff(2172,plain,
% 0.88/1.09 (~r(s(elem!1), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[483, 2171, 2024])).
% 0.88/1.09 tff(2173,plain,
% 0.88/1.09 (b(s(elem!1), s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[488, 2172, 2148])).
% 0.88/1.09 tff(2174,plain,
% 0.88/1.09 (~r(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[200, 2171, 1988])).
% 0.88/1.09 tff(2175,plain,
% 0.88/1.09 (b(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[135, 2174, 2149])).
% 0.88/1.09 tff(2176,plain,
% 0.88/1.09 (b(s(s(z)), s(elem!1))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2175, 2143])).
% 0.88/1.09 tff(2177,assumption,(~r(z, s(s(z)))), introduced(assumption)).
% 0.88/1.09 tff(2178,plain,
% 0.88/1.09 ((z = s(s(z))) | b(z, s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1511, 51, 2177])).
% 0.88/1.09 tff(2179,plain,
% 0.88/1.09 (b(z, s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2178, 1450])).
% 0.88/1.09 tff(2180,assumption,(b(s(s(z)), s(elem!1))), introduced(assumption)).
% 0.88/1.09 tff(2181,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2182,plain,
% 0.88/1.09 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2183,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1)))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2182])).
% 0.88/1.09 tff(2184,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2183, 2181])).
% 0.88/1.09 tff(2185,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(z)))))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2186,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 0.88/1.09 tff(2187,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2186, 238, 490, 2180, 2179, 2085])).
% 0.88/1.09 tff(2188,plain,(r(z, s(s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(z, elem!1)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2189,plain,
% 0.88/1.09 (r(z, s(s(z)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2188, 2176, 2173, 2081, 381])).
% 0.88/1.09 tff(2190,plain,
% 0.88/1.09 (~r(z, s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1583, 2189, 2171])).
% 0.88/1.09 tff(2191,plain,
% 0.88/1.09 (b(z, s(z))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1542, 2190])).
% 0.88/1.09 tff(2192,plain,
% 0.88/1.09 (~b(s(s(s(s(s(z))))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1842, 238, 2191, 2018, 1783])).
% 0.88/1.09 tff(2193,plain,
% 0.88/1.09 (r(s(s(s(s(s(z))))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 2192])).
% 0.88/1.09 tff(2194,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2195,plain,
% 0.88/1.09 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2196,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2195])).
% 0.88/1.09 tff(2197,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2196, 2194])).
% 0.88/1.09 tff(2198,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2199,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 0.88/1.09 tff(2200,plain,
% 0.88/1.09 (~b(s(s(s(s(z)))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2199, 238, 2191, 2018, 2169])).
% 0.88/1.09 tff(2201,plain,
% 0.88/1.09 (r(s(s(s(s(z)))), z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1499, 51, 726, 2200])).
% 0.88/1.09 tff(2202,plain,
% 0.88/1.09 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1794, 2169, 2018, 1783])).
% 0.88/1.09 tff(2203,plain,
% 0.88/1.09 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1904, 2202])).
% 0.88/1.09 tff(2204,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2205,plain,
% 0.88/1.09 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2206,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2205])).
% 0.88/1.09 tff(2207,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2206, 2204])).
% 0.88/1.09 tff(2208,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2209,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 0.88/1.09 tff(2210,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2209, 124, 2203, 2201, 2193])).
% 0.88/1.09 tff(2211,plain,((~(elem!1 = s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2212,plain,
% 0.88/1.09 (~(elem!1 = s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2211, 1976, 1815, 345, 1400])).
% 0.88/1.09 tff(2213,assumption,(~b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 0.88/1.09 tff(2214,plain,
% 0.88/1.09 (~r(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[200, 160, 169])).
% 0.88/1.09 tff(2215,plain,
% 0.88/1.09 (s(s(z)) = s(s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[135, 2214, 2213])).
% 0.88/1.09 tff(2216,plain,
% 0.88/1.09 (s(elem!1) = s(z)),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[21, 2215])).
% 0.88/1.09 tff(2217,plain,
% 0.88/1.09 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2216])).
% 0.88/1.09 tff(2218,plain,
% 0.88/1.09 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.88/1.09 inference(symmetry,[status(thm)],[2217])).
% 0.88/1.09 tff(2219,plain,
% 0.88/1.09 (r(s(elem!1), s(s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[160, 2218])).
% 0.88/1.09 tff(2220,plain,
% 0.88/1.09 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2215])).
% 0.88/1.09 tff(2221,plain,
% 0.88/1.09 ((~r(s(elem!1), s(s(z)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2220])).
% 0.88/1.09 tff(2222,assumption,(~r(s(elem!1), s(s(z)))), introduced(assumption)).
% 0.88/1.09 tff(2223,plain,
% 0.88/1.09 (~r(s(elem!1), s(s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 0.88/1.09 tff(2224,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2223, 2219])).
% 0.88/1.09 tff(2225,plain,((~r(s(z), s(s(elem!1)))) | r(s(elem!1), s(s(z))) | b(s(s(z)), s(s(elem!1))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2226,plain,
% 0.88/1.09 (b(s(s(z)), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2225, 2155, 160, 169])).
% 0.88/1.09 tff(2227,plain,
% 0.88/1.09 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[1626])).
% 0.88/1.09 tff(2228,plain,
% 0.88/1.09 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.09 inference(symmetry,[status(thm)],[2227])).
% 0.88/1.09 tff(2229,plain,
% 0.88/1.09 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[1786, 2228])).
% 0.88/1.09 tff(2230,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1081, 2229])).
% 0.88/1.09 tff(2231,plain,((~(s(elem!1) = s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2232,plain,
% 0.88/1.09 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2231, 281, 1081])).
% 0.88/1.09 tff(2233,plain,
% 0.88/1.09 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1904, 2232])).
% 0.88/1.09 tff(2234,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2235,plain,
% 0.88/1.09 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2236,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2235])).
% 0.88/1.09 tff(2237,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2236, 2234])).
% 0.88/1.09 tff(2238,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.09 inference(quant_inst,[status(thm)],[])).
% 0.88/1.09 tff(2239,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.88/1.09 tff(2240,plain,
% 0.88/1.09 ($false),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2239, 124, 1651, 1652, 161, 1818])).
% 0.88/1.09 tff(2241,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.09 tff(2242,plain,
% 0.88/1.09 (~r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[2241, 2233, 161, 1815])).
% 0.88/1.09 tff(2243,plain,
% 0.88/1.09 (b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[1709, 2242])).
% 0.88/1.09 tff(2244,plain,
% 0.88/1.09 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[281])).
% 0.88/1.09 tff(2245,plain,
% 0.88/1.09 (b(elem!1, s(elem!1)) <=> b(s(z), s(elem!1))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[276])).
% 0.88/1.09 tff(2246,plain,
% 0.88/1.09 (b(elem!1, s(elem!1)) <=> b(s(z), s(s(z)))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2245, 2244])).
% 0.88/1.09 tff(2247,plain,
% 0.88/1.09 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[276])).
% 0.88/1.09 tff(2248,plain,
% 0.88/1.09 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 0.88/1.09 inference(symmetry,[status(thm)],[2247])).
% 0.88/1.09 tff(2249,plain,
% 0.88/1.09 (r(elem!1, s(s(elem!1)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[160, 2248])).
% 0.88/1.09 tff(2250,plain,
% 0.88/1.09 (b(s(elem!1), s(s(s(elem!1))))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[462, 286])).
% 0.88/1.09 tff(2251,plain,
% 0.88/1.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[218, 161, 160])).
% 0.88/1.09 tff(2252,plain,
% 0.88/1.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[223, 545, 2251])).
% 0.88/1.09 tff(2253,plain,
% 0.88/1.09 (~b(s(s(elem!1)), s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[298, 284, 2252, 2250])).
% 0.88/1.09 tff(2254,plain,
% 0.88/1.09 (r(s(s(elem!1)), s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[323, 2253, 275])).
% 0.88/1.09 tff(2255,plain,
% 0.88/1.09 (~r(elem!1, s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[599, 2254, 2249])).
% 0.88/1.09 tff(2256,plain,
% 0.88/1.09 (b(elem!1, s(elem!1))),
% 0.88/1.09 inference(unit_resolution,[status(thm)],[629, 2255, 391])).
% 0.88/1.09 tff(2257,plain,
% 0.88/1.09 (b(s(z), s(s(z)))),
% 0.88/1.09 inference(modus_ponens,[status(thm)],[2256, 2246])).
% 0.88/1.09 tff(2258,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 0.88/1.09 tff(2259,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2260,plain,
% 0.88/1.09 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.88/1.09 inference(rewrite,[status(thm)],[])).
% 0.88/1.09 tff(2261,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.88/1.09 inference(monotonicity,[status(thm)],[2260])).
% 0.88/1.09 tff(2262,plain,
% 0.88/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.88/1.09 inference(transitivity,[status(thm)],[2261, 2259])).
% 0.88/1.09 tff(2263,plain,
% 0.88/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2264,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2263, 2262])).
% 0.88/1.10 tff(2265,plain,
% 0.88/1.10 ($false),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2264, 238, 227, 2258, 1906, 1785])).
% 0.88/1.10 tff(2266,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.10 tff(2267,plain,
% 0.88/1.10 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2266, 2257, 2243, 227])).
% 0.88/1.10 tff(2268,plain,
% 0.88/1.10 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1420])).
% 0.88/1.10 tff(2269,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2268])).
% 0.88/1.10 tff(2270,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[281])).
% 0.88/1.10 tff(2271,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2270, 2269])).
% 0.88/1.10 tff(2272,plain,
% 0.88/1.10 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2271])).
% 0.88/1.10 tff(2273,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[276])).
% 0.88/1.10 tff(2274,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(symmetry,[status(thm)],[2273])).
% 0.88/1.10 tff(2275,plain,
% 0.88/1.10 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2268])).
% 0.88/1.10 tff(2276,plain,
% 0.88/1.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2275])).
% 0.88/1.10 tff(2277,plain,
% 0.88/1.10 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(transitivity,[status(thm)],[2276, 2274])).
% 0.88/1.10 tff(2278,plain,
% 0.88/1.10 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1435])).
% 0.88/1.10 tff(2279,plain,
% 0.88/1.10 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2278])).
% 0.88/1.10 tff(2280,plain,
% 0.88/1.10 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[1611, 124, 169, 1544])).
% 0.88/1.10 tff(2281,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[1603, 2280, 1599])).
% 0.88/1.10 tff(2282,plain,
% 0.88/1.10 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 0.88/1.10 inference(commutativity,[status(thm)],[])).
% 0.88/1.10 tff(2283,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1436])).
% 0.88/1.10 tff(2284,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2283, 2282])).
% 0.88/1.10 tff(2285,plain,
% 0.88/1.10 ((s(s(z)) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2284])).
% 0.88/1.10 tff(2286,plain,
% 0.88/1.10 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2285])).
% 0.88/1.10 tff(2287,plain,
% 0.88/1.10 (~(s(s(s(z))) = s(s(z)))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[114, 2286])).
% 0.88/1.10 tff(2288,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.88/1.10 tff(2289,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2290,plain,
% 0.88/1.10 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2291,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2290])).
% 0.88/1.10 tff(2292,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2291, 2289])).
% 0.88/1.10 tff(2293,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2294,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 0.88/1.10 tff(2295,plain,
% 0.88/1.10 (~r(s(s(s(z))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2294, 124, 169, 2288])).
% 0.88/1.10 tff(2296,plain,
% 0.88/1.10 (((~![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))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2297,plain,
% 0.88/1.10 ((~![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))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2298,plain,
% 0.88/1.10 ((~![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)))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 0.88/1.10 tff(2299,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2298, 51, 2295])).
% 0.88/1.10 tff(2300,plain,
% 0.88/1.10 (b(s(s(s(z))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2299, 2287])).
% 0.88/1.10 tff(2301,plain,
% 0.88/1.10 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.10 inference(commutativity,[status(thm)],[])).
% 0.88/1.10 tff(2302,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1436, 1662])).
% 0.88/1.10 tff(2303,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2302, 2301])).
% 0.88/1.10 tff(2304,plain,
% 0.88/1.10 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2303])).
% 0.88/1.10 tff(2305,plain,
% 0.88/1.10 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2304])).
% 0.88/1.10 tff(2306,plain,
% 0.88/1.10 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1436])).
% 0.88/1.10 tff(2307,plain,
% 0.88/1.10 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2306])).
% 0.88/1.10 tff(2308,plain,
% 0.88/1.10 (s(s(s(z))) = s(s(s(s(z))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[1436, 203, 2307])).
% 0.88/1.10 tff(2309,plain,
% 0.88/1.10 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2308])).
% 0.88/1.10 tff(2310,plain,
% 0.88/1.10 (s(s(z)) = s(s(elem!1))),
% 0.88/1.10 inference(transitivity,[status(thm)],[144, 2309, 715, 1436])).
% 0.88/1.10 tff(2311,plain,
% 0.88/1.10 ($false),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[114, 2310])).
% 0.88/1.10 tff(2312,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.10 tff(2313,plain,
% 0.88/1.10 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2312, 114, 375])).
% 0.88/1.10 tff(2314,plain,
% 0.88/1.10 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2313, 2305])).
% 0.88/1.10 tff(2315,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2316,plain,
% 0.88/1.10 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2317,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2316])).
% 0.88/1.10 tff(2318,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2317, 2315])).
% 0.88/1.10 tff(2319,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2320,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 0.88/1.10 tff(2321,plain,
% 0.88/1.10 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2320, 124, 1544, 2288])).
% 0.88/1.10 tff(2322,plain,
% 0.88/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2323,plain,
% 0.88/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2324,plain,
% 0.88/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 0.88/1.10 tff(2325,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z)))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2324, 51, 2321])).
% 0.88/1.10 tff(2326,plain,
% 0.88/1.10 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2325, 2314])).
% 0.88/1.10 tff(2327,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2328,plain,
% 0.88/1.10 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2329,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2328])).
% 0.88/1.10 tff(2330,plain,
% 0.88/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2329, 2327])).
% 0.88/1.10 tff(2331,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2332,plain,
% 0.88/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 0.88/1.10 tff(2333,plain,
% 0.88/1.10 ($false),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2332, 238, 1587, 1501, 2326, 2300])).
% 0.88/1.10 tff(2334,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (s(s(z)) = s(s(elem!1))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.10 tff(2335,plain,
% 0.88/1.10 (~r(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2334, 375, 2281, 114, 169, 1544, 1565])).
% 0.88/1.10 tff(2336,plain,
% 0.88/1.10 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 0.88/1.10 inference(commutativity,[status(thm)],[])).
% 0.88/1.10 tff(2337,plain,
% 0.88/1.10 ((s(z) = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1435])).
% 0.88/1.10 tff(2338,plain,
% 0.88/1.10 ((s(z) = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2337, 2336])).
% 0.88/1.10 tff(2339,plain,
% 0.88/1.10 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(z)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2338])).
% 0.88/1.10 tff(2340,plain,
% 0.88/1.10 (~(s(s(s(z))) = s(z))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[41, 2339])).
% 0.88/1.10 tff(2341,plain,
% 0.88/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.88/1.10 inference(rewrite,[status(thm)],[])).
% 0.88/1.10 tff(2342,plain,
% 0.88/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.88/1.10 inference(quant_inst,[status(thm)],[])).
% 0.88/1.10 tff(2343,plain,
% 0.88/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2342, 2341])).
% 0.88/1.10 tff(2344,plain,
% 0.88/1.10 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2343, 51])).
% 0.88/1.10 tff(2345,plain,
% 0.88/1.10 (b(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2344, 2340, 2335])).
% 0.88/1.10 tff(2346,plain,
% 0.88/1.10 (b(s(s(elem!1)), s(z))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2345, 2279])).
% 0.88/1.10 tff(2347,plain,
% 0.88/1.10 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 0.88/1.10 inference(commutativity,[status(thm)],[])).
% 0.88/1.10 tff(2348,plain,
% 0.88/1.10 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1435])).
% 0.88/1.10 tff(2349,plain,
% 0.88/1.10 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2348, 2347])).
% 0.88/1.10 tff(2350,plain,
% 0.88/1.10 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2349])).
% 0.88/1.10 tff(2351,plain,
% 0.88/1.10 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2350])).
% 0.88/1.10 tff(2352,plain,
% 0.88/1.10 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[1092, 2351])).
% 0.88/1.10 tff(2353,plain,
% 0.88/1.10 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[375])).
% 0.88/1.10 tff(2354,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2353])).
% 0.88/1.10 tff(2355,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1626])).
% 0.88/1.10 tff(2356,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2355])).
% 0.88/1.10 tff(2357,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2356, 2354])).
% 0.88/1.10 tff(2358,plain,
% 0.88/1.10 (b(s(elem!1), s(s(s(elem!1))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[2281, 2357])).
% 0.88/1.10 tff(2359,plain,
% 0.88/1.10 (elem!1 = s(z)),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[379, 375])).
% 0.88/1.10 tff(2360,plain,
% 0.88/1.10 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2359])).
% 0.88/1.10 tff(2361,plain,
% 0.88/1.10 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(symmetry,[status(thm)],[2360])).
% 0.88/1.10 tff(2362,plain,
% 0.88/1.10 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1626])).
% 0.88/1.10 tff(2363,plain,
% 0.88/1.10 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2362])).
% 0.88/1.10 tff(2364,plain,
% 0.88/1.10 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(transitivity,[status(thm)],[2363, 2361])).
% 0.88/1.10 tff(2365,plain,
% 0.88/1.10 (r(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[1544, 2364])).
% 0.88/1.10 tff(2366,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1436])).
% 0.88/1.10 tff(2367,plain,
% 0.88/1.10 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2366])).
% 0.88/1.10 tff(2368,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(z))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[227, 2367])).
% 0.88/1.10 tff(2369,plain,
% 0.88/1.10 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.88/1.10 inference(commutativity,[status(thm)],[])).
% 0.88/1.10 tff(2370,plain,
% 0.88/1.10 ((s(s(s(z))) = s(z)) <=> (s(s(elem!1)) = s(z))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1436])).
% 0.88/1.10 tff(2371,plain,
% 0.88/1.10 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.88/1.10 inference(transitivity,[status(thm)],[2370, 2369])).
% 0.88/1.10 tff(2372,plain,
% 0.88/1.10 ((s(z) = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2371])).
% 0.88/1.10 tff(2373,plain,
% 0.88/1.10 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(z)))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[2372])).
% 0.88/1.10 tff(2374,plain,
% 0.88/1.10 (~(s(s(s(z))) = s(z))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[41, 2373])).
% 0.88/1.10 tff(2375,plain,
% 0.88/1.10 (s(z) = elem!1),
% 0.88/1.10 inference(symmetry,[status(thm)],[2359])).
% 0.88/1.10 tff(2376,plain,
% 0.88/1.10 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1662, 2375])).
% 0.88/1.10 tff(2377,plain,
% 0.88/1.10 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2376])).
% 0.88/1.10 tff(2378,plain,
% 0.88/1.10 (r(s(s(s(s(z)))), s(z))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[649, 2377])).
% 0.88/1.10 tff(2379,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.88/1.10 inference(monotonicity,[status(thm)],[1434, 1662])).
% 0.88/1.10 tff(2380,plain,
% 0.88/1.10 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.10 inference(symmetry,[status(thm)],[2379])).
% 0.88/1.10 tff(2381,plain,
% 0.88/1.10 (b(s(s(z)), s(s(s(s(z)))))),
% 0.88/1.10 inference(modus_ponens,[status(thm)],[290, 2380])).
% 0.88/1.10 tff(2382,plain,
% 0.88/1.10 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[1552, 124, 169])).
% 0.88/1.10 tff(2383,plain,
% 0.88/1.10 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2382, 2378])).
% 0.88/1.10 tff(2384,plain,
% 0.88/1.10 (b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[1561, 51, 2383, 1556])).
% 0.88/1.10 tff(2385,plain,
% 0.88/1.10 (~r(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2334, 2384, 2381, 114, 375, 2378, 169])).
% 0.88/1.10 tff(2386,plain,
% 0.88/1.10 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2343, 51, 2385])).
% 0.88/1.10 tff(2387,plain,
% 0.88/1.10 (b(s(s(s(z))), s(z))),
% 0.88/1.10 inference(unit_resolution,[status(thm)],[2386, 2374])).
% 0.88/1.10 tff(2388,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.88/1.10 tff(2389,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.88/1.11 tff(2390,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2391,plain,
% 0.88/1.11 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2392,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2391])).
% 0.88/1.11 tff(2393,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2392, 2390])).
% 0.88/1.11 tff(2394,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2395,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.88/1.11 tff(2396,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2395, 238, 2389, 2384, 2388, 2387])).
% 0.88/1.11 tff(2397,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (s(s(s(s(z)))) = s(s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2398,plain,
% 0.88/1.11 ((~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2397, 730])).
% 0.88/1.11 tff(2399,plain,
% 0.88/1.11 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2398, 2368, 114, 2365, 2358, 169, 375])).
% 0.88/1.11 tff(2400,plain,
% 0.88/1.11 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[1662, 1436])).
% 0.88/1.11 tff(2401,plain,
% 0.88/1.11 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 0.88/1.11 inference(symmetry,[status(thm)],[2400])).
% 0.88/1.11 tff(2402,plain,
% 0.88/1.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[226, 2401])).
% 0.88/1.11 tff(2403,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.88/1.11 tff(2404,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2403, 2402])).
% 0.88/1.11 tff(2405,plain,(b(s(s(s(s(z)))), s(s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2406,plain,
% 0.88/1.11 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2405, 2399, 375])).
% 0.88/1.11 tff(2407,plain,
% 0.88/1.11 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[223, 2406, 545])).
% 0.88/1.11 tff(2408,plain,
% 0.88/1.11 (~r(s(z), s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[218, 160, 210])).
% 0.88/1.11 tff(2409,plain,
% 0.88/1.11 (b(s(z), s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[101, 2408])).
% 0.88/1.11 tff(2410,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2411,plain,
% 0.88/1.11 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2412,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2411])).
% 0.88/1.11 tff(2413,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2412, 2410])).
% 0.88/1.11 tff(2414,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2415,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 0.88/1.11 tff(2416,plain,
% 0.88/1.11 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2415, 238, 2409, 23, 1783])).
% 0.88/1.11 tff(2417,assumption,(~(s(s(s(s(s(z))))) = s(s(elem!1)))), introduced(assumption)).
% 0.88/1.11 tff(2418,plain,
% 0.88/1.11 (((~![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))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2419,plain,
% 0.88/1.11 ((~![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))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2420,plain,
% 0.88/1.11 ((~![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)))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2419, 2418])).
% 0.88/1.11 tff(2421,plain,
% 0.88/1.11 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2420, 51, 2417, 2416])).
% 0.88/1.11 tff(2422,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2423,plain,
% 0.88/1.11 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2424,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2423])).
% 0.88/1.11 tff(2425,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2424, 2422])).
% 0.88/1.11 tff(2426,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2427,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 0.88/1.11 tff(2428,plain,
% 0.88/1.11 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2427, 124, 210, 2421])).
% 0.88/1.11 tff(2429,plain,
% 0.88/1.11 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1814, 2428, 1380])).
% 0.88/1.11 tff(2430,plain,
% 0.88/1.11 (~r(s(z), s(s(s(s(s(z))))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2016, 2421, 160])).
% 0.88/1.11 tff(2431,plain,
% 0.88/1.11 (b(s(z), s(s(s(s(s(z))))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1709, 2430])).
% 0.88/1.11 tff(2432,plain,
% 0.88/1.11 (~r(s(s(s(elem!1))), s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[562, 124, 160, 210])).
% 0.88/1.11 tff(2433,plain,
% 0.88/1.11 (b(s(s(s(elem!1))), s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[576, 51, 94, 2432])).
% 0.88/1.11 tff(2434,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2435,plain,
% 0.88/1.11 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2436,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2435])).
% 0.88/1.11 tff(2437,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2436, 2434])).
% 0.88/1.11 tff(2438,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2439,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(z)))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 0.88/1.11 tff(2440,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2439, 238, 2433, 2431, 1783, 2429])).
% 0.88/1.11 tff(2441,plain,((~b(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2442,plain,
% 0.88/1.11 (~b(s(s(elem!1)), s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2441, 2407, 1783, 160, 2352, 1380])).
% 0.88/1.11 tff(2443,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2442, 2346])).
% 0.88/1.11 tff(2444,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2445,plain,
% 0.88/1.11 (~r(s(s(s(s(z)))), s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2444, 281, 160, 1380, 1976, 114, 545, 169, 227])).
% 0.88/1.11 tff(2446,plain,
% 0.88/1.11 (b(s(s(s(s(z)))), s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1623, 2445, 1619])).
% 0.88/1.11 tff(2447,plain,
% 0.88/1.11 (b(s(s(s(elem!1))), elem!1)),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2446, 2277])).
% 0.88/1.11 tff(2448,plain,
% 0.88/1.11 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[639, 2256, 2447, 284])).
% 0.88/1.11 tff(2449,plain,
% 0.88/1.11 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2448, 2272])).
% 0.88/1.11 tff(2450,plain,
% 0.88/1.11 (r(s(s(s(s(z)))), s(s(z)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1561, 51, 2449, 730])).
% 0.88/1.11 tff(2451,plain,
% 0.88/1.11 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1928, 2450, 2233])).
% 0.88/1.11 tff(2452,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1738, 2451, 2267])).
% 0.88/1.11 tff(2453,plain,((~(elem!1 = s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2454,plain,
% 0.88/1.11 (~(elem!1 = s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2453, 2226, 2212, 272, 160, 161, 1380, 114, 209, 169, 1081])).
% 0.88/1.11 tff(2455,plain,
% 0.88/1.11 (r(elem!1, s(z))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[363, 2454, 1400])).
% 0.88/1.11 tff(2456,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2457,plain,
% 0.88/1.11 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), 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)))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2458,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2457])).
% 0.88/1.11 tff(2459,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2458, 2456])).
% 0.88/1.11 tff(2460,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2461,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2460, 2459])).
% 0.88/1.11 tff(2462,plain,
% 0.88/1.11 (~r(elem!1, s(s(z)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2461, 124, 169, 2455])).
% 0.88/1.11 tff(2463,plain,
% 0.88/1.11 (b(elem!1, s(s(z)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[763, 2462, 1974])).
% 0.88/1.11 tff(2464,plain,
% 0.88/1.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[223, 209, 2251])).
% 0.88/1.11 tff(2465,plain,
% 0.88/1.11 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 0.88/1.11 inference(symmetry,[status(thm)],[327])).
% 0.88/1.11 tff(2466,plain,
% 0.88/1.11 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2465])).
% 0.88/1.11 tff(2467,plain,
% 0.88/1.11 (~(s(z) = elem!1)),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2454, 2466])).
% 0.88/1.11 tff(2468,plain,
% 0.88/1.11 ((s(z) = elem!1) | r(s(z), elem!1)),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[349, 51, 345])).
% 0.88/1.11 tff(2469,plain,
% 0.88/1.11 (r(s(z), elem!1)),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2468, 2467])).
% 0.88/1.11 tff(2470,plain,
% 0.88/1.11 (~r(s(s(elem!1)), elem!1)),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[342, 2469, 160])).
% 0.88/1.11 tff(2471,plain,
% 0.88/1.11 (b(s(s(elem!1)), elem!1)),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[255, 2470, 167])).
% 0.88/1.11 tff(2472,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2473,plain,
% 0.88/1.11 (((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.88/1.11 inference(rewrite,[status(thm)],[])).
% 0.88/1.11 tff(2474,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2473])).
% 0.88/1.11 tff(2475,plain,
% 0.88/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 0.88/1.11 inference(transitivity,[status(thm)],[2474, 2472])).
% 0.88/1.11 tff(2476,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)))),
% 0.88/1.11 inference(quant_inst,[status(thm)],[])).
% 0.88/1.11 tff(2477,plain,
% 0.88/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 0.88/1.11 tff(2478,plain,
% 0.88/1.11 ((~r(s(z), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2477, 124])).
% 0.88/1.11 tff(2479,plain,
% 0.88/1.11 (~r(elem!1, s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2478, 2469, 160, 2455])).
% 0.88/1.11 tff(2480,plain,
% 0.88/1.11 (~r(elem!1, s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1378, 161, 1370])).
% 0.88/1.11 tff(2481,plain,
% 0.88/1.11 (b(elem!1, s(s(s(elem!1))))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[1319, 2480, 514])).
% 0.88/1.11 tff(2482,plain,
% 0.88/1.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[223, 2251, 545])).
% 0.88/1.11 tff(2483,plain,
% 0.88/1.11 ($false),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[615, 2482, 2481, 250, 150, 602])).
% 0.88/1.11 tff(2484,plain,((~r(s(z), s(s(s(elem!1))))) | r(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.11 tff(2485,plain,
% 0.88/1.11 (elem!1 = s(s(s(elem!1)))),
% 0.88/1.11 inference(unit_resolution,[status(thm)],[2484, 2479, 160, 161, 150, 209, 2470, 2455])).
% 0.88/1.11 tff(2486,plain,
% 0.88/1.11 (s(s(s(elem!1))) = elem!1),
% 0.88/1.11 inference(symmetry,[status(thm)],[501])).
% 0.88/1.11 tff(2487,plain,
% 0.88/1.11 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 0.88/1.11 inference(monotonicity,[status(thm)],[2486])).
% 0.88/1.11 tff(2488,plain,
% 0.88/1.11 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.11 inference(symmetry,[status(thm)],[2487])).
% 0.88/1.11 tff(2489,plain,
% 0.88/1.11 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.11 inference(modus_ponens,[status(thm)],[228, 2488])).
% 0.88/1.12 tff(2490,plain,
% 0.88/1.12 (b(s(s(s(elem!1))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2486])).
% 0.88/1.12 tff(2491,plain,
% 0.88/1.12 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2490])).
% 0.88/1.12 tff(2492,plain,
% 0.88/1.12 (b(s(s(s(elem!1))), s(s(z)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[753, 2491])).
% 0.88/1.12 tff(2493,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2494,plain,
% 0.88/1.12 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2495,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2494])).
% 0.88/1.12 tff(2496,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2495, 2493])).
% 0.88/1.12 tff(2497,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 0.88/1.12 inference(quant_inst,[status(thm)],[])).
% 0.88/1.12 tff(2498,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 0.88/1.12 tff(2499,plain,
% 0.88/1.12 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2498, 238, 227, 226])).
% 0.88/1.12 tff(2500,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2499, 2492, 2489])).
% 0.88/1.12 tff(2501,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~(elem!1 = s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2502,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2501, 2485, 2471, 2464, 2226, 2463])).
% 0.88/1.12 tff(2503,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(s(z), elem!1) | b(elem!1, s(z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2504,plain,
% 0.88/1.12 (elem!1 = s(s(elem!1))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2503, 1970, 161, 544, 345, 1400, 1380, 114, 1081, 306])).
% 0.88/1.12 tff(2505,plain,
% 0.88/1.12 (s(s(elem!1)) = elem!1),
% 0.88/1.12 inference(symmetry,[status(thm)],[2504])).
% 0.88/1.12 tff(2506,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2505])).
% 0.88/1.12 tff(2507,plain,
% 0.88/1.12 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2506])).
% 0.88/1.12 tff(2508,plain,
% 0.88/1.12 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2505])).
% 0.88/1.12 tff(2509,plain,
% 0.88/1.12 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2508])).
% 0.88/1.12 tff(2510,plain,
% 0.88/1.12 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2504])).
% 0.88/1.12 tff(2511,plain,
% 0.88/1.12 ((elem!1 = s(z)) <=> (s(s(elem!1)) = s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2504])).
% 0.88/1.12 tff(2512,plain,
% 0.88/1.12 ((elem!1 = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2511, 2369])).
% 0.88/1.12 tff(2513,plain,
% 0.88/1.12 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2512])).
% 0.88/1.12 tff(2514,plain,
% 0.88/1.12 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2513])).
% 0.88/1.12 tff(2515,plain,
% 0.88/1.12 (~(elem!1 = s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[41, 2514])).
% 0.88/1.12 tff(2516,plain,
% 0.88/1.12 (r(elem!1, s(z))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[363, 2515, 1400])).
% 0.88/1.12 tff(2517,plain,
% 0.88/1.12 (r(s(s(elem!1)), s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2516, 2510])).
% 0.88/1.12 tff(2518,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2519,plain,
% 0.88/1.12 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2520,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2519])).
% 0.88/1.12 tff(2521,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2520, 2518])).
% 0.88/1.12 tff(2522,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(quant_inst,[status(thm)],[])).
% 0.88/1.12 tff(2523,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 0.88/1.12 tff(2524,plain,
% 0.88/1.12 (~r(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2523, 124, 1970, 2517])).
% 0.88/1.12 tff(2525,plain,
% 0.88/1.12 (~r(elem!1, s(s(z)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2524, 2509])).
% 0.88/1.12 tff(2526,plain,
% 0.88/1.12 (b(elem!1, s(s(z)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[763, 2525, 1974])).
% 0.88/1.12 tff(2527,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2526, 2507])).
% 0.88/1.12 tff(2528,plain,
% 0.88/1.12 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2301])).
% 0.88/1.12 tff(2529,plain,
% 0.88/1.12 (s(elem!1) = s(s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2097, 2504])).
% 0.88/1.12 tff(2530,plain,
% 0.88/1.12 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2529])).
% 0.88/1.12 tff(2531,plain,
% 0.88/1.12 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2530, 2528])).
% 0.88/1.12 tff(2532,plain,
% 0.88/1.12 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2531])).
% 0.88/1.12 tff(2533,plain,
% 0.88/1.12 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2504])).
% 0.88/1.12 tff(2534,plain,
% 0.88/1.12 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2533, 267])).
% 0.88/1.12 tff(2535,plain,
% 0.88/1.12 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2534])).
% 0.88/1.12 tff(2536,plain,
% 0.88/1.12 (~(s(elem!1) = s(s(elem!1)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2212, 2535])).
% 0.88/1.12 tff(2537,plain,
% 0.88/1.12 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2536, 2532])).
% 0.88/1.12 tff(2538,plain,
% 0.88/1.12 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2529])).
% 0.88/1.12 tff(2539,plain,
% 0.88/1.12 (r(s(s(s(elem!1))), s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[306, 2538])).
% 0.88/1.12 tff(2540,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2541,plain,
% 0.88/1.12 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(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(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2542,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2541])).
% 0.88/1.12 tff(2543,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2542, 2540])).
% 0.88/1.12 tff(2544,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.88/1.12 inference(quant_inst,[status(thm)],[])).
% 0.88/1.12 tff(2545,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2544, 2543])).
% 0.88/1.12 tff(2546,plain,
% 0.88/1.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2545, 124, 2517, 2539])).
% 0.88/1.12 tff(2547,plain,
% 0.88/1.12 (((~![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)))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2548,plain,
% 0.88/1.12 ((~![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)))))),
% 0.88/1.12 inference(quant_inst,[status(thm)],[])).
% 0.88/1.12 tff(2549,plain,
% 0.88/1.12 ((~![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))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 0.88/1.12 tff(2550,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2549, 51, 2546, 2537])).
% 0.88/1.12 tff(2551,plain,
% 0.88/1.12 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[177, 1970, 161])).
% 0.88/1.12 tff(2552,plain,
% 0.88/1.12 (b(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[190, 2551])).
% 0.88/1.12 tff(2553,plain,
% 0.88/1.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[218, 161, 544])).
% 0.88/1.12 tff(2554,plain,
% 0.88/1.12 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2530])).
% 0.88/1.12 tff(2555,plain,
% 0.88/1.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2536, 2554])).
% 0.88/1.12 tff(2556,plain,
% 0.88/1.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[223, 2555, 2553])).
% 0.88/1.12 tff(2557,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2558,plain,
% 0.88/1.12 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2559,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2558])).
% 0.88/1.12 tff(2560,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2559, 2557])).
% 0.88/1.12 tff(2561,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.88/1.12 inference(quant_inst,[status(thm)],[])).
% 0.88/1.12 tff(2562,plain,
% 0.88/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2561, 2560])).
% 0.88/1.12 tff(2563,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2562, 238, 2556, 2552, 2550, 2527])).
% 0.88/1.12 tff(2564,plain,((~r(s(z), s(s(s(elem!1))))) | b(elem!1, s(z)) | (~r(s(elem!1), s(z))) | b(s(z), elem!1) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2565,plain,
% 0.88/1.12 (~r(s(z), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2564, 2, 1816, 345, 1380, 114, 1081, 1400])).
% 0.88/1.12 tff(2566,plain,
% 0.88/1.12 (b(s(z), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[101, 2565])).
% 0.88/1.12 tff(2567,plain,
% 0.88/1.12 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[58])).
% 0.88/1.12 tff(2568,plain,
% 0.88/1.12 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2567])).
% 0.88/1.12 tff(2569,plain,
% 0.88/1.12 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2568])).
% 0.88/1.12 tff(2570,plain,
% 0.88/1.12 (~b(s(z), s(s(s(elem!1))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2, 2569])).
% 0.88/1.12 tff(2571,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[546, 2570])).
% 0.88/1.12 tff(2572,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2573,plain,
% 0.88/1.12 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2572, 2566, 2])).
% 0.88/1.12 tff(2574,plain,
% 0.88/1.12 (~r(s(elem!1), s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[526, 160, 306])).
% 0.88/1.12 tff(2575,plain,
% 0.88/1.12 (s(s(elem!1)) = elem!1),
% 0.88/1.12 inference(symmetry,[status(thm)],[2073])).
% 0.88/1.12 tff(2576,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2575])).
% 0.88/1.12 tff(2577,plain,
% 0.88/1.12 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2576])).
% 0.88/1.12 tff(2578,plain,
% 0.88/1.12 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2575])).
% 0.88/1.12 tff(2579,plain,
% 0.88/1.12 ((~r(s(s(elem!1)), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2578])).
% 0.88/1.12 tff(2580,plain,
% 0.88/1.12 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2073])).
% 0.88/1.12 tff(2581,plain,
% 0.88/1.12 ((elem!1 = s(z)) <=> (s(s(elem!1)) = s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2073])).
% 0.88/1.12 tff(2582,plain,
% 0.88/1.12 ((elem!1 = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.88/1.12 inference(transitivity,[status(thm)],[2581, 2369])).
% 0.88/1.12 tff(2583,plain,
% 0.88/1.12 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 0.88/1.12 inference(symmetry,[status(thm)],[2582])).
% 0.88/1.12 tff(2584,plain,
% 0.88/1.12 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2583])).
% 0.88/1.12 tff(2585,plain,
% 0.88/1.12 (~(elem!1 = s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[41, 2584])).
% 0.88/1.12 tff(2586,plain,
% 0.88/1.12 (r(elem!1, s(z))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[363, 2585, 1400])).
% 0.88/1.12 tff(2587,plain,
% 0.88/1.12 (r(s(s(elem!1)), s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2586, 2580])).
% 0.88/1.12 tff(2588,plain,
% 0.88/1.12 (~r(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2523, 124, 169, 2587])).
% 0.88/1.12 tff(2589,plain,
% 0.88/1.12 (~r(elem!1, s(s(z)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2588, 2579])).
% 0.88/1.12 tff(2590,plain,
% 0.88/1.12 (b(elem!1, s(s(z)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[763, 2589, 541])).
% 0.88/1.12 tff(2591,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(z)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2590, 2577])).
% 0.88/1.12 tff(2592,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.88/1.12 tff(2593,plain,
% 0.88/1.12 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[2592, 2301])).
% 0.88/1.12 tff(2594,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[545, 2593])).
% 0.88/1.12 tff(2595,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2596,plain,
% 0.88/1.12 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2595, 545])).
% 0.88/1.12 tff(2597,plain,
% 0.88/1.12 (s(elem!1) = s(s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2097, 2073])).
% 0.88/1.12 tff(2598,plain,
% 0.88/1.12 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2597])).
% 0.88/1.12 tff(2599,plain,
% 0.88/1.12 (r(s(s(s(elem!1))), s(z))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[306, 2598])).
% 0.88/1.12 tff(2600,plain,
% 0.88/1.12 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2545, 124, 2587, 2599])).
% 0.88/1.12 tff(2601,plain,
% 0.88/1.12 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2549, 51, 2600, 2596])).
% 0.88/1.12 tff(2602,plain,
% 0.88/1.12 (r(s(s(z)), s(elem!1)) <=> r(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2597])).
% 0.88/1.12 tff(2603,plain,
% 0.88/1.12 ((~r(s(s(z)), s(elem!1))) <=> (~r(s(s(z)), s(s(s(elem!1)))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2602])).
% 0.88/1.12 tff(2604,plain,
% 0.88/1.12 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[1257, 2603])).
% 0.88/1.12 tff(2605,plain,
% 0.88/1.12 (b(s(s(z)), s(s(s(elem!1))))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[188, 51, 185, 2604])).
% 0.88/1.12 tff(2606,plain,
% 0.88/1.12 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2597])).
% 0.88/1.12 tff(2607,plain,
% 0.88/1.12 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2606])).
% 0.88/1.12 tff(2608,plain,
% 0.88/1.12 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.12 inference(modus_ponens,[status(thm)],[529, 2607])).
% 0.88/1.12 tff(2609,plain,
% 0.88/1.12 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[223, 2608, 545])).
% 0.88/1.12 tff(2610,plain,
% 0.88/1.12 ($false),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2562, 238, 2609, 2605, 2601, 2591])).
% 0.88/1.12 tff(2611,plain,((~(elem!1 = s(s(elem!1)))) | (elem!1 = s(s(z))) | (~r(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(elem!1, s(z)) | (~r(s(elem!1), s(z))) | r(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.88/1.12 tff(2612,plain,
% 0.88/1.12 (~(elem!1 = s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2611, 545, 169, 1974, 1400, 306, 2574])).
% 0.88/1.12 tff(2613,plain,
% 0.88/1.12 (~(s(elem!1) = s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[158, 2612])).
% 0.88/1.12 tff(2614,plain,
% 0.88/1.12 (b(s(elem!1), s(s(elem!1)))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[534, 2613, 2574])).
% 0.88/1.12 tff(2615,plain,
% 0.88/1.12 (~(elem!1 = s(elem!1))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[386, 2613])).
% 0.88/1.12 tff(2616,plain,
% 0.88/1.12 (~(s(s(elem!1)) = elem!1)),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[166, 2612])).
% 0.88/1.12 tff(2617,plain,
% 0.88/1.12 (~(s(z) = elem!1)),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[332, 330])).
% 0.88/1.12 tff(2618,plain,
% 0.88/1.12 (r(s(z), elem!1)),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[2468, 2617])).
% 0.88/1.12 tff(2619,plain,
% 0.88/1.12 (r(elem!1, s(z))),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[363, 330, 1400])).
% 0.88/1.12 tff(2620,plain,
% 0.88/1.12 (~(s(elem!1) = elem!1)),
% 0.88/1.12 inference(unit_resolution,[status(thm)],[393, 391])).
% 0.88/1.12 tff(2621,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2622,plain,
% 0.88/1.12 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.88/1.12 inference(rewrite,[status(thm)],[])).
% 0.88/1.12 tff(2623,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 0.88/1.12 inference(monotonicity,[status(thm)],[2622])).
% 0.88/1.12 tff(2624,plain,
% 0.88/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.98/1.12 inference(transitivity,[status(thm)],[2623, 2621])).
% 0.98/1.12 tff(2625,plain,
% 0.98/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))),
% 0.98/1.12 inference(quant_inst,[status(thm)],[])).
% 0.98/1.12 tff(2626,plain,
% 0.98/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[2625, 2624])).
% 0.98/1.12 tff(2627,plain,
% 0.98/1.12 (~r(s(elem!1), elem!1)),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2626, 124, 1370, 306])).
% 0.98/1.12 tff(2628,plain,
% 0.98/1.12 (b(s(elem!1), elem!1)),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[408, 2627, 2620])).
% 0.98/1.12 tff(2629,plain,
% 0.98/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.98/1.12 inference(rewrite,[status(thm)],[])).
% 0.98/1.12 tff(2630,plain,
% 0.98/1.12 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.98/1.12 inference(rewrite,[status(thm)],[])).
% 0.98/1.12 tff(2631,plain,
% 0.98/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 0.98/1.12 inference(monotonicity,[status(thm)],[2630])).
% 0.98/1.12 tff(2632,plain,
% 0.98/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.98/1.12 inference(transitivity,[status(thm)],[2631, 2629])).
% 0.98/1.12 tff(2633,plain,
% 0.98/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))))),
% 0.98/1.12 inference(quant_inst,[status(thm)],[])).
% 0.98/1.12 tff(2634,plain,
% 0.98/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 0.98/1.12 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 0.98/1.12 tff(2635,plain,
% 0.98/1.12 (~r(elem!1, s(elem!1))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[2634, 124, 1370, 306])).
% 0.98/1.12 tff(2636,plain,
% 0.98/1.12 (b(elem!1, s(elem!1))),
% 0.98/1.12 inference(unit_resolution,[status(thm)],[629, 2635, 391])).
% 0.98/1.12 tff(2637,plain,
% 0.98/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.98/1.12 inference(rewrite,[status(thm)],[])).
% 0.98/1.12 tff(2638,plain,
% 0.98/1.12 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2639,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2638])).
% 0.98/1.13 tff(2640,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2639, 2637])).
% 0.98/1.13 tff(2641,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.98/1.13 inference(quant_inst,[status(thm)],[])).
% 0.98/1.13 tff(2642,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2641, 2640])).
% 0.98/1.13 tff(2643,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2642, 238, 2636, 2628, 228, 288])).
% 0.98/1.13 tff(2644,plain,((~r(s(elem!1), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2645,plain,
% 0.98/1.13 (~b(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2644, 2619, 306, 391, 288])).
% 0.98/1.13 tff(2646,plain,
% 0.98/1.13 (r(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[255, 2645, 248])).
% 0.98/1.13 tff(2647,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[342, 2646, 2618, 160])).
% 0.98/1.13 tff(2648,plain,((elem!1 = s(z)) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | b(s(z), elem!1) | (~r(s(elem!1), s(z))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2649,plain,
% 0.98/1.13 (elem!1 = s(z)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2648, 2616, 160, 345, 306, 2615, 2614, 1400])).
% 0.98/1.13 tff(2650,plain,
% 0.98/1.13 (s(elem!1) = s(s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[280, 2649])).
% 0.98/1.13 tff(2651,plain,
% 0.98/1.13 (s(s(elem!1)) = s(s(s(z)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2650])).
% 0.98/1.13 tff(2652,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2651])).
% 0.98/1.13 tff(2653,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2652, 2347])).
% 0.98/1.13 tff(2654,plain,
% 0.98/1.13 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2653])).
% 0.98/1.13 tff(2655,plain,
% 0.98/1.13 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2654])).
% 0.98/1.13 tff(2656,plain,
% 0.98/1.13 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1092, 2655])).
% 0.98/1.13 tff(2657,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2658,plain,
% 0.98/1.13 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2659,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2658])).
% 0.98/1.13 tff(2660,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2659, 2657])).
% 0.98/1.13 tff(2661,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.98/1.13 inference(quant_inst,[status(thm)],[])).
% 0.98/1.13 tff(2662,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 0.98/1.13 tff(2663,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2662, 124, 160, 1711, 2008])).
% 0.98/1.13 tff(2664,plain,((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2665,plain,
% 0.98/1.13 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2664, 1711, 160])).
% 0.98/1.13 tff(2666,assumption,(~r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 0.98/1.13 tff(2667,plain,
% 0.98/1.13 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[276])).
% 0.98/1.13 tff(2668,plain,
% 0.98/1.13 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 0.98/1.13 inference(symmetry,[status(thm)],[2667])).
% 0.98/1.13 tff(2669,plain,
% 0.98/1.13 (r(s(elem!1), elem!1)),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[306, 2668])).
% 0.98/1.13 tff(2670,plain,
% 0.98/1.13 (b(s(elem!1), s(s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[534, 159, 2574])).
% 0.98/1.13 tff(2671,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[1420])).
% 0.98/1.13 tff(2672,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2671, 2347])).
% 0.98/1.13 tff(2673,plain,
% 0.98/1.13 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2672])).
% 0.98/1.13 tff(2674,plain,
% 0.98/1.13 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2673])).
% 0.98/1.13 tff(2675,plain,
% 0.98/1.13 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1092, 2674])).
% 0.98/1.13 tff(2676,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[281])).
% 0.98/1.13 tff(2677,plain,
% 0.98/1.13 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2676])).
% 0.98/1.13 tff(2678,plain,
% 0.98/1.13 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2677])).
% 0.98/1.13 tff(2679,plain,
% 0.98/1.13 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1729, 2678])).
% 0.98/1.13 tff(2680,plain,
% 0.98/1.13 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[281])).
% 0.98/1.13 tff(2681,plain,
% 0.98/1.13 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2680])).
% 0.98/1.13 tff(2682,plain,
% 0.98/1.13 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2681])).
% 0.98/1.13 tff(2683,plain,
% 0.98/1.13 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[1732, 2682])).
% 0.98/1.13 tff(2684,assumption,(~r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 0.98/1.13 tff(2685,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 0.98/1.13 tff(2686,plain,
% 0.98/1.13 (b(s(s(s(s(s(z))))), s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1118, 51, 2685, 2684])).
% 0.98/1.13 tff(2687,plain,
% 0.98/1.13 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2420, 51, 2666, 2417])).
% 0.98/1.13 tff(2688,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2689,plain,
% 0.98/1.13 (((~b(s(s(elem!1)), 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(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2690,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2689])).
% 0.98/1.13 tff(2691,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2690, 2688])).
% 0.98/1.13 tff(2692,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 0.98/1.13 inference(quant_inst,[status(thm)],[])).
% 0.98/1.13 tff(2693,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 0.98/1.13 tff(2694,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2693, 238, 289, 288, 2687, 2686])).
% 0.98/1.13 tff(2695,plain,(r(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(elem!1)) | r(s(s(s(s(s(z))))), s(s(elem!1))) | (s(s(s(s(s(z))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2696,plain,
% 0.98/1.13 (~b(s(s(elem!1)), s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2695, 2683, 2679, 2675, 2666, 2670])).
% 0.98/1.13 tff(2697,plain,
% 0.98/1.13 (r(s(s(elem!1)), s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[323, 2696, 272])).
% 0.98/1.13 tff(2698,plain,
% 0.98/1.13 (~r(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[403, 2697, 2669])).
% 0.98/1.13 tff(2699,plain,
% 0.98/1.13 (b(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[255, 2698, 167])).
% 0.98/1.13 tff(2700,plain,
% 0.98/1.13 (b(s(s(s(z))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1428, 2699, 276])).
% 0.98/1.13 tff(2701,plain,
% 0.98/1.13 (s(s(s(z))) = s(s(elem!1))),
% 0.98/1.13 inference(symmetry,[status(thm)],[1420])).
% 0.98/1.13 tff(2702,plain,
% 0.98/1.13 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2701])).
% 0.98/1.13 tff(2703,plain,
% 0.98/1.13 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2702])).
% 0.98/1.13 tff(2704,plain,
% 0.98/1.13 (b(s(s(z)), s(s(s(z))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2226, 2703])).
% 0.98/1.13 tff(2705,plain,
% 0.98/1.13 (b(elem!1, s(s(s(elem!1))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[546, 1355])).
% 0.98/1.13 tff(2706,plain,
% 0.98/1.13 (~(s(s(s(elem!1))) = elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[516, 1365])).
% 0.98/1.13 tff(2707,plain,
% 0.98/1.13 (~r(elem!1, s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[599, 2697, 2249])).
% 0.98/1.13 tff(2708,plain,
% 0.98/1.13 (b(elem!1, s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[629, 2707, 387])).
% 0.98/1.13 tff(2709,plain,
% 0.98/1.13 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1397, 210, 307])).
% 0.98/1.13 tff(2710,plain,
% 0.98/1.13 (b(s(s(s(elem!1))), s(elem!1))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[459, 2709, 421])).
% 0.98/1.13 tff(2711,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2712,plain,
% 0.98/1.13 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2713,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2712])).
% 0.98/1.13 tff(2714,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2713, 2711])).
% 0.98/1.13 tff(2715,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.98/1.13 inference(quant_inst,[status(thm)],[])).
% 0.98/1.13 tff(2716,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 0.98/1.13 tff(2717,plain,
% 0.98/1.13 ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2716, 238])).
% 0.98/1.13 tff(2718,plain,
% 0.98/1.13 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2717, 2710, 543, 631])).
% 0.98/1.13 tff(2719,plain,
% 0.98/1.13 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1203, 2710, 631, 150, 823, 210])).
% 0.98/1.13 tff(2720,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[539, 2719, 2718, 415])).
% 0.98/1.13 tff(2721,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2722,plain,
% 0.98/1.13 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2721, 2708, 150, 2706, 2705, 2697])).
% 0.98/1.13 tff(2723,plain,
% 0.98/1.13 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[223, 2722, 545])).
% 0.98/1.13 tff(2724,plain,
% 0.98/1.13 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2405, 2723, 281])).
% 0.98/1.13 tff(2725,plain,
% 0.98/1.13 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2395, 238, 2724, 2704, 2700])).
% 0.98/1.13 tff(2726,plain,
% 0.98/1.13 (r(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1564, 2725])).
% 0.98/1.13 tff(2727,plain,
% 0.98/1.13 (~r(s(s(s(s(z)))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1554, 2726, 169])).
% 0.98/1.13 tff(2728,plain,
% 0.98/1.13 (b(s(s(s(s(z)))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1623, 2727, 1619])).
% 0.98/1.13 tff(2729,plain,
% 0.98/1.13 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2268])).
% 0.98/1.13 tff(2730,plain,
% 0.98/1.13 (b(s(z), s(s(s(s(z)))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[546, 2729])).
% 0.98/1.13 tff(2731,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2732,plain,
% 0.98/1.13 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.98/1.13 inference(rewrite,[status(thm)],[])).
% 0.98/1.13 tff(2733,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2732])).
% 0.98/1.13 tff(2734,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2733, 2731])).
% 0.98/1.13 tff(2735,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.98/1.13 inference(quant_inst,[status(thm)],[])).
% 0.98/1.13 tff(2736,plain,
% 0.98/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 0.98/1.13 tff(2737,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2736, 238, 2724, 2730, 2728, 2700])).
% 0.98/1.13 tff(2738,plain,((~(elem!1 = s(z))) | (~r(s(s(z)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(s(s(z))))), s(s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2739,plain,
% 0.98/1.13 (~(elem!1 = s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2738, 150, 545, 169, 2666, 546, 1732, 160, 306])).
% 0.98/1.13 tff(2740,plain,
% 0.98/1.13 (~(s(z) = elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[332, 2739])).
% 0.98/1.13 tff(2741,plain,
% 0.98/1.13 (r(s(z), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2468, 2740])).
% 0.98/1.13 tff(2742,plain,
% 0.98/1.13 (r(elem!1, s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[363, 2739, 1400])).
% 0.98/1.13 tff(2743,plain,
% 0.98/1.13 (~b(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2644, 2742, 306, 387, 2670])).
% 0.98/1.13 tff(2744,plain,
% 0.98/1.13 (r(s(s(elem!1)), elem!1)),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[255, 2743, 167])).
% 0.98/1.13 tff(2745,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[342, 2744, 2741, 160])).
% 0.98/1.13 tff(2746,plain,((elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | b(s(z), elem!1) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | r(s(s(s(s(s(z))))), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2747,plain,
% 0.98/1.13 ($false),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2746, 1726, 2665, 345, 306, 1400, 545, 169, 160, 546, 150])).
% 0.98/1.13 tff(2748,plain,((~r(s(s(s(s(s(z))))), s(z))) | b(s(z), elem!1) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.13 tff(2749,plain,
% 0.98/1.13 (~r(s(s(s(s(s(z))))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2748, 545, 306, 1400, 345, 169, 160, 546, 2612])).
% 0.98/1.13 tff(2750,plain,
% 0.98/1.13 (b(s(s(s(s(s(z))))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[1781, 2749])).
% 0.98/1.13 tff(2751,plain,
% 0.98/1.13 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2651])).
% 0.98/1.13 tff(2752,plain,
% 0.98/1.13 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2751])).
% 0.98/1.13 tff(2753,plain,
% 0.98/1.13 ((s(z) = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2651])).
% 0.98/1.13 tff(2754,plain,
% 0.98/1.13 ((s(z) = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 0.98/1.13 inference(transitivity,[status(thm)],[2753, 2336])).
% 0.98/1.13 tff(2755,plain,
% 0.98/1.13 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(z)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2754])).
% 0.98/1.13 tff(2756,plain,
% 0.98/1.13 (~(s(s(s(z))) = s(z))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[41, 2755])).
% 0.98/1.13 tff(2757,plain,
% 0.98/1.13 (s(s(s(z))) = s(s(elem!1))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2651])).
% 0.98/1.13 tff(2758,plain,
% 0.98/1.13 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2757])).
% 0.98/1.13 tff(2759,plain,
% 0.98/1.13 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 0.98/1.13 inference(symmetry,[status(thm)],[2758])).
% 0.98/1.13 tff(2760,plain,
% 0.98/1.13 (b(s(s(z)), s(s(s(z))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[2226, 2759])).
% 0.98/1.13 tff(2761,plain,
% 0.98/1.13 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2651])).
% 0.98/1.13 tff(2762,plain,
% 0.98/1.13 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 0.98/1.13 inference(monotonicity,[status(thm)],[2761])).
% 0.98/1.13 tff(2763,plain,
% 0.98/1.13 (b(s(z), s(s(s(s(z)))))),
% 0.98/1.13 inference(modus_ponens,[status(thm)],[546, 2762])).
% 0.98/1.13 tff(2764,plain,
% 0.98/1.13 (~r(s(s(s(s(z)))), s(z))),
% 0.98/1.13 inference(unit_resolution,[status(thm)],[2444, 1783, 160, 1380, 545, 114, 169, 375, 227])).
% 0.98/1.13 tff(2765,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.98/1.13 tff(2766,plain,
% 0.98/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), z)) | (~b(z, s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2767,plain,
% 0.98/1.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2768,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), z)) | (~b(z, s(z)))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2767])).
% 0.98/1.14 tff(2769,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), z)) | (~b(z, s(z))))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2768, 2766])).
% 0.98/1.14 tff(2770,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2771,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), z)) | (~b(z, s(z)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 0.98/1.14 tff(2772,plain,
% 0.98/1.14 (~b(s(s(s(s(z)))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2771, 238, 2765, 1457, 1784])).
% 0.98/1.14 tff(2773,plain,
% 0.98/1.14 (r(s(s(s(s(z)))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1499, 51, 726, 2772])).
% 0.98/1.14 tff(2774,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2775,plain,
% 0.98/1.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2776,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2775])).
% 0.98/1.14 tff(2777,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2776, 2774])).
% 0.98/1.14 tff(2778,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2779,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 0.98/1.14 tff(2780,plain,
% 0.98/1.14 (~b(s(s(s(s(s(z))))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2779, 238, 2765, 1457, 1783])).
% 0.98/1.14 tff(2781,plain,
% 0.98/1.14 (r(s(s(s(s(s(z))))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 2780])).
% 0.98/1.14 tff(2782,plain,
% 0.98/1.14 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[1898, 1009])).
% 0.98/1.14 tff(2783,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2784,plain,
% 0.98/1.14 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2785,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2784])).
% 0.98/1.14 tff(2786,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2785, 2783])).
% 0.98/1.14 tff(2787,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2788,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 0.98/1.14 tff(2789,plain,
% 0.98/1.14 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2788, 238, 2765, 1784, 1783])).
% 0.98/1.14 tff(2790,plain,
% 0.98/1.14 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1051, 51, 2789, 2782])).
% 0.98/1.14 tff(2791,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2792,plain,
% 0.98/1.14 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2793,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2792])).
% 0.98/1.14 tff(2794,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2793, 2791])).
% 0.98/1.14 tff(2795,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2796,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 0.98/1.14 tff(2797,plain,
% 0.98/1.14 ($false),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2796, 124, 2790, 2781, 2773])).
% 0.98/1.14 tff(2798,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.14 tff(2799,plain,
% 0.98/1.14 (~b(s(s(s(s(z)))), s(z))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2798, 1783, 2765, 1457])).
% 0.98/1.14 tff(2800,plain,
% 0.98/1.14 ($false),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1623, 2799, 2764, 1619])).
% 0.98/1.14 tff(2801,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.14 tff(2802,plain,
% 0.98/1.14 (~b(z, s(z))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2801, 2750, 2763, 160, 1380, 545, 114, 169, 2650, 2226])).
% 0.98/1.14 tff(2803,plain,
% 0.98/1.14 (r(z, s(z))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1542, 2802])).
% 0.98/1.14 tff(2804,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2805,plain,
% 0.98/1.14 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2806,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2805])).
% 0.98/1.14 tff(2807,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2806, 2804])).
% 0.98/1.14 tff(2808,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2809,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 0.98/1.14 tff(2810,plain,
% 0.98/1.14 (~r(s(s(z)), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2809, 124, 169, 1545])).
% 0.98/1.14 tff(2811,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2812,plain,
% 0.98/1.14 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2813,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2812])).
% 0.98/1.14 tff(2814,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2813, 2811])).
% 0.98/1.14 tff(2815,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2816,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2815, 2814])).
% 0.98/1.14 tff(2817,plain,
% 0.98/1.14 (~r(z, s(s(s(z))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2816, 124, 2288, 1545])).
% 0.98/1.14 tff(2818,plain,
% 0.98/1.14 (b(z, s(s(s(z))))),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1474, 2817, 1470])).
% 0.98/1.14 tff(2819,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.98/1.14 tff(2820,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2821,plain,
% 0.98/1.14 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2822,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2821])).
% 0.98/1.14 tff(2823,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2822, 2820])).
% 0.98/1.14 tff(2824,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2825,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 0.98/1.14 tff(2826,plain,
% 0.98/1.14 ($false),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2825, 124, 2819, 2288, 1545])).
% 0.98/1.14 tff(2827,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.14 tff(2828,plain,
% 0.98/1.14 (~r(s(s(s(z))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2827, 1545, 2288])).
% 0.98/1.14 tff(2829,plain,
% 0.98/1.14 (b(s(s(s(z))), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[1524, 2828])).
% 0.98/1.14 tff(2830,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2831,plain,
% 0.98/1.14 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2832,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 0.98/1.14 inference(monotonicity,[status(thm)],[2831])).
% 0.98/1.14 tff(2833,plain,
% 0.98/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.98/1.14 inference(transitivity,[status(thm)],[2832, 2830])).
% 0.98/1.14 tff(2834,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.14 tff(2835,plain,
% 0.98/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 0.98/1.14 inference(modus_ponens,[status(thm)],[2834, 2833])).
% 0.98/1.14 tff(2836,plain,
% 0.98/1.14 (~b(s(s(z)), z)),
% 0.98/1.14 inference(unit_resolution,[status(thm)],[2835, 238, 2829, 2388, 2818])).
% 0.98/1.14 tff(2837,plain,
% 0.98/1.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.98/1.14 inference(rewrite,[status(thm)],[])).
% 0.98/1.14 tff(2838,plain,
% 0.98/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.98/1.14 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(2839,plain,
% 0.98/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 0.98/1.15 tff(2840,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2839, 51, 1449, 2836, 2810])).
% 0.98/1.15 tff(2841,plain,((~r(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2842,plain,
% 0.98/1.15 (~r(s(s(s(z))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2841, 2803, 2760, 169])).
% 0.98/1.15 tff(2843,plain,
% 0.98/1.15 (b(s(s(s(z))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2344, 2842, 2756])).
% 0.98/1.15 tff(2844,plain,
% 0.98/1.15 (b(s(s(elem!1)), s(z))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2843, 2752])).
% 0.98/1.15 tff(2845,plain,
% 0.98/1.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2441, 2844, 2750, 160, 2656, 1380])).
% 0.98/1.15 tff(2846,plain,
% 0.98/1.15 (~r(s(s(s(s(z)))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2444, 2750, 160, 1380, 545, 114, 169, 2650, 2226])).
% 0.98/1.15 tff(2847,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[1623, 2846, 1619])).
% 0.98/1.15 tff(2848,plain,
% 0.98/1.15 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2736, 238, 2763, 2847, 2843])).
% 0.98/1.15 tff(2849,plain,
% 0.98/1.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2405, 2848, 2650])).
% 0.98/1.15 tff(2850,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[223, 2849, 2845, 545])).
% 0.98/1.15 tff(2851,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | b(s(z), elem!1) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2852,plain,
% 0.98/1.15 (~r(s(s(z)), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2851, 2573, 1380, 544, 114, 1816, 1400, 345, 2566])).
% 0.98/1.15 tff(2853,plain,
% 0.98/1.15 (b(s(s(z)), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[79, 2852])).
% 0.98/1.15 tff(2854,plain,
% 0.98/1.15 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[375])).
% 0.98/1.15 tff(2855,plain,
% 0.98/1.15 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2854])).
% 0.98/1.15 tff(2856,plain,
% 0.98/1.15 (b(s(elem!1), s(z))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[1817, 2855])).
% 0.98/1.15 tff(2857,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[1808, 2856])).
% 0.98/1.15 tff(2858,plain,((~(s(elem!1) = s(s(z)))) | b(s(elem!1), s(z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2859,plain,
% 0.98/1.15 (~(s(elem!1) = s(s(z)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2858, 2853, 1808])).
% 0.98/1.15 tff(2860,plain,
% 0.98/1.15 (~(elem!1 = s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[280, 2859])).
% 0.98/1.15 tff(2861,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2648, 2670, 167, 160, 345, 306, 330, 387, 1400])).
% 0.98/1.15 tff(2862,plain,((elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | b(s(z), elem!1) | (~r(s(elem!1), s(z))) | (elem!1 = s(z)) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2863,plain,
% 0.98/1.15 (elem!1 = s(s(elem!1))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2862, 544, 345, 1816, 2860, 1400])).
% 0.98/1.15 tff(2864,plain,
% 0.98/1.15 (s(elem!1) = s(s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2097, 2863])).
% 0.98/1.15 tff(2865,plain,
% 0.98/1.15 (s(s(s(elem!1))) = s(elem!1)),
% 0.98/1.15 inference(symmetry,[status(thm)],[2864])).
% 0.98/1.15 tff(2866,plain,
% 0.98/1.15 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2865])).
% 0.98/1.15 tff(2867,plain,
% 0.98/1.15 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2866])).
% 0.98/1.15 tff(2868,plain,
% 0.98/1.15 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2867])).
% 0.98/1.15 tff(2869,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 0.98/1.15 inference(commutativity,[status(thm)],[])).
% 0.98/1.15 tff(2870,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2865])).
% 0.98/1.15 tff(2871,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(s(z)))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2870, 2869])).
% 0.98/1.15 tff(2872,plain,
% 0.98/1.15 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2871])).
% 0.98/1.15 tff(2873,plain,
% 0.98/1.15 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2102])).
% 0.98/1.15 tff(2874,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.98/1.15 tff(2875,plain,
% 0.98/1.15 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2874])).
% 0.98/1.15 tff(2876,plain,
% 0.98/1.15 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2875, 2873])).
% 0.98/1.15 tff(2877,plain,
% 0.98/1.15 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2106, 410])).
% 0.98/1.15 tff(2878,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2877, 2876])).
% 0.98/1.15 tff(2879,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2880,plain,
% 0.98/1.15 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2879, 2864])).
% 0.98/1.15 tff(2881,plain,
% 0.98/1.15 (~(s(elem!1) = s(s(s(s(z)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2880, 2872])).
% 0.98/1.15 tff(2882,plain,
% 0.98/1.15 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2881, 2868])).
% 0.98/1.15 tff(2883,plain,
% 0.98/1.15 (s(s(elem!1)) = elem!1),
% 0.98/1.15 inference(symmetry,[status(thm)],[2863])).
% 0.98/1.15 tff(2884,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2883])).
% 0.98/1.15 tff(2885,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2884])).
% 0.98/1.15 tff(2886,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2883])).
% 0.98/1.15 tff(2887,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2886, 767])).
% 0.98/1.15 tff(2888,plain,
% 0.98/1.15 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.98/1.15 inference(transitivity,[status(thm)],[2887, 789])).
% 0.98/1.15 tff(2889,plain,
% 0.98/1.15 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2888])).
% 0.98/1.15 tff(2890,assumption,(s(s(s(s(z)))) = s(s(elem!1))), introduced(assumption)).
% 0.98/1.15 tff(2891,plain,
% 0.98/1.15 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2890])).
% 0.98/1.15 tff(2892,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[1380, 2891])).
% 0.98/1.15 tff(2893,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2894,plain,
% 0.98/1.15 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2893, 1380])).
% 0.98/1.15 tff(2895,plain,
% 0.98/1.15 (~(s(s(s(s(z)))) = elem!1)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2894, 2889])).
% 0.98/1.15 tff(2896,plain,
% 0.98/1.15 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2883])).
% 0.98/1.15 tff(2897,plain,
% 0.98/1.15 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2896])).
% 0.98/1.15 tff(2898,plain,
% 0.98/1.15 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2883])).
% 0.98/1.15 tff(2899,plain,
% 0.98/1.15 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2898])).
% 0.98/1.15 tff(2900,plain,
% 0.98/1.15 (r(elem!1, s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[363, 2860, 1400])).
% 0.98/1.15 tff(2901,plain,
% 0.98/1.15 (~r(s(elem!1), elem!1)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2626, 124, 2900, 1816])).
% 0.98/1.15 tff(2902,plain,
% 0.98/1.15 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 0.98/1.15 inference(symmetry,[status(thm)],[388])).
% 0.98/1.15 tff(2903,plain,
% 0.98/1.15 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2863])).
% 0.98/1.15 tff(2904,plain,
% 0.98/1.15 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2903, 267])).
% 0.98/1.15 tff(2905,plain,
% 0.98/1.15 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(elem!1))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2904])).
% 0.98/1.15 tff(2906,plain,
% 0.98/1.15 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2864])).
% 0.98/1.15 tff(2907,plain,
% 0.98/1.15 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2906])).
% 0.98/1.15 tff(2908,plain,
% 0.98/1.15 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = elem!1)),
% 0.98/1.15 inference(transitivity,[status(thm)],[2907, 2905, 2902])).
% 0.98/1.15 tff(2909,plain,
% 0.98/1.15 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(elem!1) = elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2908])).
% 0.98/1.15 tff(2910,plain,
% 0.98/1.15 (~(s(elem!1) = elem!1)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2573, 2909])).
% 0.98/1.15 tff(2911,plain,
% 0.98/1.15 (b(s(elem!1), elem!1)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[408, 2910, 2901])).
% 0.98/1.15 tff(2912,plain,
% 0.98/1.15 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2863])).
% 0.98/1.15 tff(2913,plain,
% 0.98/1.15 (r(s(s(elem!1)), s(z))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2900, 2912])).
% 0.98/1.15 tff(2914,plain,
% 0.98/1.15 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2864])).
% 0.98/1.15 tff(2915,plain,
% 0.98/1.15 (r(s(s(s(elem!1))), s(z))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[1816, 2914])).
% 0.98/1.15 tff(2916,plain,
% 0.98/1.15 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2864])).
% 0.98/1.15 tff(2917,plain,
% 0.98/1.15 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[682])).
% 0.98/1.15 tff(2918,plain,
% 0.98/1.15 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.98/1.15 inference(transitivity,[status(thm)],[826, 2917, 88])).
% 0.98/1.15 tff(2919,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[545, 2918])).
% 0.98/1.15 tff(2920,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2921,plain,
% 0.98/1.15 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2920, 2573])).
% 0.98/1.15 tff(2922,plain,
% 0.98/1.15 (~r(elem!1, s(elem!1))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2634, 124, 2900, 1816])).
% 0.98/1.15 tff(2923,plain,
% 0.98/1.15 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2873])).
% 0.98/1.15 tff(2924,plain,
% 0.98/1.15 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2923, 2301])).
% 0.98/1.15 tff(2925,plain,
% 0.98/1.15 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2924, 2528])).
% 0.98/1.15 tff(2926,plain,
% 0.98/1.15 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2925])).
% 0.98/1.15 tff(2927,plain,
% 0.98/1.15 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[777, 2926])).
% 0.98/1.15 tff(2928,plain,
% 0.98/1.15 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[410])).
% 0.98/1.15 tff(2929,plain,
% 0.98/1.15 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2928])).
% 0.98/1.15 tff(2930,plain,
% 0.98/1.15 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[317, 2929])).
% 0.98/1.15 tff(2931,plain,
% 0.98/1.15 (elem!1 = s(s(elem!1))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[414, 410])).
% 0.98/1.15 tff(2932,plain,
% 0.98/1.15 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2931])).
% 0.98/1.15 tff(2933,plain,
% 0.98/1.15 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2932])).
% 0.98/1.15 tff(2934,plain,
% 0.98/1.15 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[410])).
% 0.98/1.15 tff(2935,plain,
% 0.98/1.15 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2934])).
% 0.98/1.15 tff(2936,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 0.98/1.15 tff(2937,plain,
% 0.98/1.15 (~r(elem!1, s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 0.98/1.15 tff(2938,plain,
% 0.98/1.15 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2937, 2933])).
% 0.98/1.15 tff(2939,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2549, 51, 2938, 2930, 2927])).
% 0.98/1.15 tff(2940,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(elem!1)) | r(elem!1, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2941,plain,
% 0.98/1.15 (b(s(s(elem!1)), s(elem!1))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2940, 2864, 2922, 2921])).
% 0.98/1.15 tff(2942,plain,
% 0.98/1.15 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2941, 2916])).
% 0.98/1.15 tff(2943,plain,
% 0.98/1.15 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2864])).
% 0.98/1.15 tff(2944,plain,
% 0.98/1.15 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2943])).
% 0.98/1.15 tff(2945,plain,
% 0.98/1.15 (~r(s(elem!1), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[526, 544, 1816])).
% 0.98/1.15 tff(2946,plain,
% 0.98/1.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2945, 2944])).
% 0.98/1.15 tff(2947,plain,
% 0.98/1.15 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[223, 2946, 2573])).
% 0.98/1.15 tff(2948,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2575])).
% 0.98/1.15 tff(2949,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.15 inference(symmetry,[status(thm)],[2948])).
% 0.98/1.15 tff(2950,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 0.98/1.15 tff(2951,plain,
% 0.98/1.15 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2575])).
% 0.98/1.15 tff(2952,plain,
% 0.98/1.15 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2951])).
% 0.98/1.15 tff(2953,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2954,plain,
% 0.98/1.15 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2955,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2954])).
% 0.98/1.15 tff(2956,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2955, 2953])).
% 0.98/1.15 tff(2957,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(2958,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2957, 2956])).
% 0.98/1.15 tff(2959,plain,
% 0.98/1.15 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2958, 124, 162, 1544])).
% 0.98/1.15 tff(2960,plain,
% 0.98/1.15 (~r(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2959, 2952])).
% 0.98/1.15 tff(2961,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), elem!1)),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2131, 2960, 2950])).
% 0.98/1.15 tff(2962,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2961, 2949])).
% 0.98/1.15 tff(2963,plain,
% 0.98/1.15 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2879, 2597])).
% 0.98/1.15 tff(2964,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.98/1.15 tff(2965,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2966,plain,
% 0.98/1.15 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2967,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2966])).
% 0.98/1.15 tff(2968,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2967, 2965])).
% 0.98/1.15 tff(2969,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(2970,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 0.98/1.15 tff(2971,plain,
% 0.98/1.15 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2970, 124, 1544, 2964])).
% 0.98/1.15 tff(2972,plain,
% 0.98/1.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2973,plain,
% 0.98/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(2974,plain,
% 0.98/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2973, 2972])).
% 0.98/1.15 tff(2975,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2974, 51, 2971, 2963])).
% 0.98/1.15 tff(2976,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2977,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.15 inference(quant_inst,[status(thm)],[])).
% 0.98/1.15 tff(2978,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 0.98/1.15 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 0.98/1.15 tff(2979,plain,
% 0.98/1.15 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2978, 238, 226, 744, 2975])).
% 0.98/1.15 tff(2980,plain,
% 0.98/1.15 ($false),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2979, 2962])).
% 0.98/1.15 tff(2981,plain,((~r(s(s(s(s(z)))), s(z))) | (~(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))))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.15 tff(2982,plain,
% 0.98/1.15 (~r(s(s(s(s(z)))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[2981, 2863, 2947, 2942, 2895, 2915, 2913])).
% 0.98/1.15 tff(2983,plain,
% 0.98/1.15 (b(s(s(s(s(z)))), s(z))),
% 0.98/1.15 inference(unit_resolution,[status(thm)],[1623, 2982, 1619])).
% 0.98/1.15 tff(2984,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2985,plain,
% 0.98/1.15 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(rewrite,[status(thm)],[])).
% 0.98/1.15 tff(2986,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 0.98/1.15 inference(monotonicity,[status(thm)],[2985])).
% 0.98/1.15 tff(2987,plain,
% 0.98/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.15 inference(transitivity,[status(thm)],[2986, 2984])).
% 0.98/1.15 tff(2988,plain,
% 0.98/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(2989,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[2988, 2987])).
% 0.98/1.16 tff(2990,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[2989, 238, 226, 546, 1784, 1041])).
% 0.98/1.16 tff(2991,plain,((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(2992,plain,
% 0.98/1.16 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[2991, 2947, 2566, 2983])).
% 0.98/1.16 tff(2993,plain,
% 0.98/1.16 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[2974, 51, 2992, 2880])).
% 0.98/1.16 tff(2994,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(2995,plain,
% 0.98/1.16 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(2996,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[2995])).
% 0.98/1.16 tff(2997,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[2996, 2994])).
% 0.98/1.16 tff(2998,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(2999,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 0.98/1.16 tff(3000,plain,
% 0.98/1.16 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[2999, 238, 2853, 2566, 2983])).
% 0.98/1.16 tff(3001,plain,
% 0.98/1.16 (r(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[1564, 3000])).
% 0.98/1.16 tff(3002,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 0.98/1.16 tff(3003,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3004,plain,
% 0.98/1.16 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3005,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3004])).
% 0.98/1.16 tff(3006,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3005, 3003])).
% 0.98/1.16 tff(3007,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3008,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3007, 3006])).
% 0.98/1.16 tff(3009,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3008, 124, 1546, 861, 3002])).
% 0.98/1.16 tff(3010,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(3011,plain,
% 0.98/1.16 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3010, 3001, 2993])).
% 0.98/1.16 tff(3012,plain,
% 0.98/1.16 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[2102])).
% 0.98/1.16 tff(3013,plain,
% 0.98/1.16 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.98/1.16 inference(symmetry,[status(thm)],[3012])).
% 0.98/1.16 tff(3014,plain,
% 0.98/1.16 (r(s(s(s(elem!1))), s(s(z)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[475, 3013])).
% 0.98/1.16 tff(3015,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 0.98/1.16 tff(3016,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3015, 3014])).
% 0.98/1.16 tff(3017,plain,(r(s(s(s(elem!1))), s(s(z))) | (~r(s(elem!1), s(s(z)))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(3018,plain,
% 0.98/1.16 (~r(s(elem!1), s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3017, 3011, 2864])).
% 0.98/1.16 tff(3019,plain,
% 0.98/1.16 (b(s(elem!1), s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[488, 3018, 2859])).
% 0.98/1.16 tff(3020,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3021,plain,
% 0.98/1.16 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3022,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3021])).
% 0.98/1.16 tff(3023,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3022, 3020])).
% 0.98/1.16 tff(3024,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3025,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 0.98/1.16 tff(3026,plain,
% 0.98/1.16 ($false),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3025, 238, 507, 1817, 490, 753])).
% 0.98/1.16 tff(3027,plain,((~b(elem!1, s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.16 tff(3028,plain,
% 0.98/1.16 (~b(elem!1, s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3027, 3019, 2853, 2911])).
% 0.98/1.16 tff(3029,plain,
% 0.98/1.16 (r(elem!1, s(s(z)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[763, 3028, 1974])).
% 0.98/1.16 tff(3030,plain,
% 0.98/1.16 (r(s(s(elem!1)), s(s(z)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3029, 2899])).
% 0.98/1.16 tff(3031,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3032,plain,
% 0.98/1.16 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3033,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3032])).
% 0.98/1.16 tff(3034,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3033, 3031])).
% 0.98/1.16 tff(3035,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3036,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 0.98/1.16 tff(3037,plain,
% 0.98/1.16 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3036, 124, 3001, 3030])).
% 0.98/1.16 tff(3038,plain,
% 0.98/1.16 (~r(s(s(s(s(z)))), elem!1)),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3037, 2897])).
% 0.98/1.16 tff(3039,plain,
% 0.98/1.16 (b(s(s(s(s(z)))), elem!1)),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[2131, 3038, 2895])).
% 0.98/1.16 tff(3040,plain,
% 0.98/1.16 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3039, 2885])).
% 0.98/1.16 tff(3041,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3042,plain,
% 0.98/1.16 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(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(s(s(z))))))) <=> ((~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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3043,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3042])).
% 0.98/1.16 tff(3044,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3043, 3041])).
% 0.98/1.16 tff(3045,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3046,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3045, 3044])).
% 0.98/1.16 tff(3047,plain,
% 0.98/1.16 ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3046, 238, 2947, 2942])).
% 0.98/1.16 tff(3048,plain,
% 0.98/1.16 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3047, 3040])).
% 0.98/1.16 tff(3049,plain,
% 0.98/1.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3050,plain,
% 0.98/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3051,plain,
% 0.98/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3050, 3049])).
% 0.98/1.16 tff(3052,plain,
% 0.98/1.16 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3051, 51, 3048])).
% 0.98/1.16 tff(3053,plain,
% 0.98/1.16 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3052, 2882])).
% 0.98/1.16 tff(3054,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3055,plain,
% 0.98/1.16 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3056,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3055])).
% 0.98/1.16 tff(3057,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3056, 3054])).
% 0.98/1.16 tff(3058,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3059,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3058, 3057])).
% 0.98/1.16 tff(3060,plain,
% 0.98/1.16 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3059, 238, 2853, 2566, 2983])).
% 0.98/1.16 tff(3061,plain,
% 0.98/1.16 (r(s(s(z)), s(s(s(s(z)))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[1603, 3060, 1599])).
% 0.98/1.16 tff(3062,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3063,plain,
% 0.98/1.16 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3064,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3063])).
% 0.98/1.16 tff(3065,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3064, 3062])).
% 0.98/1.16 tff(3066,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.98/1.16 inference(quant_inst,[status(thm)],[])).
% 0.98/1.16 tff(3067,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.98/1.16 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 0.98/1.16 tff(3068,plain,
% 0.98/1.16 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[3067, 124, 3061, 3053])).
% 0.98/1.16 tff(3069,plain,
% 0.98/1.16 (b(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.16 inference(unit_resolution,[status(thm)],[190, 3068])).
% 0.98/1.16 tff(3070,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3071,plain,
% 0.98/1.16 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(rewrite,[status(thm)],[])).
% 0.98/1.16 tff(3072,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.16 inference(monotonicity,[status(thm)],[3071])).
% 0.98/1.16 tff(3073,plain,
% 0.98/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.16 inference(transitivity,[status(thm)],[3072, 3070])).
% 0.98/1.16 tff(3074,plain,
% 0.98/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3075,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 0.98/1.17 tff(3076,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3075, 238, 2853, 2947, 2566, 3069])).
% 0.98/1.17 tff(3077,plain,(b(s(z), s(s(elem!1))) | b(s(z), elem!1) | b(elem!1, s(z)) | b(s(elem!1), s(z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3078,plain,
% 0.98/1.17 (b(s(z), s(s(elem!1)))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3077, 114, 1400, 1808, 1380, 345, 1081])).
% 0.98/1.17 tff(3079,plain,
% 0.98/1.17 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[2073])).
% 0.98/1.17 tff(3080,plain,
% 0.98/1.17 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 0.98/1.17 inference(symmetry,[status(thm)],[3079])).
% 0.98/1.17 tff(3081,plain,
% 0.98/1.17 (b(s(z), elem!1)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[1137, 3080])).
% 0.98/1.17 tff(3082,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[345, 3081])).
% 0.98/1.17 tff(3083,plain,((~(elem!1 = s(s(elem!1)))) | b(s(z), elem!1) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3084,plain,
% 0.98/1.17 (~(elem!1 = s(s(elem!1)))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3083, 3078, 345])).
% 0.98/1.17 tff(3085,plain,
% 0.98/1.17 (b(elem!1, s(elem!1))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[629, 2635, 387])).
% 0.98/1.17 tff(3086,plain,
% 0.98/1.17 (b(s(elem!1), elem!1)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[408, 2627, 394])).
% 0.98/1.17 tff(3087,plain,
% 0.98/1.17 (~b(z, s(z))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1872, 1836, 1817, 1828])).
% 0.98/1.17 tff(3088,plain,
% 0.98/1.17 (r(z, s(z))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1542, 3087])).
% 0.98/1.17 tff(3089,plain,
% 0.98/1.17 (~r(s(elem!1), z)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1880, 124, 306, 3088])).
% 0.98/1.17 tff(3090,plain,
% 0.98/1.17 (b(s(elem!1), z)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1884, 51, 39, 3089])).
% 0.98/1.17 tff(3091,plain,
% 0.98/1.17 (~b(s(s(s(s(z)))), s(z))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1930, 1836, 1817, 1828])).
% 0.98/1.17 tff(3092,plain,
% 0.98/1.17 (r(s(s(s(s(z)))), s(z))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1623, 3091, 1619])).
% 0.98/1.17 tff(3093,plain,
% 0.98/1.17 (~r(s(s(s(s(z)))), z)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1938, 124, 3092, 3088])).
% 0.98/1.17 tff(3094,plain,
% 0.98/1.17 (b(s(s(s(s(z)))), z)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1499, 51, 726, 3093])).
% 0.98/1.17 tff(3095,plain,
% 0.98/1.17 (~r(z, s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1571, 124, 3092, 3088])).
% 0.98/1.17 tff(3096,plain,
% 0.98/1.17 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1487, 51, 3095])).
% 0.98/1.17 tff(3097,plain,
% 0.98/1.17 (b(z, s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3096, 1454])).
% 0.98/1.17 tff(3098,plain,
% 0.98/1.17 (~b(s(elem!1), s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1949, 238, 3097, 3094, 3090])).
% 0.98/1.17 tff(3099,plain,
% 0.98/1.17 (~r(s(elem!1), s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1956, 124, 306, 3092])).
% 0.98/1.17 tff(3100,plain,
% 0.98/1.17 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[1960, 51, 3099])).
% 0.98/1.17 tff(3101,plain,
% 0.98/1.17 (s(elem!1) = s(s(s(s(z))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3100, 3098])).
% 0.98/1.17 tff(3102,plain,
% 0.98/1.17 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 0.98/1.17 inference(commutativity,[status(thm)],[])).
% 0.98/1.17 tff(3103,plain,
% 0.98/1.17 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 0.98/1.17 inference(symmetry,[status(thm)],[3102])).
% 0.98/1.17 tff(3104,plain,
% 0.98/1.17 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3103])).
% 0.98/1.17 tff(3105,plain,
% 0.98/1.17 (~(z = s(elem!1))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[39, 3104])).
% 0.98/1.17 tff(3106,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3107,plain,
% 0.98/1.17 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3108,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3107])).
% 0.98/1.17 tff(3109,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3108, 3106])).
% 0.98/1.17 tff(3110,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(elem!1))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3111,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 0.98/1.17 tff(3112,plain,
% 0.98/1.17 (~r(z, s(elem!1))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3111, 124, 306, 3088])).
% 0.98/1.17 tff(3113,plain,
% 0.98/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3114,plain,
% 0.98/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3115,plain,
% 0.98/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 0.98/1.17 tff(3116,plain,
% 0.98/1.17 ((z = s(elem!1)) | b(z, s(elem!1))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3115, 51, 3112])).
% 0.98/1.17 tff(3117,plain,
% 0.98/1.17 (b(z, s(elem!1))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3116, 3105])).
% 0.98/1.17 tff(3118,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3119,plain,
% 0.98/1.17 (((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3120,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3119])).
% 0.98/1.17 tff(3121,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3120, 3118])).
% 0.98/1.17 tff(3122,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3123,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3122, 3121])).
% 0.98/1.17 tff(3124,plain,
% 0.98/1.17 (~b(z, elem!1)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3123, 238, 631, 507, 3117])).
% 0.98/1.17 tff(3125,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3126,plain,
% 0.98/1.17 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3127,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3126])).
% 0.98/1.17 tff(3128,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3127, 3125])).
% 0.98/1.17 tff(3129,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3130,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 0.98/1.17 tff(3131,plain,
% 0.98/1.17 (~r(z, elem!1)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3130, 124, 1370, 3088])).
% 0.98/1.17 tff(3132,plain,
% 0.98/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3133,plain,
% 0.98/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3134,plain,
% 0.98/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3133, 3132])).
% 0.98/1.17 tff(3135,plain,
% 0.98/1.17 ((z = elem!1) | b(z, elem!1)),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3134, 51, 3131])).
% 0.98/1.17 tff(3136,plain,
% 0.98/1.17 (z = elem!1),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3135, 3124])).
% 0.98/1.17 tff(3137,plain,
% 0.98/1.17 (s(z) = s(elem!1)),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3136])).
% 0.98/1.17 tff(3138,plain,
% 0.98/1.17 (s(z) = s(s(s(s(z))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3137, 3101])).
% 0.98/1.17 tff(3139,plain,
% 0.98/1.17 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[798])).
% 0.98/1.17 tff(3140,plain,
% 0.98/1.17 (~(s(z) = s(s(s(s(z)))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[1619, 3139])).
% 0.98/1.17 tff(3141,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3140, 3138])).
% 0.98/1.17 tff(3142,plain,((~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3143,plain,
% 0.98/1.17 (~r(s(z), s(s(s(elem!1))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3142, 1817, 3086, 306, 1370, 3085, 1818])).
% 0.98/1.17 tff(3144,plain,
% 0.98/1.17 (b(s(z), s(s(s(elem!1))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[101, 3143])).
% 0.98/1.17 tff(3145,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3146,plain,
% 0.98/1.17 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3147,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3146])).
% 0.98/1.17 tff(3148,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3147, 3145])).
% 0.98/1.17 tff(3149,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3150,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 0.98/1.17 tff(3151,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3150, 238, 228, 1137, 226, 546])).
% 0.98/1.17 tff(3152,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3153,plain,
% 0.98/1.17 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3152, 228, 1137, 546])).
% 0.98/1.17 tff(3154,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3155,plain,
% 0.98/1.17 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3156,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3155])).
% 0.98/1.17 tff(3157,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3156, 3154])).
% 0.98/1.17 tff(3158,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3159,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 0.98/1.17 tff(3160,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3159, 238, 1817, 228, 1137, 227])).
% 0.98/1.17 tff(3161,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3162,plain,
% 0.98/1.17 (~b(s(s(z)), s(s(elem!1)))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3161, 228, 1817, 1137])).
% 0.98/1.17 tff(3163,plain,
% 0.98/1.17 (r(s(s(z)), s(s(elem!1)))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[135, 3162, 114])).
% 0.98/1.17 tff(3164,plain,
% 0.98/1.17 (b(s(s(s(elem!1))), s(elem!1))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[459, 421, 452])).
% 0.98/1.17 tff(3165,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3166,plain,
% 0.98/1.17 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3167,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3166])).
% 0.98/1.17 tff(3168,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3167, 3165])).
% 0.98/1.17 tff(3169,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3170,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 0.98/1.17 tff(3171,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3170, 238, 1817, 491, 546, 225])).
% 0.98/1.17 tff(3172,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.17 tff(3173,plain,
% 0.98/1.17 (~b(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3172, 3164, 546, 1817])).
% 0.98/1.17 tff(3174,plain,
% 0.98/1.17 (r(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[190, 3173])).
% 0.98/1.17 tff(3175,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3176,plain,
% 0.98/1.17 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.98/1.17 inference(rewrite,[status(thm)],[])).
% 0.98/1.17 tff(3177,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 0.98/1.17 inference(monotonicity,[status(thm)],[3176])).
% 0.98/1.17 tff(3178,plain,
% 0.98/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.98/1.17 inference(transitivity,[status(thm)],[3177, 3175])).
% 0.98/1.17 tff(3179,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.98/1.17 inference(quant_inst,[status(thm)],[])).
% 0.98/1.17 tff(3180,plain,
% 0.98/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 0.98/1.17 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 0.98/1.17 tff(3181,plain,
% 0.98/1.17 ($false),
% 0.98/1.17 inference(unit_resolution,[status(thm)],[3180, 124, 192, 210, 168])).
% 0.98/1.17 tff(3182,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3183,plain,
% 0.98/1.18 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3182, 3174, 192])).
% 0.98/1.18 tff(3184,plain,
% 0.98/1.18 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[223, 3183, 545])).
% 0.98/1.18 tff(3185,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3186,plain,
% 0.98/1.18 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3187,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3186])).
% 0.98/1.18 tff(3188,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3187, 3185])).
% 0.98/1.18 tff(3189,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3190,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 0.98/1.18 tff(3191,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3190, 238, 1137, 226, 546, 23])).
% 0.98/1.18 tff(3192,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3193,plain,
% 0.98/1.18 (~b(s(s(elem!1)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3192, 3184, 546, 1137])).
% 0.98/1.18 tff(3194,plain,
% 0.98/1.18 (~b(s(s(elem!1)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3152, 3184, 1137, 546])).
% 0.98/1.18 tff(3195,plain,
% 0.98/1.18 (r(s(s(elem!1)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[255, 3194, 167])).
% 0.98/1.18 tff(3196,plain,
% 0.98/1.18 (~r(s(s(elem!1)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[263, 3195, 1370])).
% 0.98/1.18 tff(3197,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[110, 51, 3196, 3193, 106])).
% 0.98/1.18 tff(3198,plain,((elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3199,plain,
% 0.98/1.18 (r(s(s(s(elem!1))), s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3198, 3163, 546, 1137, 150, 1370, 1817, 209])).
% 0.98/1.18 tff(3200,plain,
% 0.98/1.18 (~r(s(s(elem!1)), s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1397, 3199, 210])).
% 0.98/1.18 tff(3201,plain,
% 0.98/1.18 (b(s(s(elem!1)), s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[323, 3200, 272])).
% 0.98/1.18 tff(3202,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3203,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3204,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3203, 3202])).
% 0.98/1.18 tff(3205,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3204, 238, 631, 507, 3201, 228])).
% 0.98/1.18 tff(3206,plain,((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3207,plain,
% 0.98/1.18 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3206, 228, 507, 631, 546, 1137, 150, 1370, 1817, 114])).
% 0.98/1.18 tff(3208,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[223, 3207, 3153, 209])).
% 0.98/1.18 tff(3209,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3210,plain,
% 0.98/1.18 (~b(s(s(elem!1)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3209, 3144, 1137, 3086, 3085, 150, 1370, 1817, 114])).
% 0.98/1.18 tff(3211,plain,
% 0.98/1.18 (r(s(s(elem!1)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[255, 3210, 167])).
% 0.98/1.18 tff(3212,plain,
% 0.98/1.18 (~r(s(s(elem!1)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[263, 3211, 1370])).
% 0.98/1.18 tff(3213,plain,
% 0.98/1.18 (b(s(s(elem!1)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[110, 51, 3212, 106])).
% 0.98/1.18 tff(3214,plain,
% 0.98/1.18 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3192, 3213, 1137, 3144])).
% 0.98/1.18 tff(3215,plain,
% 0.98/1.18 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[223, 3214, 209])).
% 0.98/1.18 tff(3216,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3217,plain,
% 0.98/1.18 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3218,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3217])).
% 0.98/1.18 tff(3219,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3218, 3216])).
% 0.98/1.18 tff(3220,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3221,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 0.98/1.18 tff(3222,plain,
% 0.98/1.18 (~b(s(s(z)), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3221, 238, 1817, 3144, 3213])).
% 0.98/1.18 tff(3223,plain,
% 0.98/1.18 (r(s(s(z)), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[135, 3222, 114])).
% 0.98/1.18 tff(3224,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3225,plain,
% 0.98/1.18 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3226,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3225])).
% 0.98/1.18 tff(3227,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3226, 3224])).
% 0.98/1.18 tff(3228,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3229,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 0.98/1.18 tff(3230,plain,
% 0.98/1.18 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3229, 124, 3223, 3215])).
% 0.98/1.18 tff(3231,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 0.98/1.18 tff(3232,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1294, 51, 1291, 3015, 3231])).
% 0.98/1.18 tff(3233,plain,(r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3234,plain,
% 0.98/1.18 (b(s(s(s(elem!1))), s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3233, 3230])).
% 0.98/1.18 tff(3235,plain,
% 0.98/1.18 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3182, 3223, 3215])).
% 0.98/1.18 tff(3236,plain,
% 0.98/1.18 (b(s(s(z)), s(s(s(elem!1))))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[190, 3235])).
% 0.98/1.18 tff(3237,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3238,plain,
% 0.98/1.18 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3239,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3238])).
% 0.98/1.18 tff(3240,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3239, 3237])).
% 0.98/1.18 tff(3241,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3242,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3241, 3240])).
% 0.98/1.18 tff(3243,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3242, 238, 1817, 3144, 3236, 3234])).
% 0.98/1.18 tff(3244,plain,((~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3245,plain,
% 0.98/1.18 (~b(s(s(z)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3244, 2619, 1137, 114, 150, 306, 1818])).
% 0.98/1.18 tff(3246,plain,
% 0.98/1.18 (r(s(s(z)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[79, 3245])).
% 0.98/1.18 tff(3247,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3248,plain,
% 0.98/1.18 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3249,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3248])).
% 0.98/1.18 tff(3250,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3249, 3247])).
% 0.98/1.18 tff(3251,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3252,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3251, 3250])).
% 0.98/1.18 tff(3253,plain,
% 0.98/1.18 (~r(s(s(z)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3252, 124, 3246, 2619])).
% 0.98/1.18 tff(3254,plain,
% 0.98/1.18 (b(s(s(z)), elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1275, 3253, 374])).
% 0.98/1.18 tff(3255,plain,
% 0.98/1.18 (~(elem!1 = s(s(z)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[374, 1973])).
% 0.98/1.18 tff(3256,plain,
% 0.98/1.18 (~r(elem!1, s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[2461, 124, 3246, 2619])).
% 0.98/1.18 tff(3257,plain,
% 0.98/1.18 (b(elem!1, s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[763, 3256, 3255])).
% 0.98/1.18 tff(3258,plain,
% 0.98/1.18 (~(s(elem!1) = s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[379, 330])).
% 0.98/1.18 tff(3259,plain,
% 0.98/1.18 (~r(s(elem!1), s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[483, 3246, 306])).
% 0.98/1.18 tff(3260,plain,
% 0.98/1.18 (b(s(elem!1), s(s(z)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[488, 3259, 3258])).
% 0.98/1.18 tff(3261,plain,
% 0.98/1.18 (~r(elem!1, s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[2634, 124, 2619, 306])).
% 0.98/1.18 tff(3262,plain,
% 0.98/1.18 (b(elem!1, s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[629, 3261, 387])).
% 0.98/1.18 tff(3263,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3264,plain,
% 0.98/1.18 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.98/1.18 inference(rewrite,[status(thm)],[])).
% 0.98/1.18 tff(3265,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3264])).
% 0.98/1.18 tff(3266,plain,
% 0.98/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.98/1.18 inference(transitivity,[status(thm)],[3265, 3263])).
% 0.98/1.18 tff(3267,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 0.98/1.18 inference(quant_inst,[status(thm)],[])).
% 0.98/1.18 tff(3268,plain,
% 0.98/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3267, 3266])).
% 0.98/1.18 tff(3269,plain,
% 0.98/1.18 ($false),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3268, 238, 3262, 3260, 3257, 3254])).
% 0.98/1.18 tff(3270,plain,((elem!1 = s(z)) | (s(s(z)) = elem!1) | (~r(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.18 tff(3271,plain,
% 0.98/1.18 (elem!1 = s(z)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[3270, 1816, 1386, 3078, 114, 3084, 1815, 1400])).
% 0.98/1.18 tff(3272,plain,
% 0.98/1.18 (s(elem!1) = s(s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[280, 3271])).
% 0.98/1.18 tff(3273,plain,
% 0.98/1.18 (s(s(elem!1)) = s(s(s(z)))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3272])).
% 0.98/1.18 tff(3274,plain,
% 0.98/1.18 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3273])).
% 0.98/1.18 tff(3275,plain,
% 0.98/1.18 (b(s(z), s(s(s(z))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[3078, 3274])).
% 0.98/1.18 tff(3276,plain,
% 0.98/1.18 (~(s(s(elem!1)) = elem!1)),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[166, 3084])).
% 0.98/1.18 tff(3277,plain,
% 0.98/1.18 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[3271])).
% 0.98/1.18 tff(3278,plain,
% 0.98/1.18 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 0.98/1.18 inference(symmetry,[status(thm)],[3277])).
% 0.98/1.18 tff(3279,plain,
% 0.98/1.18 (r(s(elem!1), elem!1)),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1816, 3278])).
% 0.98/1.18 tff(3280,plain,
% 0.98/1.18 (~(s(elem!1) = s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[158, 3084])).
% 0.98/1.18 tff(3281,plain,
% 0.98/1.18 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[208, 3280])).
% 0.98/1.18 tff(3282,plain,
% 0.98/1.18 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[2231, 3272, 1081])).
% 0.98/1.18 tff(3283,plain,
% 0.98/1.18 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[1904, 3282])).
% 0.98/1.18 tff(3284,plain,
% 0.98/1.18 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[414, 3084])).
% 0.98/1.18 tff(3285,plain,
% 0.98/1.18 (~b(s(s(z)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[2858, 3272, 1808])).
% 0.98/1.18 tff(3286,plain,
% 0.98/1.18 (r(s(s(z)), s(z))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[79, 3285])).
% 0.98/1.18 tff(3287,plain,
% 0.98/1.18 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[1420])).
% 0.98/1.18 tff(3288,plain,
% 0.98/1.18 (b(s(z), s(s(s(z))))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1137, 3287])).
% 0.98/1.18 tff(3289,plain,
% 0.98/1.18 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.98/1.18 inference(monotonicity,[status(thm)],[276])).
% 0.98/1.18 tff(3290,plain,
% 0.98/1.18 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.98/1.18 inference(symmetry,[status(thm)],[3289])).
% 0.98/1.18 tff(3291,plain,
% 0.98/1.18 (b(elem!1, s(s(elem!1)))),
% 0.98/1.18 inference(modus_ponens,[status(thm)],[1137, 3290])).
% 0.98/1.18 tff(3292,plain,
% 0.98/1.18 (~r(s(elem!1), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[700, 301, 395])).
% 0.98/1.18 tff(3293,plain,
% 0.98/1.18 (b(s(elem!1), s(s(elem!1)))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[534, 3292, 206])).
% 0.98/1.18 tff(3294,plain,
% 0.98/1.18 (~(s(s(elem!1)) = s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[271, 206])).
% 0.98/1.18 tff(3295,plain,
% 0.98/1.18 (~r(s(s(elem!1)), s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[403, 301, 395])).
% 0.98/1.18 tff(3296,plain,
% 0.98/1.18 (b(s(s(elem!1)), s(elem!1))),
% 0.98/1.18 inference(unit_resolution,[status(thm)],[323, 3295, 3294])).
% 0.98/1.18 tff(3297,plain,
% 0.98/1.18 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[298, 3296, 226, 3293])).
% 0.98/1.19 tff(3298,plain,
% 0.98/1.19 (r(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[539, 3297, 418])).
% 0.98/1.19 tff(3299,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3300,plain,
% 0.98/1.19 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3301,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3300])).
% 0.98/1.19 tff(3302,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3301, 3299])).
% 0.98/1.19 tff(3303,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3304,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3303, 3302])).
% 0.98/1.19 tff(3305,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3304, 238, 1185, 543, 289, 226])).
% 0.98/1.19 tff(3306,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3307,plain,
% 0.98/1.19 (~b(elem!1, s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3306, 3296, 1185, 226])).
% 0.98/1.19 tff(3308,plain,
% 0.98/1.19 (r(elem!1, s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1319, 3307, 514])).
% 0.98/1.19 tff(3309,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3310,plain,
% 0.98/1.19 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3311,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3310])).
% 0.98/1.19 tff(3312,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3311, 3309])).
% 0.98/1.19 tff(3313,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3314,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3313, 3312])).
% 0.98/1.19 tff(3315,plain,
% 0.98/1.19 ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3314, 124])).
% 0.98/1.19 tff(3316,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3315, 3308, 3298, 395])).
% 0.98/1.19 tff(3317,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3318,plain,
% 0.98/1.19 (~r(s(s(elem!1)), elem!1)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3317, 226, 1365, 418, 3291, 395, 206])).
% 0.98/1.19 tff(3319,plain,
% 0.98/1.19 (b(s(s(elem!1)), elem!1)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[255, 3318, 248])).
% 0.98/1.19 tff(3320,plain,
% 0.98/1.19 (b(s(s(s(z))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1428, 3319, 276])).
% 0.98/1.19 tff(3321,plain,
% 0.98/1.19 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2405, 226, 281])).
% 0.98/1.19 tff(3322,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3323,plain,
% 0.98/1.19 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3324,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3323])).
% 0.98/1.19 tff(3325,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3324, 3322])).
% 0.98/1.19 tff(3326,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3327,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3326, 3325])).
% 0.98/1.19 tff(3328,plain,
% 0.98/1.19 (~b(s(s(s(s(z)))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3327, 238, 3321, 3320, 3288])).
% 0.98/1.19 tff(3329,plain,
% 0.98/1.19 (r(s(s(s(s(z)))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1623, 3328, 1619])).
% 0.98/1.19 tff(3330,plain,
% 0.98/1.19 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1554, 3329, 169])).
% 0.98/1.19 tff(3331,plain,
% 0.98/1.19 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[2268])).
% 0.98/1.19 tff(3332,plain,
% 0.98/1.19 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[285, 3331])).
% 0.98/1.19 tff(3333,plain,
% 0.98/1.19 (~b(s(z), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3152, 3319, 1137, 226])).
% 0.98/1.19 tff(3334,plain,
% 0.98/1.19 (r(elem!1, s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1368, 3333, 276])).
% 0.98/1.19 tff(3335,plain,
% 0.98/1.19 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3315, 3334, 395])).
% 0.98/1.19 tff(3336,plain,
% 0.98/1.19 (b(s(elem!1), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[539, 3335, 418])).
% 0.98/1.19 tff(3337,plain,
% 0.98/1.19 (b(s(s(z)), s(s(s(s(z)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3336, 3332])).
% 0.98/1.19 tff(3338,plain,
% 0.98/1.19 (r(s(z), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[101, 3333])).
% 0.98/1.19 tff(3339,plain,
% 0.98/1.19 (~r(s(z), s(s(s(s(s(z))))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2241, 3338, 1652, 1818])).
% 0.98/1.19 tff(3340,plain,
% 0.98/1.19 (b(s(z), s(s(s(s(s(z))))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1709, 3339])).
% 0.98/1.19 tff(3341,plain,
% 0.98/1.19 (~r(s(s(s(s(s(z))))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1826, 3338, 1818])).
% 0.98/1.19 tff(3342,plain,
% 0.98/1.19 (b(s(s(s(s(s(z))))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1781, 3341])).
% 0.98/1.19 tff(3343,plain,
% 0.98/1.19 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1435])).
% 0.98/1.19 tff(3344,plain,
% 0.98/1.19 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3343])).
% 0.98/1.19 tff(3345,plain,
% 0.98/1.19 ((~b(z, s(s(s(z))))) <=> (~b(z, s(s(elem!1))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3344])).
% 0.98/1.19 tff(3346,plain,
% 0.98/1.19 (~r(s(s(s(z))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2334, 1544, 375, 114, 169, 1501, 1587])).
% 0.98/1.19 tff(3347,plain,
% 0.98/1.19 (b(s(s(s(z))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2344, 3346, 2340])).
% 0.98/1.19 tff(3348,plain,
% 0.98/1.19 (~r(z, s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1595, 1544, 1501, 1587, 169])).
% 0.98/1.19 tff(3349,plain,
% 0.98/1.19 (b(z, s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1542, 3348])).
% 0.98/1.19 tff(3350,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3351,plain,
% 0.98/1.19 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3352,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3351])).
% 0.98/1.19 tff(3353,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3352, 3350])).
% 0.98/1.19 tff(3354,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3355,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3354, 3353])).
% 0.98/1.19 tff(3356,plain,
% 0.98/1.19 (~b(z, s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3355, 238, 3349, 1785, 3347])).
% 0.98/1.19 tff(3357,plain,
% 0.98/1.19 (~b(z, s(s(elem!1)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3356, 3345])).
% 0.98/1.19 tff(3358,plain,
% 0.98/1.19 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1435])).
% 0.98/1.19 tff(3359,plain,
% 0.98/1.19 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3358])).
% 0.98/1.19 tff(3360,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3361,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3362,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3361, 3360])).
% 0.98/1.19 tff(3363,plain,
% 0.98/1.19 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3362, 238, 1783, 3347, 1455])).
% 0.98/1.19 tff(3364,plain,
% 0.98/1.19 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1101, 3363])).
% 0.98/1.19 tff(3365,plain,
% 0.98/1.19 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3364, 3359])).
% 0.98/1.19 tff(3366,plain,
% 0.98/1.19 (~r(z, s(s(elem!1)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2050, 3348, 1783, 3365, 1785])).
% 0.98/1.19 tff(3367,plain,
% 0.98/1.19 (b(z, s(s(elem!1)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[2071, 3366])).
% 0.98/1.19 tff(3368,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3367, 3357])).
% 0.98/1.19 tff(3369,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3370,plain,
% 0.98/1.19 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3369, 3329, 281, 3342, 3340, 3337, 169, 3288, 114])).
% 0.98/1.19 tff(3371,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1564, 3370, 3330])).
% 0.98/1.19 tff(3372,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3373,plain,
% 0.98/1.19 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3372, 3286, 114, 3284, 3279, 3283, 1815, 3271, 3078, 3276, 3280])).
% 0.98/1.19 tff(3374,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[223, 3373, 3281])).
% 0.98/1.19 tff(3375,plain,
% 0.98/1.19 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3271])).
% 0.98/1.19 tff(3376,plain,
% 0.98/1.19 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3375])).
% 0.98/1.19 tff(3377,plain,
% 0.98/1.19 (b(elem!1, s(s(elem!1)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3078, 3376])).
% 0.98/1.19 tff(3378,plain,
% 0.98/1.19 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.98/1.19 inference(commutativity,[status(thm)],[])).
% 0.98/1.19 tff(3379,plain,
% 0.98/1.19 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3378])).
% 0.98/1.19 tff(3380,plain,
% 0.98/1.19 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3273])).
% 0.98/1.19 tff(3381,plain,
% 0.98/1.19 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3380, 3379])).
% 0.98/1.19 tff(3382,plain,
% 0.98/1.19 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3381])).
% 0.98/1.19 tff(3383,plain,
% 0.98/1.19 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[2894, 3382])).
% 0.98/1.19 tff(3384,plain,
% 0.98/1.19 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 0.98/1.19 inference(commutativity,[status(thm)],[])).
% 0.98/1.19 tff(3385,plain,
% 0.98/1.19 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[2268])).
% 0.98/1.19 tff(3386,plain,
% 0.98/1.19 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[276, 3385])).
% 0.98/1.19 tff(3387,plain,
% 0.98/1.19 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3386, 3384])).
% 0.98/1.19 tff(3388,plain,
% 0.98/1.19 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3387])).
% 0.98/1.19 tff(3389,plain,
% 0.98/1.19 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3388])).
% 0.98/1.19 tff(3390,plain,
% 0.98/1.19 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[728, 3389])).
% 0.98/1.19 tff(3391,plain,
% 0.98/1.19 (~r(s(z), s(s(s(elem!1))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1826, 1711, 1818])).
% 0.98/1.19 tff(3392,plain,
% 0.98/1.19 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[1626])).
% 0.98/1.19 tff(3393,plain,
% 0.98/1.19 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3392])).
% 0.98/1.19 tff(3394,plain,
% 0.98/1.19 (r(s(z), s(s(s(elem!1))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1650, 3393])).
% 0.98/1.19 tff(3395,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[63, 3394])).
% 0.98/1.19 tff(3396,plain,((~r(s(z), s(s(s(s(z)))))) | r(s(z), s(s(s(elem!1)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3397,plain,
% 0.98/1.19 (~r(s(z), s(s(s(s(z)))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3396, 3391, 281])).
% 0.98/1.19 tff(3398,plain,
% 0.98/1.19 (b(s(z), s(s(s(s(z)))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[893, 3397, 3140])).
% 0.98/1.19 tff(3399,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[276])).
% 0.98/1.19 tff(3400,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.98/1.19 inference(symmetry,[status(thm)],[3399])).
% 0.98/1.19 tff(3401,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[2268])).
% 0.98/1.19 tff(3402,plain,
% 0.98/1.19 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.98/1.19 inference(symmetry,[status(thm)],[3401])).
% 0.98/1.19 tff(3403,plain,
% 0.98/1.19 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.98/1.19 inference(transitivity,[status(thm)],[3402, 3400])).
% 0.98/1.19 tff(3404,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), elem!1)),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[1544, 3403])).
% 0.98/1.19 tff(3405,plain,
% 0.98/1.19 (~r(s(s(elem!1)), elem!1)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1182, 3404, 210])).
% 0.98/1.19 tff(3406,plain,
% 0.98/1.19 (b(s(s(elem!1)), elem!1)),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[255, 3405, 248])).
% 0.98/1.19 tff(3407,plain,
% 0.98/1.19 (b(s(s(s(z))), s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1428, 3406, 276])).
% 0.98/1.19 tff(3408,plain,
% 0.98/1.19 (~r(z, s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1595, 2281, 1544, 1565, 169])).
% 0.98/1.19 tff(3409,plain,
% 0.98/1.19 (b(z, s(z))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1542, 3408])).
% 0.98/1.19 tff(3410,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.98/1.19 tff(3411,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3412,plain,
% 0.98/1.19 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 0.98/1.19 inference(rewrite,[status(thm)],[])).
% 0.98/1.19 tff(3413,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[3412])).
% 0.98/1.19 tff(3414,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 0.98/1.19 inference(transitivity,[status(thm)],[3413, 3411])).
% 0.98/1.19 tff(3415,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.98/1.19 inference(quant_inst,[status(thm)],[])).
% 0.98/1.19 tff(3416,plain,
% 0.98/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 0.98/1.19 tff(3417,plain,
% 0.98/1.19 ($false),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3416, 238, 2765, 1457, 3410, 1456])).
% 0.98/1.19 tff(3418,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.19 tff(3419,plain,
% 0.98/1.19 (~b(z, s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[3418, 3409, 2765, 3407])).
% 0.98/1.19 tff(3420,plain,
% 0.98/1.19 (r(z, s(s(s(z))))),
% 0.98/1.19 inference(unit_resolution,[status(thm)],[1474, 3419, 1470])).
% 0.98/1.19 tff(3421,plain,
% 0.98/1.19 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 0.98/1.19 inference(monotonicity,[status(thm)],[2268, 1420])).
% 0.98/1.19 tff(3422,plain,
% 0.98/1.19 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.98/1.19 inference(modus_ponens,[status(thm)],[210, 3421])).
% 0.98/1.19 tff(3423,plain,
% 0.98/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3424,plain,
% 1.05/1.20 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3425,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3424])).
% 1.05/1.20 tff(3426,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3425, 3423])).
% 1.05/1.20 tff(3427,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3428,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3427, 3426])).
% 1.05/1.20 tff(3429,plain,
% 1.05/1.20 (~r(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3428, 124, 1544, 3422, 3420])).
% 1.05/1.20 tff(3430,plain,
% 1.05/1.20 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1487, 51, 3429])).
% 1.05/1.20 tff(3431,plain,
% 1.05/1.20 (b(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3430, 1454])).
% 1.05/1.20 tff(3432,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3433,plain,
% 1.05/1.20 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3434,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3433])).
% 1.05/1.20 tff(3435,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3434, 3432])).
% 1.05/1.20 tff(3436,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3437,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.05/1.20 tff(3438,plain,
% 1.05/1.20 ($false),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3437, 238, 1565, 2765, 3409, 3431])).
% 1.05/1.20 tff(3439,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.20 tff(3440,plain,
% 1.05/1.20 (~r(s(s(s(s(z)))), s(z))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3439, 3398, 276, 169, 248, 210])).
% 1.05/1.20 tff(3441,plain,
% 1.05/1.20 (b(s(s(s(s(z)))), s(z))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1623, 3440, 1619])).
% 1.05/1.20 tff(3442,plain,
% 1.05/1.20 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[1420])).
% 1.05/1.20 tff(3443,plain,
% 1.05/1.20 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.20 inference(symmetry,[status(thm)],[3442])).
% 1.05/1.20 tff(3444,plain,
% 1.05/1.20 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3443])).
% 1.05/1.20 tff(3445,plain,
% 1.05/1.20 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1764, 1691])).
% 1.05/1.20 tff(3446,plain,
% 1.05/1.20 (~r(z, s(z))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1759, 3445, 1711, 169])).
% 1.05/1.20 tff(3447,plain,
% 1.05/1.20 (b(z, s(z))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1542, 3446])).
% 1.05/1.20 tff(3448,plain,
% 1.05/1.20 (~r(s(z), s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1660, 1651, 1652])).
% 1.05/1.20 tff(3449,plain,
% 1.05/1.20 (b(s(z), s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[893, 3448, 3140])).
% 1.05/1.20 tff(3450,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3451,plain,
% 1.05/1.20 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3452,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3451])).
% 1.05/1.20 tff(3453,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3452, 3450])).
% 1.05/1.20 tff(3454,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3455,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.05/1.20 tff(3456,plain,
% 1.05/1.20 (~b(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3455, 238, 3449, 3447, 1784])).
% 1.05/1.20 tff(3457,plain,
% 1.05/1.20 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1487, 51, 3456])).
% 1.05/1.20 tff(3458,plain,
% 1.05/1.20 (r(z, s(s(s(s(z)))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3457, 1454])).
% 1.05/1.20 tff(3459,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3460,plain,
% 1.05/1.20 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3461,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3460])).
% 1.05/1.20 tff(3462,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3461, 3459])).
% 1.05/1.20 tff(3463,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3464,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3463, 3462])).
% 1.05/1.20 tff(3465,plain,
% 1.05/1.20 (~r(z, s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3464, 124, 1711, 1652, 3458])).
% 1.05/1.20 tff(3466,plain,
% 1.05/1.20 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1749, 51, 3465])).
% 1.05/1.20 tff(3467,plain,
% 1.05/1.20 (b(z, s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3466, 1715])).
% 1.05/1.20 tff(3468,plain,
% 1.05/1.20 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), 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))))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3469,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), 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)))))))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3468])).
% 1.05/1.20 tff(3470,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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))))))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3469, 1740])).
% 1.05/1.20 tff(3471,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3472,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), 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)))))))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 1.05/1.20 tff(3473,plain,
% 1.05/1.20 (~b(z, s(s(z)))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3472, 238, 1739, 3467, 3445])).
% 1.05/1.20 tff(3474,plain,
% 1.05/1.20 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1511, 51, 3473])).
% 1.05/1.20 tff(3475,plain,
% 1.05/1.20 (r(z, s(s(z)))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3474, 1450])).
% 1.05/1.20 tff(3476,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.05/1.20 tff(3477,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3478,plain,
% 1.05/1.20 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3479,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3478])).
% 1.05/1.20 tff(3480,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3479, 3477])).
% 1.05/1.20 tff(3481,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3482,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 1.05/1.20 tff(3483,plain,
% 1.05/1.20 ($false),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3482, 124, 1546, 3476, 1575])).
% 1.05/1.20 tff(3484,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.20 tff(3485,plain,
% 1.05/1.20 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3484, 3458, 3475])).
% 1.05/1.20 tff(3486,plain,
% 1.05/1.20 (b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1564, 3485])).
% 1.05/1.20 tff(3487,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3488,plain,
% 1.05/1.20 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3489,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.05/1.20 inference(monotonicity,[status(thm)],[3488])).
% 1.05/1.20 tff(3490,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.05/1.20 inference(transitivity,[status(thm)],[3489, 3487])).
% 1.05/1.20 tff(3491,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.20 inference(quant_inst,[status(thm)],[])).
% 1.05/1.20 tff(3492,plain,
% 1.05/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.05/1.20 inference(modus_ponens,[status(thm)],[3491, 3490])).
% 1.05/1.20 tff(3493,plain,
% 1.05/1.20 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[3492, 238, 3486, 1739, 3445])).
% 1.05/1.20 tff(3494,plain,
% 1.05/1.20 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.20 inference(unit_resolution,[status(thm)],[1051, 51, 3493, 2782])).
% 1.05/1.20 tff(3495,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.05/1.20 tff(3496,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.05/1.20 tff(3497,plain,
% 1.05/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.20 inference(rewrite,[status(thm)],[])).
% 1.05/1.20 tff(3498,plain,
% 1.05/1.20 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3499,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3498])).
% 1.05/1.21 tff(3500,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3499, 3497])).
% 1.05/1.21 tff(3501,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3502,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3501, 3500])).
% 1.05/1.21 tff(3503,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3502, 124, 3496, 3495, 1477])).
% 1.05/1.21 tff(3504,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3505,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3504, 3494, 3422])).
% 1.05/1.21 tff(3506,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3505, 3444])).
% 1.05/1.21 tff(3507,plain,
% 1.05/1.21 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.05/1.21 inference(symmetry,[status(thm)],[2268])).
% 1.05/1.21 tff(3508,plain,
% 1.05/1.21 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3507])).
% 1.05/1.21 tff(3509,plain,
% 1.05/1.21 (~b(s(s(s(s(z)))), z)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2771, 238, 3449, 3447, 1784])).
% 1.05/1.21 tff(3510,plain,
% 1.05/1.21 (r(s(s(s(s(z)))), z)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1499, 51, 726, 3509])).
% 1.05/1.21 tff(3511,plain,
% 1.05/1.21 (r(s(s(s(elem!1))), z)),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3510, 3508])).
% 1.05/1.21 tff(3512,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.05/1.21 tff(3513,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3514,plain,
% 1.05/1.21 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3515,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3514])).
% 1.05/1.21 tff(3516,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3515, 3513])).
% 1.05/1.21 tff(3517,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3518,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 1.05/1.21 tff(3519,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3518, 124, 210, 2026, 3512])).
% 1.05/1.21 tff(3520,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3521,plain,
% 1.05/1.21 (~r(z, s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3520, 3511, 210])).
% 1.05/1.21 tff(3522,plain,
% 1.05/1.21 (b(z, s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2071, 3521])).
% 1.05/1.21 tff(3523,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 1.05/1.21 tff(3524,plain,
% 1.05/1.21 (~b(z, s(s(elem!1)))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3523, 3345])).
% 1.05/1.21 tff(3525,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2078, 3524])).
% 1.05/1.21 tff(3526,plain,(b(z, s(s(s(z)))) | (~b(z, s(s(elem!1)))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3527,plain,
% 1.05/1.21 (b(z, s(s(s(z))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3526, 3522, 281])).
% 1.05/1.21 tff(3528,plain,
% 1.05/1.21 (~b(s(s(s(z))), s(z))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3418, 3449, 3447, 3527])).
% 1.05/1.21 tff(3529,plain,
% 1.05/1.21 (~b(s(s(elem!1)), elem!1)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1428, 3528, 276])).
% 1.05/1.21 tff(3530,plain,
% 1.05/1.21 (r(s(s(elem!1)), elem!1)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[255, 3529, 248])).
% 1.05/1.21 tff(3531,plain,
% 1.05/1.21 (~r(s(s(elem!1)), s(elem!1))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[403, 3530, 395])).
% 1.05/1.21 tff(3532,plain,
% 1.05/1.21 (b(s(s(elem!1)), s(elem!1))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[323, 3531, 3294])).
% 1.05/1.21 tff(3533,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[1726, 2682])).
% 1.05/1.21 tff(3534,plain,
% 1.05/1.21 (~r(s(elem!1), s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[700, 3530, 395])).
% 1.05/1.21 tff(3535,plain,
% 1.05/1.21 (b(s(elem!1), s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[534, 3534, 206])).
% 1.05/1.21 tff(3536,plain,
% 1.05/1.21 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2695, 3535, 2679, 2675, 3533, 3532])).
% 1.05/1.21 tff(3537,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3536, 3506])).
% 1.05/1.21 tff(3538,plain,((~r(s(z), s(s(s(s(s(z))))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3539,plain,
% 1.05/1.21 (~r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3538, 3441, 395, 248, 276, 1711, 1652, 210, 206, 169])).
% 1.05/1.21 tff(3540,plain,
% 1.05/1.21 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[2375, 1663])).
% 1.05/1.21 tff(3541,plain,
% 1.05/1.21 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.05/1.21 inference(symmetry,[status(thm)],[3540])).
% 1.05/1.21 tff(3542,plain,
% 1.05/1.21 ((~(elem!1 = s(s(s(s(elem!1)))))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3541])).
% 1.05/1.21 tff(3543,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.05/1.21 tff(3544,plain,
% 1.05/1.21 (~(s(z) = s(s(s(s(s(z))))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3543, 3542])).
% 1.05/1.21 tff(3545,plain,
% 1.05/1.21 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[2375, 1663])).
% 1.05/1.21 tff(3546,plain,
% 1.05/1.21 (b(elem!1, s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.21 inference(symmetry,[status(thm)],[3545])).
% 1.05/1.21 tff(3547,plain,
% 1.05/1.21 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(s(z), s(s(s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3546])).
% 1.05/1.21 tff(3548,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.05/1.21 tff(3549,plain,
% 1.05/1.21 (~b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3548, 3547])).
% 1.05/1.21 tff(3550,plain,
% 1.05/1.21 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1707, 51, 1704])).
% 1.05/1.21 tff(3551,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3550, 3549, 3544])).
% 1.05/1.21 tff(3552,plain,(b(elem!1, s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(s(z)))))) | (~(s(elem!1) = s(s(z)))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3553,plain,
% 1.05/1.21 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3552, 3539, 281, 3390])).
% 1.05/1.21 tff(3554,plain,
% 1.05/1.21 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3385, 1420])).
% 1.05/1.21 tff(3555,plain,
% 1.05/1.21 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3554])).
% 1.05/1.21 tff(3556,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.05/1.21 tff(3557,plain,
% 1.05/1.21 (~b(s(s(elem!1)), elem!1)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1428, 1425, 276])).
% 1.05/1.21 tff(3558,plain,
% 1.05/1.21 (r(s(s(elem!1)), elem!1)),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[255, 3557, 248])).
% 1.05/1.21 tff(3559,plain,
% 1.05/1.21 (~r(s(s(elem!1)), s(elem!1))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[403, 3558, 395])).
% 1.05/1.21 tff(3560,plain,
% 1.05/1.21 (b(s(s(elem!1)), s(elem!1))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[323, 3559, 275])).
% 1.05/1.21 tff(3561,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3562,plain,
% 1.05/1.21 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3563,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3562])).
% 1.05/1.21 tff(3564,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3563, 3561])).
% 1.05/1.21 tff(3565,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3566,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 1.05/1.21 tff(3567,plain,
% 1.05/1.21 ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3566, 238])).
% 1.05/1.21 tff(3568,plain,
% 1.05/1.21 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3567, 3560, 1185, 3556])).
% 1.05/1.21 tff(3569,plain,
% 1.05/1.21 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3568, 3555])).
% 1.05/1.21 tff(3570,plain,
% 1.05/1.21 ((s(z) = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[1420])).
% 1.05/1.21 tff(3571,plain,
% 1.05/1.21 ((s(z) = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3570, 2336])).
% 1.05/1.21 tff(3572,plain,
% 1.05/1.21 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(z)))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3571])).
% 1.05/1.21 tff(3573,plain,
% 1.05/1.21 (~(s(s(s(z))) = s(z))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[41, 3572])).
% 1.05/1.21 tff(3574,plain,
% 1.05/1.21 (r(s(s(s(z))), s(z))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2344, 1425, 3573])).
% 1.05/1.21 tff(3575,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3576,plain,
% 1.05/1.21 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3577,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3576])).
% 1.05/1.21 tff(3578,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3577, 3575])).
% 1.05/1.21 tff(3579,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3580,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 1.05/1.21 tff(3581,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3580, 124, 1711, 3574])).
% 1.05/1.21 tff(3582,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1099, 51, 3581, 3569, 1094])).
% 1.05/1.21 tff(3583,plain,(b(s(s(s(z))), s(z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3584,plain,
% 1.05/1.21 (b(s(s(s(z))), s(z))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3583, 3553, 1185, 1711, 3294, 395, 248, 276])).
% 1.05/1.21 tff(3585,plain,
% 1.05/1.21 (b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1709, 3539])).
% 1.05/1.21 tff(3586,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.05/1.21 tff(3587,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3588,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3589,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3588, 3587])).
% 1.05/1.21 tff(3590,plain,
% 1.05/1.21 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3589, 238, 3398, 3441, 3584])).
% 1.05/1.21 tff(3591,plain,
% 1.05/1.21 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[2324, 51])).
% 1.05/1.21 tff(3592,plain,
% 1.05/1.21 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3591, 3590, 3586])).
% 1.05/1.21 tff(3593,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3594,plain,
% 1.05/1.21 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3595,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3594])).
% 1.05/1.21 tff(3596,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3595, 3593])).
% 1.05/1.21 tff(3597,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3598,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3597, 3596])).
% 1.05/1.21 tff(3599,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3598, 124, 1652, 3592])).
% 1.05/1.21 tff(3600,plain,
% 1.05/1.21 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[1101, 3599])).
% 1.05/1.21 tff(3601,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3602,plain,
% 1.05/1.21 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.05/1.21 inference(rewrite,[status(thm)],[])).
% 1.05/1.21 tff(3603,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))))),
% 1.05/1.21 inference(monotonicity,[status(thm)],[3602])).
% 1.05/1.21 tff(3604,plain,
% 1.05/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.05/1.21 inference(transitivity,[status(thm)],[3603, 3601])).
% 1.05/1.21 tff(3605,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.05/1.21 inference(quant_inst,[status(thm)],[])).
% 1.05/1.21 tff(3606,plain,
% 1.05/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))),
% 1.05/1.21 inference(modus_ponens,[status(thm)],[3605, 3604])).
% 1.05/1.21 tff(3607,plain,
% 1.05/1.21 ($false),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3606, 238, 3600, 3585, 3584, 1455])).
% 1.05/1.21 tff(3608,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.21 tff(3609,plain,
% 1.05/1.21 (~r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.21 inference(unit_resolution,[status(thm)],[3608, 3275, 3283, 3383, 3377, 3279, 3276, 3271, 3374, 3280, 3286, 1815])).
% 1.05/1.22 tff(3610,plain,
% 1.05/1.22 (b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1781, 3609])).
% 1.05/1.22 tff(3611,plain,
% 1.05/1.22 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.05/1.22 inference(transitivity,[status(thm)],[2273, 2275])).
% 1.05/1.22 tff(3612,plain,
% 1.05/1.22 (~r(s(s(s(elem!1))), elem!1)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1182, 3558, 210])).
% 1.05/1.22 tff(3613,plain,
% 1.05/1.22 (b(s(s(s(elem!1))), elem!1)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[647, 3612, 2706])).
% 1.05/1.22 tff(3614,plain,
% 1.05/1.22 (b(s(s(s(s(z)))), s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3613, 3611])).
% 1.05/1.22 tff(3615,plain,
% 1.05/1.22 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[2701])).
% 1.05/1.22 tff(3616,plain,
% 1.05/1.22 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3615])).
% 1.05/1.22 tff(3617,plain,
% 1.05/1.22 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[281])).
% 1.05/1.22 tff(3618,plain,
% 1.05/1.22 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3617, 3616])).
% 1.05/1.22 tff(3619,plain,
% 1.05/1.22 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(z)), s(s(s(z)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3618])).
% 1.05/1.22 tff(3620,plain,
% 1.05/1.22 (~r(s(elem!1), s(s(elem!1)))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[700, 3558, 395])).
% 1.05/1.22 tff(3621,plain,
% 1.05/1.22 (~r(s(s(z)), s(s(s(z))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3620, 3619])).
% 1.05/1.22 tff(3622,plain,
% 1.05/1.22 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3623,plain,
% 1.05/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(3624,plain,
% 1.05/1.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 1.05/1.22 tff(3625,plain,
% 1.05/1.22 (b(s(s(z)), s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3624, 51, 147, 3621])).
% 1.05/1.22 tff(3626,plain,
% 1.05/1.22 (~r(z, s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2841, 3625, 3574, 169])).
% 1.05/1.22 tff(3627,plain,
% 1.05/1.22 (b(z, s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1542, 3626])).
% 1.05/1.22 tff(3628,plain,
% 1.05/1.22 (~b(s(z), s(s(s(s(z)))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2798, 3627, 1783, 3614])).
% 1.05/1.22 tff(3629,plain,
% 1.05/1.22 (r(s(z), s(s(s(s(z)))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[893, 3628, 3140])).
% 1.05/1.22 tff(3630,plain,
% 1.05/1.22 (~b(s(s(s(s(z)))), z)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2199, 238, 1457, 1785, 1784])).
% 1.05/1.22 tff(3631,plain,
% 1.05/1.22 (r(s(s(s(s(z)))), z)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1499, 51, 726, 3630])).
% 1.05/1.22 tff(3632,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3633,plain,
% 1.05/1.22 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3634,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3633])).
% 1.05/1.22 tff(3635,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3634, 3632])).
% 1.05/1.22 tff(3636,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(3637,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 1.05/1.22 tff(3638,plain,
% 1.05/1.22 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3637, 238, 1785, 1784, 1783])).
% 1.05/1.22 tff(3639,plain,
% 1.05/1.22 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1051, 51, 3638, 2782])).
% 1.05/1.22 tff(3640,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2796, 124, 3639, 1847, 3631])).
% 1.05/1.22 tff(3641,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3642,plain,
% 1.05/1.22 (~b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3641, 3627, 1783, 3614])).
% 1.05/1.22 tff(3643,plain,
% 1.05/1.22 (r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1709, 3642])).
% 1.05/1.22 tff(3644,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1660, 3643, 3629, 1652])).
% 1.05/1.22 tff(3645,plain,(b(s(s(s(z))), s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3646,plain,
% 1.05/1.22 (b(s(s(s(z))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3645, 3283, 3610, 3286, 3271, 3374, 3279, 3276])).
% 1.05/1.22 tff(3647,plain,
% 1.05/1.22 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3362, 238, 3610, 3646, 3275])).
% 1.05/1.22 tff(3648,plain,
% 1.05/1.22 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1101, 3647])).
% 1.05/1.22 tff(3649,plain,
% 1.05/1.22 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3273])).
% 1.05/1.22 tff(3650,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3649, 3273])).
% 1.05/1.22 tff(3651,plain,
% 1.05/1.22 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3374, 3650])).
% 1.05/1.22 tff(3652,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3653,plain,
% 1.05/1.22 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3654,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3653])).
% 1.05/1.22 tff(3655,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3654, 3652])).
% 1.05/1.22 tff(3656,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(3657,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 1.05/1.22 tff(3658,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3657, 124, 3283, 3651, 3648])).
% 1.05/1.22 tff(3659,plain,((s(s(z)) = s(s(elem!1))) | b(s(elem!1), s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | b(elem!1, s(z)) | b(s(z), elem!1) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3660,plain,
% 1.05/1.22 (s(s(z)) = s(s(elem!1))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3659, 1380, 1081, 1400, 345, 1808])).
% 1.05/1.22 tff(3661,plain,
% 1.05/1.22 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3660])).
% 1.05/1.22 tff(3662,plain,
% 1.05/1.22 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3661])).
% 1.05/1.22 tff(3663,plain,
% 1.05/1.22 ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) <=> (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3662])).
% 1.05/1.22 tff(3664,plain,
% 1.05/1.22 (s(elem!1) = s(z)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[21, 3660])).
% 1.05/1.22 tff(3665,plain,
% 1.05/1.22 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.22 tff(3666,plain,
% 1.05/1.22 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3665])).
% 1.05/1.22 tff(3667,plain,
% 1.05/1.22 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3660])).
% 1.05/1.22 tff(3668,plain,
% 1.05/1.22 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3667, 3666])).
% 1.05/1.22 tff(3669,plain,
% 1.05/1.22 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.22 tff(3670,plain,
% 1.05/1.22 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3669])).
% 1.05/1.22 tff(3671,plain,
% 1.05/1.22 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.22 tff(3672,plain,
% 1.05/1.22 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3671])).
% 1.05/1.22 tff(3673,plain,
% 1.05/1.22 (z = elem!1),
% 1.05/1.22 inference(transitivity,[status(thm)],[769, 3672, 154])).
% 1.05/1.22 tff(3674,plain,
% 1.05/1.22 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3673])).
% 1.05/1.22 tff(3675,plain,
% 1.05/1.22 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3674, 327])).
% 1.05/1.22 tff(3676,plain,
% 1.05/1.22 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3675, 3670])).
% 1.05/1.22 tff(3677,plain,
% 1.05/1.22 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3676])).
% 1.05/1.22 tff(3678,plain,
% 1.05/1.22 (~(elem!1 = s(elem!1))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[72, 3677])).
% 1.05/1.22 tff(3679,plain,
% 1.05/1.22 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.22 tff(3680,plain,
% 1.05/1.22 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3679])).
% 1.05/1.22 tff(3681,plain,
% 1.05/1.22 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3680])).
% 1.05/1.22 tff(3682,plain,
% 1.05/1.22 (~b(elem!1, s(elem!1))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1400, 3681])).
% 1.05/1.22 tff(3683,plain,
% 1.05/1.22 (r(elem!1, s(elem!1))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[629, 3682, 3678])).
% 1.05/1.22 tff(3684,plain,
% 1.05/1.22 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3675])).
% 1.05/1.22 tff(3685,plain,
% 1.05/1.22 (~(elem!1 = s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[72, 3684])).
% 1.05/1.22 tff(3686,plain,
% 1.05/1.22 (r(elem!1, s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[363, 3685, 1400])).
% 1.05/1.22 tff(3687,plain,
% 1.05/1.22 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.05/1.22 inference(transitivity,[status(thm)],[3675, 2465])).
% 1.05/1.22 tff(3688,plain,
% 1.05/1.22 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3687])).
% 1.05/1.22 tff(3689,plain,
% 1.05/1.22 (~(s(z) = elem!1)),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[72, 3688])).
% 1.05/1.22 tff(3690,plain,
% 1.05/1.22 (r(s(z), elem!1)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2468, 3689])).
% 1.05/1.22 tff(3691,plain,
% 1.05/1.22 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1083, 3660, 1081])).
% 1.05/1.22 tff(3692,plain,
% 1.05/1.22 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1101, 3691])).
% 1.05/1.22 tff(3693,plain,
% 1.05/1.22 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3673])).
% 1.05/1.22 tff(3694,plain,
% 1.05/1.22 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3693])).
% 1.05/1.22 tff(3695,plain,
% 1.05/1.22 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3694])).
% 1.05/1.22 tff(3696,plain,
% 1.05/1.22 (~b(z, s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1400, 3695])).
% 1.05/1.22 tff(3697,plain,
% 1.05/1.22 (r(z, s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1542, 3696])).
% 1.05/1.22 tff(3698,plain,
% 1.05/1.22 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1076])).
% 1.05/1.22 tff(3699,plain,
% 1.05/1.22 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3698])).
% 1.05/1.22 tff(3700,plain,
% 1.05/1.22 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3699])).
% 1.05/1.22 tff(3701,plain,
% 1.05/1.22 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1076])).
% 1.05/1.22 tff(3702,plain,
% 1.05/1.22 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3701, 1076])).
% 1.05/1.22 tff(3703,plain,
% 1.05/1.22 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3702])).
% 1.05/1.22 tff(3704,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.05/1.22 tff(3705,plain,
% 1.05/1.22 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3704, 3703])).
% 1.05/1.22 tff(3706,plain,
% 1.05/1.22 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.22 tff(3707,plain,
% 1.05/1.22 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3706])).
% 1.05/1.22 tff(3708,plain,
% 1.05/1.22 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1291, 3707])).
% 1.05/1.22 tff(3709,plain,
% 1.05/1.22 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2920, 3708])).
% 1.05/1.22 tff(3710,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3709, 3705])).
% 1.05/1.22 tff(3711,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3712,plain,
% 1.05/1.22 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3711, 13])).
% 1.05/1.22 tff(3713,plain,
% 1.05/1.22 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3712, 3700])).
% 1.05/1.22 tff(3714,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.22 tff(3715,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3714])).
% 1.05/1.22 tff(3716,plain,
% 1.05/1.22 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.05/1.22 inference(commutativity,[status(thm)],[])).
% 1.05/1.22 tff(3717,plain,
% 1.05/1.22 (s(elem!1) = s(z)),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[21, 13])).
% 1.05/1.22 tff(3718,plain,
% 1.05/1.22 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.22 tff(3719,plain,
% 1.05/1.22 (elem!1 = z),
% 1.05/1.22 inference(transitivity,[status(thm)],[155, 3718, 26])).
% 1.05/1.22 tff(3720,plain,
% 1.05/1.22 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3719])).
% 1.05/1.22 tff(3721,plain,
% 1.05/1.22 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.05/1.22 inference(transitivity,[status(thm)],[3720, 3716])).
% 1.05/1.22 tff(3722,plain,
% 1.05/1.22 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3721])).
% 1.05/1.22 tff(3723,plain,
% 1.05/1.22 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3722])).
% 1.05/1.22 tff(3724,plain,
% 1.05/1.22 (~(elem!1 = s(s(s(elem!1))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[821, 3723])).
% 1.05/1.22 tff(3725,plain,
% 1.05/1.22 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.22 tff(3726,plain,
% 1.05/1.22 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3725])).
% 1.05/1.22 tff(3727,plain,
% 1.05/1.22 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.22 tff(3728,plain,
% 1.05/1.22 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3727, 3726])).
% 1.05/1.22 tff(3729,plain,
% 1.05/1.22 (b(s(s(elem!1)), s(elem!1))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1817, 3728])).
% 1.05/1.22 tff(3730,plain,
% 1.05/1.22 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.05/1.22 inference(commutativity,[status(thm)],[])).
% 1.05/1.22 tff(3731,plain,
% 1.05/1.22 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.05/1.22 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.22 tff(3732,plain,
% 1.05/1.22 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3731, 3730])).
% 1.05/1.22 tff(3733,plain,
% 1.05/1.22 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3732])).
% 1.05/1.22 tff(3734,plain,
% 1.05/1.22 (~(elem!1 = s(s(elem!1)))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1386, 3733])).
% 1.05/1.22 tff(3735,plain,
% 1.05/1.22 (b(s(s(elem!1)), s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[1817, 3727])).
% 1.05/1.22 tff(3736,plain,
% 1.05/1.22 ((s(s(s(z))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.22 tff(3737,plain,
% 1.05/1.22 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(z))) = s(z))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3736])).
% 1.05/1.22 tff(3738,plain,
% 1.05/1.22 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(z))) = s(z)))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3737])).
% 1.05/1.22 tff(3739,plain,
% 1.05/1.22 (~(s(s(s(z))) = s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[94, 3738])).
% 1.05/1.22 tff(3740,plain,
% 1.05/1.22 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.22 tff(3741,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(z))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[2288, 3740])).
% 1.05/1.22 tff(3742,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.22 tff(3743,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3742])).
% 1.05/1.22 tff(3744,plain,
% 1.05/1.22 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3740, 3743])).
% 1.05/1.22 tff(3745,plain,
% 1.05/1.22 (r(s(s(s(elem!1))), s(elem!1))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[2288, 3744])).
% 1.05/1.22 tff(3746,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3747,plain,
% 1.05/1.22 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3748,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3747])).
% 1.05/1.22 tff(3749,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3748, 3746])).
% 1.05/1.22 tff(3750,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(3751,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 1.05/1.22 tff(3752,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3751, 124, 590, 1321, 442])).
% 1.05/1.22 tff(3753,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3754,plain,
% 1.05/1.22 (~r(elem!1, s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3753, 3745, 590])).
% 1.05/1.22 tff(3755,plain,
% 1.05/1.22 (b(elem!1, s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1319, 3754, 3724])).
% 1.05/1.22 tff(3756,plain,
% 1.05/1.22 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.22 tff(3757,plain,
% 1.05/1.22 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3756])).
% 1.05/1.22 tff(3758,plain,
% 1.05/1.22 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.05/1.22 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.22 tff(3759,plain,
% 1.05/1.22 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3758, 767])).
% 1.05/1.22 tff(3760,plain,
% 1.05/1.22 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3759])).
% 1.05/1.22 tff(3761,plain,
% 1.05/1.22 (~(elem!1 = s(s(s(s(z)))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[726, 3760])).
% 1.05/1.22 tff(3762,plain,
% 1.05/1.22 (elem!1 = z),
% 1.05/1.22 inference(transitivity,[status(thm)],[155, 813, 26])).
% 1.05/1.22 tff(3763,plain,
% 1.05/1.22 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3762])).
% 1.05/1.22 tff(3764,plain,
% 1.05/1.22 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.05/1.22 inference(symmetry,[status(thm)],[3763])).
% 1.05/1.22 tff(3765,plain,
% 1.05/1.22 ((~r(z, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3764])).
% 1.05/1.22 tff(3766,plain,
% 1.05/1.22 (~b(elem!1, s(s(elem!1)))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3306, 226, 289, 543])).
% 1.05/1.22 tff(3767,plain,
% 1.05/1.22 (r(elem!1, s(s(elem!1)))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[606, 3766, 150])).
% 1.05/1.22 tff(3768,plain,
% 1.05/1.22 (~r(s(z), s(s(elem!1)))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[2478, 3767, 334, 1370])).
% 1.05/1.22 tff(3769,plain,
% 1.05/1.22 (b(s(z), s(s(elem!1)))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[56, 3768])).
% 1.05/1.22 tff(3770,plain,
% 1.05/1.22 (~b(s(z), s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3192, 3769, 23, 226])).
% 1.05/1.22 tff(3771,plain,
% 1.05/1.22 (r(s(z), s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[101, 3770])).
% 1.05/1.22 tff(3772,plain,
% 1.05/1.22 (~r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1826, 3771, 1818])).
% 1.05/1.22 tff(3773,plain,
% 1.05/1.22 (b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1781, 3772])).
% 1.05/1.22 tff(3774,plain,
% 1.05/1.22 (~r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1834, 124, 3771, 1818])).
% 1.05/1.22 tff(3775,plain,
% 1.05/1.22 (b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1709, 3774])).
% 1.05/1.22 tff(3776,plain,
% 1.05/1.22 (~b(s(s(s(s(z)))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1930, 3775, 1817, 3773])).
% 1.05/1.22 tff(3777,plain,
% 1.05/1.22 (r(s(s(s(s(z)))), s(z))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1623, 3776, 1619])).
% 1.05/1.22 tff(3778,plain,
% 1.05/1.22 (~r(z, s(s(s(s(z)))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[1571, 124, 3777, 1545])).
% 1.05/1.22 tff(3779,plain,
% 1.05/1.22 (~r(elem!1, s(s(s(s(z)))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3778, 3765])).
% 1.05/1.22 tff(3780,plain,
% 1.05/1.22 (b(elem!1, s(s(s(s(z)))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[935, 3779, 3761])).
% 1.05/1.22 tff(3781,plain,
% 1.05/1.22 (b(z, s(s(s(s(z)))))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3780, 3757])).
% 1.05/1.22 tff(3782,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.05/1.22 tff(3783,plain,
% 1.05/1.22 (s(s(s(elem!1))) = z),
% 1.05/1.22 inference(symmetry,[status(thm)],[3782])).
% 1.05/1.22 tff(3784,plain,
% 1.05/1.22 ($false),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[821, 3783])).
% 1.05/1.22 tff(3785,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.22 tff(3786,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3787,plain,
% 1.05/1.22 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.05/1.22 inference(rewrite,[status(thm)],[])).
% 1.05/1.22 tff(3788,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.05/1.22 inference(monotonicity,[status(thm)],[3787])).
% 1.05/1.22 tff(3789,plain,
% 1.05/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.05/1.22 inference(transitivity,[status(thm)],[3788, 3786])).
% 1.05/1.22 tff(3790,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.05/1.22 inference(quant_inst,[status(thm)],[])).
% 1.05/1.22 tff(3791,plain,
% 1.05/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.05/1.22 inference(modus_ponens,[status(thm)],[3790, 3789])).
% 1.05/1.22 tff(3792,plain,
% 1.05/1.22 (~r(z, s(s(s(elem!1))))),
% 1.05/1.22 inference(unit_resolution,[status(thm)],[3791, 124, 2964, 1545])).
% 1.05/1.22 tff(3793,plain,
% 1.05/1.23 (((~![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)))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3794,plain,
% 1.05/1.23 ((~![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)))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3795,plain,
% 1.05/1.23 ((~![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))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 1.05/1.23 tff(3796,plain,
% 1.05/1.23 (b(z, s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3795, 51, 3792, 3785])).
% 1.05/1.23 tff(3797,assumption,(~(s(s(s(s(z)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.05/1.23 tff(3798,plain,
% 1.05/1.23 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2970, 124, 3777, 2964])).
% 1.05/1.23 tff(3799,plain,
% 1.05/1.23 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2974, 51, 3798, 3797])).
% 1.05/1.23 tff(3800,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3801,plain,
% 1.05/1.23 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3802,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3801])).
% 1.05/1.23 tff(3803,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.05/1.23 inference(transitivity,[status(thm)],[3802, 3800])).
% 1.05/1.23 tff(3804,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3805,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 1.05/1.23 tff(3806,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3805, 238, 226, 3799, 3796, 3781])).
% 1.05/1.23 tff(3807,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3808,plain,
% 1.05/1.23 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3807, 3741, 3713, 3717, 1545, 1817, 1818, 3735, 334, 1370, 3734, 3729, 3755])).
% 1.05/1.23 tff(3809,plain,
% 1.05/1.23 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[223, 3808, 3708])).
% 1.05/1.23 tff(3810,plain,
% 1.05/1.23 (s(z) = s(elem!1)),
% 1.05/1.23 inference(symmetry,[status(thm)],[3717])).
% 1.05/1.23 tff(3811,plain,
% 1.05/1.23 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3810])).
% 1.05/1.23 tff(3812,plain,
% 1.05/1.23 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3811])).
% 1.05/1.23 tff(3813,plain,
% 1.05/1.23 (~(s(elem!1) = s(s(elem!1)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[41, 3812])).
% 1.05/1.23 tff(3814,plain,
% 1.05/1.23 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.05/1.23 inference(symmetry,[status(thm)],[3718])).
% 1.05/1.23 tff(3815,plain,
% 1.05/1.23 (z = elem!1),
% 1.05/1.23 inference(transitivity,[status(thm)],[769, 3814, 154])).
% 1.05/1.23 tff(3816,plain,
% 1.05/1.23 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.05/1.23 inference(monotonicity,[status(thm)],[1075, 3815])).
% 1.05/1.23 tff(3817,plain,
% 1.05/1.23 (~r(s(s(s(z))), z)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2827, 2288, 1545])).
% 1.05/1.23 tff(3818,plain,
% 1.05/1.23 (b(s(s(s(z))), z)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1524, 3817])).
% 1.05/1.23 tff(3819,plain,
% 1.05/1.23 (b(s(s(s(elem!1))), elem!1)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3818, 3816])).
% 1.05/1.23 tff(3820,plain,
% 1.05/1.23 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = z)),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3719])).
% 1.05/1.23 tff(3821,plain,
% 1.05/1.23 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.05/1.23 inference(symmetry,[status(thm)],[3820])).
% 1.05/1.23 tff(3822,plain,
% 1.05/1.23 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3821])).
% 1.05/1.23 tff(3823,plain,
% 1.05/1.23 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[1006, 3822])).
% 1.05/1.23 tff(3824,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.05/1.23 tff(3825,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3826,plain,
% 1.05/1.23 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(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(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3827,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3826])).
% 1.05/1.23 tff(3828,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.05/1.23 inference(transitivity,[status(thm)],[3827, 3825])).
% 1.05/1.23 tff(3829,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3830,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3829, 3828])).
% 1.05/1.23 tff(3831,plain,
% 1.05/1.23 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3830, 124, 210, 442, 3824])).
% 1.05/1.23 tff(3832,plain,
% 1.05/1.23 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1814, 3831, 1380])).
% 1.05/1.23 tff(3833,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3834,plain,
% 1.05/1.23 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3835,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3834])).
% 1.05/1.23 tff(3836,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.05/1.23 inference(transitivity,[status(thm)],[3835, 3833])).
% 1.05/1.23 tff(3837,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3838,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3837, 3836])).
% 1.05/1.23 tff(3839,plain,
% 1.05/1.23 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3838, 124, 590, 3824])).
% 1.05/1.23 tff(3840,plain,
% 1.05/1.23 (b(s(s(s(s(s(z))))), elem!1)),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1064, 3839, 1053])).
% 1.05/1.23 tff(3841,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3842,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3843,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3842, 3841])).
% 1.05/1.23 tff(3844,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3843, 238, 543, 781, 3840, 3832])).
% 1.05/1.23 tff(3845,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3846,plain,
% 1.05/1.23 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3845, 3809, 3745, 1380, 3823, 3819, 590, 3755])).
% 1.05/1.23 tff(3847,plain,
% 1.05/1.23 (s(s(elem!1)) = s(s(z))),
% 1.05/1.23 inference(symmetry,[status(thm)],[13])).
% 1.05/1.23 tff(3848,plain,
% 1.05/1.23 (s(s(s(s(s(z))))) = s(s(z))),
% 1.05/1.23 inference(transitivity,[status(thm)],[2099, 3847])).
% 1.05/1.23 tff(3849,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1729, 3848])).
% 1.05/1.23 tff(3850,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3851,plain,
% 1.05/1.23 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3850, 13])).
% 1.05/1.23 tff(3852,plain,
% 1.05/1.23 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.23 tff(3853,plain,
% 1.05/1.23 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.23 inference(symmetry,[status(thm)],[3852])).
% 1.05/1.23 tff(3854,plain,
% 1.05/1.23 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3853])).
% 1.05/1.23 tff(3855,plain,
% 1.05/1.23 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[728, 3854])).
% 1.05/1.23 tff(3856,plain,
% 1.05/1.23 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.23 tff(3857,plain,
% 1.05/1.23 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.05/1.23 inference(symmetry,[status(thm)],[3856])).
% 1.05/1.23 tff(3858,plain,
% 1.05/1.23 (r(s(s(s(z))), s(s(elem!1)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3809, 3857])).
% 1.05/1.23 tff(3859,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 1.05/1.23 tff(3860,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3861,plain,
% 1.05/1.23 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), 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(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3862,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3861])).
% 1.05/1.23 tff(3863,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.05/1.23 inference(transitivity,[status(thm)],[3862, 3860])).
% 1.05/1.23 tff(3864,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3865,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3864, 3863])).
% 1.05/1.23 tff(3866,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3865, 124, 3495, 2008, 3859])).
% 1.05/1.23 tff(3867,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3868,plain,
% 1.05/1.23 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3867, 3858, 3495])).
% 1.05/1.23 tff(3869,plain,
% 1.05/1.23 (~b(s(elem!1), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2695, 3868, 3855, 3851, 3846, 3729])).
% 1.05/1.23 tff(3870,plain,
% 1.05/1.23 (r(s(elem!1), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[534, 3869, 3813])).
% 1.05/1.23 tff(3871,plain,
% 1.05/1.23 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.23 tff(3872,plain,
% 1.05/1.23 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.05/1.23 inference(symmetry,[status(thm)],[3871])).
% 1.05/1.23 tff(3873,plain,
% 1.05/1.23 ((~r(s(z), s(s(elem!1)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3872])).
% 1.05/1.23 tff(3874,plain,
% 1.05/1.23 (~r(s(elem!1), s(s(elem!1)))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[24, 3873])).
% 1.05/1.23 tff(3875,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[518, 3874])).
% 1.05/1.23 tff(3876,plain,((~(s(elem!1) = s(z))) | (~r(s(elem!1), s(s(elem!1)))) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3877,plain,
% 1.05/1.23 (r(s(z), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3876, 3870, 3717])).
% 1.05/1.23 tff(3878,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[562, 124, 3877, 3809, 3741])).
% 1.05/1.23 tff(3879,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3880,plain,
% 1.05/1.23 (~r(s(s(s(z))), s(z))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3879, 1817, 13, 1380, 590, 1545, 3495, 1818, 334, 1370])).
% 1.05/1.23 tff(3881,plain,
% 1.05/1.23 (b(s(s(s(z))), s(z))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2344, 3880, 3739])).
% 1.05/1.23 tff(3882,plain,
% 1.05/1.23 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.23 tff(3883,plain,
% 1.05/1.23 (b(s(s(s(elem!1))), s(z))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[1456, 3882])).
% 1.05/1.23 tff(3884,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.05/1.23 tff(3885,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3884, 3883])).
% 1.05/1.23 tff(3886,plain,((~b(s(s(s(z))), s(z))) | b(s(s(s(elem!1))), s(z)) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3887,plain,
% 1.05/1.23 (b(s(s(s(elem!1))), s(z))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3886, 3881, 13])).
% 1.05/1.23 tff(3888,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3889,plain,
% 1.05/1.23 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.23 tff(3890,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.05/1.23 inference(monotonicity,[status(thm)],[3889])).
% 1.05/1.23 tff(3891,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.05/1.23 inference(transitivity,[status(thm)],[3890, 3888])).
% 1.05/1.23 tff(3892,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.05/1.23 inference(quant_inst,[status(thm)],[])).
% 1.05/1.23 tff(3893,plain,
% 1.05/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.05/1.23 inference(modus_ponens,[status(thm)],[3892, 3891])).
% 1.05/1.23 tff(3894,plain,
% 1.05/1.23 ($false),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3893, 238, 226, 564, 546, 23])).
% 1.05/1.23 tff(3895,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.23 tff(3896,plain,
% 1.05/1.23 (~b(s(z), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3895, 226, 564, 23])).
% 1.05/1.23 tff(3897,plain,
% 1.05/1.23 (r(s(z), s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[101, 3896])).
% 1.05/1.23 tff(3898,plain,
% 1.05/1.23 (~r(elem!1, s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1378, 3897, 1370])).
% 1.05/1.23 tff(3899,plain,
% 1.05/1.23 (b(elem!1, s(s(s(elem!1))))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[1319, 3898, 514])).
% 1.05/1.23 tff(3900,plain,
% 1.05/1.23 (~b(elem!1, s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[3306, 3899, 289, 226])).
% 1.05/1.23 tff(3901,plain,
% 1.05/1.23 (r(elem!1, s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[606, 3900, 150])).
% 1.05/1.23 tff(3902,plain,
% 1.05/1.23 (~r(s(z), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[2478, 3901, 334, 1370])).
% 1.05/1.23 tff(3903,plain,
% 1.05/1.23 (b(s(z), s(s(elem!1)))),
% 1.05/1.23 inference(unit_resolution,[status(thm)],[56, 3902])).
% 1.05/1.23 tff(3904,plain,
% 1.05/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.23 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3905,plain,
% 1.05/1.24 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3906,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3905])).
% 1.05/1.24 tff(3907,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3906, 3904])).
% 1.05/1.24 tff(3908,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3909,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3908, 3907])).
% 1.05/1.24 tff(3910,plain,
% 1.05/1.24 ($false),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3909, 238, 3903, 226, 564, 23])).
% 1.05/1.24 tff(3911,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.24 tff(3912,plain,
% 1.05/1.24 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3911, 3887, 3735, 334, 1370, 3734, 3729, 3724])).
% 1.05/1.24 tff(3913,plain,
% 1.05/1.24 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[223, 3912, 3708])).
% 1.05/1.24 tff(3914,plain,
% 1.05/1.24 (r(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3913, 3715])).
% 1.05/1.24 tff(3915,plain,
% 1.05/1.24 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3847])).
% 1.05/1.24 tff(3916,plain,
% 1.05/1.24 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3915])).
% 1.05/1.24 tff(3917,plain,
% 1.05/1.24 (r(s(s(s(z))), s(s(elem!1)))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3913, 3857])).
% 1.05/1.24 tff(3918,plain,
% 1.05/1.24 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3867, 3917, 3495])).
% 1.05/1.24 tff(3919,plain,
% 1.05/1.24 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.24 tff(3920,plain,
% 1.05/1.24 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.24 inference(symmetry,[status(thm)],[3919])).
% 1.05/1.24 tff(3921,plain,
% 1.05/1.24 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3920])).
% 1.05/1.24 tff(3922,plain,
% 1.05/1.24 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[1776, 3921])).
% 1.05/1.24 tff(3923,plain,
% 1.05/1.24 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.24 tff(3924,plain,
% 1.05/1.24 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.24 inference(symmetry,[status(thm)],[3923])).
% 1.05/1.24 tff(3925,plain,
% 1.05/1.24 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3924])).
% 1.05/1.24 tff(3926,plain,
% 1.05/1.24 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[728, 3925])).
% 1.05/1.24 tff(3927,plain,
% 1.05/1.24 (s(z) = s(elem!1)),
% 1.05/1.24 inference(symmetry,[status(thm)],[353])).
% 1.05/1.24 tff(3928,plain,
% 1.05/1.24 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3927])).
% 1.05/1.24 tff(3929,plain,
% 1.05/1.24 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3928])).
% 1.05/1.24 tff(3930,plain,
% 1.05/1.24 (~(s(elem!1) = s(s(elem!1)))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[41, 3929])).
% 1.05/1.24 tff(3931,plain,
% 1.05/1.24 (b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1781, 1776])).
% 1.05/1.24 tff(3932,plain,
% 1.05/1.24 (~r(s(z), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[2441, 3931, 23, 210, 2417, 1380])).
% 1.05/1.24 tff(3933,plain,
% 1.05/1.24 (~r(s(elem!1), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3876, 3932, 353])).
% 1.05/1.24 tff(3934,plain,
% 1.05/1.24 (b(s(elem!1), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[534, 3933, 3930])).
% 1.05/1.24 tff(3935,plain,
% 1.05/1.24 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[2695, 3934, 3926, 2417, 2666, 289])).
% 1.05/1.24 tff(3936,plain,
% 1.05/1.24 ($false),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3935, 3922])).
% 1.05/1.24 tff(3937,plain,(r(s(s(s(s(s(z))))), s(z)) | (~(s(elem!1) = s(z))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.24 tff(3938,plain,
% 1.05/1.24 (r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3937, 3918, 3851, 3717, 3729, 3735, 3913, 1380])).
% 1.05/1.24 tff(3939,plain,
% 1.05/1.24 (~r(elem!1, s(s(s(s(z)))))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[1572, 3765])).
% 1.05/1.24 tff(3940,plain,
% 1.05/1.24 (b(elem!1, s(s(s(s(z)))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[935, 3939, 3761])).
% 1.05/1.24 tff(3941,plain,
% 1.05/1.24 (b(z, s(s(s(s(z)))))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3940, 3757])).
% 1.05/1.24 tff(3942,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3943,plain,
% 1.05/1.24 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3944,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3943])).
% 1.05/1.24 tff(3945,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3944, 3942])).
% 1.05/1.24 tff(3946,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3947,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 1.05/1.24 tff(3948,plain,
% 1.05/1.24 (~r(s(s(s(s(s(z))))), z)),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3947, 124, 1711, 1545])).
% 1.05/1.24 tff(3949,plain,
% 1.05/1.24 (b(s(s(s(s(s(z))))), z)),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 3948])).
% 1.05/1.24 tff(3950,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3951,plain,
% 1.05/1.24 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3952,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3951])).
% 1.05/1.24 tff(3953,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3952, 3950])).
% 1.05/1.24 tff(3954,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3955,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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)))))))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3954, 3953])).
% 1.05/1.24 tff(3956,plain,
% 1.05/1.24 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3955, 124, 1711, 1544])).
% 1.05/1.24 tff(3957,plain,
% 1.05/1.24 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1051, 51, 3956, 2782])).
% 1.05/1.24 tff(3958,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3959,plain,
% 1.05/1.24 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3960,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3959])).
% 1.05/1.24 tff(3961,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3960, 3958])).
% 1.05/1.24 tff(3962,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3963,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 1.05/1.24 tff(3964,plain,
% 1.05/1.24 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3963, 124, 1711, 1544])).
% 1.05/1.24 tff(3965,plain,
% 1.05/1.24 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1904, 3964])).
% 1.05/1.24 tff(3966,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3967,plain,
% 1.05/1.24 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3968,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3967])).
% 1.05/1.24 tff(3969,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3968, 3966])).
% 1.05/1.24 tff(3970,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3971,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 1.05/1.24 tff(3972,plain,
% 1.05/1.24 ($false),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3971, 238, 3965, 3957, 3949, 3941])).
% 1.05/1.24 tff(3973,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.24 tff(3974,plain,
% 1.05/1.24 (~r(s(s(s(s(z)))), s(z))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3973, 3938, 3717, 1545])).
% 1.05/1.24 tff(3975,plain,
% 1.05/1.24 (b(s(s(s(s(z)))), s(z))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1623, 3974, 1619])).
% 1.05/1.24 tff(3976,plain,
% 1.05/1.24 (~r(s(z), s(s(s(elem!1))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1826, 3938, 1818])).
% 1.05/1.24 tff(3977,plain,
% 1.05/1.24 (b(s(z), s(s(s(elem!1))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[101, 3976])).
% 1.05/1.24 tff(3978,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3979,plain,
% 1.05/1.24 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.05/1.24 inference(rewrite,[status(thm)],[])).
% 1.05/1.24 tff(3980,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.05/1.24 inference(monotonicity,[status(thm)],[3979])).
% 1.05/1.24 tff(3981,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.05/1.24 inference(transitivity,[status(thm)],[3980, 3978])).
% 1.05/1.24 tff(3982,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.05/1.24 inference(quant_inst,[status(thm)],[])).
% 1.05/1.24 tff(3983,plain,
% 1.05/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 1.05/1.24 tff(3984,plain,
% 1.05/1.24 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3983, 238, 3977, 3735, 3975])).
% 1.05/1.24 tff(3985,plain,
% 1.05/1.24 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.24 inference(modus_ponens,[status(thm)],[3984, 3916])).
% 1.05/1.24 tff(3986,plain,
% 1.05/1.24 (r(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[1564, 3985])).
% 1.05/1.24 tff(3987,plain,
% 1.05/1.24 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[3010, 3986, 3914])).
% 1.05/1.24 tff(3988,plain,
% 1.05/1.24 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.24 inference(unit_resolution,[status(thm)],[2974, 51, 3987, 3713])).
% 1.05/1.24 tff(3989,plain,
% 1.05/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(3990,plain,
% 1.05/1.25 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(3991,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3990])).
% 1.05/1.25 tff(3992,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.25 inference(transitivity,[status(thm)],[3991, 3989])).
% 1.05/1.25 tff(3993,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(3994,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 1.05/1.25 tff(3995,plain,
% 1.05/1.25 ($false),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[3994, 238, 3887, 3977, 3975, 3988])).
% 1.05/1.25 tff(3996,plain,((~b(s(s(z)), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.25 tff(3997,plain,
% 1.05/1.25 (~b(s(s(z)), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[3996, 3660, 3697, 1815, 1380, 3692, 3690, 3686, 3683])).
% 1.05/1.25 tff(3998,plain,
% 1.05/1.25 (r(s(s(z)), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[79, 3997])).
% 1.05/1.25 tff(3999,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(elem!1))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[3998, 3668])).
% 1.05/1.25 tff(4000,plain,
% 1.05/1.25 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.25 tff(4001,plain,
% 1.05/1.25 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4000])).
% 1.05/1.25 tff(4002,plain,
% 1.05/1.25 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4001])).
% 1.05/1.25 tff(4003,plain,
% 1.05/1.25 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[728, 4002])).
% 1.05/1.25 tff(4004,plain,
% 1.05/1.25 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3664])).
% 1.05/1.25 tff(4005,plain,
% 1.05/1.25 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4004])).
% 1.05/1.25 tff(4006,plain,
% 1.05/1.25 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4005])).
% 1.05/1.25 tff(4007,plain,
% 1.05/1.25 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3660])).
% 1.05/1.25 tff(4008,plain,
% 1.05/1.25 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4007, 3730])).
% 1.05/1.25 tff(4009,plain,
% 1.05/1.25 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4008])).
% 1.05/1.25 tff(4010,plain,
% 1.05/1.25 (~(elem!1 = s(s(elem!1)))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1386, 4009])).
% 1.05/1.25 tff(4011,plain,
% 1.05/1.25 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3673])).
% 1.05/1.25 tff(4012,plain,
% 1.05/1.25 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.05/1.25 inference(symmetry,[status(thm)],[4011])).
% 1.05/1.25 tff(4013,plain,
% 1.05/1.25 (r(s(z), z)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[3690, 4012])).
% 1.05/1.25 tff(4014,plain,
% 1.05/1.25 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3815])).
% 1.05/1.25 tff(4015,plain,
% 1.05/1.25 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4014])).
% 1.05/1.25 tff(4016,plain,
% 1.05/1.25 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4015])).
% 1.05/1.25 tff(4017,plain,
% 1.05/1.25 (~b(z, s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1400, 4016])).
% 1.05/1.25 tff(4018,plain,
% 1.05/1.25 (r(z, s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1542, 4017])).
% 1.05/1.25 tff(4019,plain,
% 1.05/1.25 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.25 tff(4020,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[169, 4019])).
% 1.05/1.25 tff(4021,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4022,plain,
% 1.05/1.25 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4023,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4022])).
% 1.05/1.25 tff(4024,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4023, 4021])).
% 1.05/1.25 tff(4025,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4026,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 1.05/1.25 tff(4027,plain,
% 1.05/1.25 (~r(s(s(elem!1)), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4026, 124, 4020, 4018])).
% 1.05/1.25 tff(4028,plain,
% 1.05/1.25 (((~![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))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4029,plain,
% 1.05/1.25 ((~![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))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4030,plain,
% 1.05/1.25 ((~![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)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.05/1.25 tff(4031,plain,
% 1.05/1.25 (b(s(s(elem!1)), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4030, 51, 92, 4027])).
% 1.05/1.25 tff(4032,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.25 tff(4033,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.05/1.25 inference(symmetry,[status(thm)],[4032])).
% 1.05/1.25 tff(4034,plain,
% 1.05/1.25 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.05/1.25 inference(transitivity,[status(thm)],[3759, 789])).
% 1.05/1.25 tff(4035,plain,
% 1.05/1.25 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4034])).
% 1.05/1.25 tff(4036,plain,
% 1.05/1.25 (~(s(s(s(s(z)))) = elem!1)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[726, 4035])).
% 1.05/1.25 tff(4037,plain,
% 1.05/1.25 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.25 tff(4038,plain,
% 1.05/1.25 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4037])).
% 1.05/1.25 tff(4039,plain,
% 1.05/1.25 (~r(s(s(s(s(z)))), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1938, 124, 1544, 1545])).
% 1.05/1.25 tff(4040,plain,
% 1.05/1.25 (~r(s(s(s(s(z)))), elem!1)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4039, 4038])).
% 1.05/1.25 tff(4041,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), elem!1)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[2131, 4040, 4036])).
% 1.05/1.25 tff(4042,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), z)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4041, 4033])).
% 1.05/1.25 tff(4043,plain,
% 1.05/1.25 (s(s(elem!1)) = s(s(z))),
% 1.05/1.25 inference(symmetry,[status(thm)],[804])).
% 1.05/1.25 tff(4044,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4043])).
% 1.05/1.25 tff(4045,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4044])).
% 1.05/1.25 tff(4046,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1565, 4045])).
% 1.05/1.25 tff(4047,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.05/1.25 tff(4048,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4049,plain,
% 1.05/1.25 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4050,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z))))))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4049])).
% 1.05/1.25 tff(4051,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4050, 4048])).
% 1.05/1.25 tff(4052,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4053,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(s(s(z))))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 1.05/1.25 tff(4054,plain,
% 1.05/1.25 (~b(s(s(s(s(z)))), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4053, 238, 4047, 3941, 4046])).
% 1.05/1.25 tff(4055,plain,
% 1.05/1.25 ($false),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4054, 4042])).
% 1.05/1.25 tff(4056,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.25 tff(4057,plain,
% 1.05/1.25 (~r(s(s(s(s(z)))), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4056, 4031, 3717, 4018, 169])).
% 1.05/1.25 tff(4058,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1623, 4057, 1619])).
% 1.05/1.25 tff(4059,plain,
% 1.05/1.25 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1083, 13, 1081])).
% 1.05/1.25 tff(4060,plain,
% 1.05/1.25 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1101, 4059])).
% 1.05/1.25 tff(4061,plain,
% 1.05/1.25 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.25 tff(4062,plain,
% 1.05/1.25 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4061])).
% 1.05/1.25 tff(4063,plain,
% 1.05/1.25 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3815])).
% 1.05/1.25 tff(4064,plain,
% 1.05/1.25 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4063, 327])).
% 1.05/1.25 tff(4065,plain,
% 1.05/1.25 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4064, 4062])).
% 1.05/1.25 tff(4066,plain,
% 1.05/1.25 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4065])).
% 1.05/1.25 tff(4067,plain,
% 1.05/1.25 (~(elem!1 = s(elem!1))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[72, 4066])).
% 1.05/1.25 tff(4068,plain,
% 1.05/1.25 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[805])).
% 1.05/1.25 tff(4069,plain,
% 1.05/1.25 ((s(s(s(z))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[805])).
% 1.05/1.25 tff(4070,plain,
% 1.05/1.25 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(z))) = s(z))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4069])).
% 1.05/1.25 tff(4071,plain,
% 1.05/1.25 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(z))) = s(z)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4070])).
% 1.05/1.25 tff(4072,plain,
% 1.05/1.25 (~(s(s(s(z))) = s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[94, 4071])).
% 1.05/1.25 tff(4073,plain,
% 1.05/1.25 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.25 tff(4074,plain,
% 1.05/1.25 ((~(elem!1 = s(elem!1))) <=> (~(elem!1 = s(z)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4073])).
% 1.05/1.25 tff(4075,plain,
% 1.05/1.25 (~(elem!1 = s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[391, 4074])).
% 1.05/1.25 tff(4076,plain,
% 1.05/1.25 (r(elem!1, s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[363, 4075, 1400])).
% 1.05/1.25 tff(4077,plain,
% 1.05/1.25 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[804])).
% 1.05/1.25 tff(4078,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[169, 4077])).
% 1.05/1.25 tff(4079,plain,
% 1.05/1.25 (~r(s(s(elem!1)), elem!1)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[263, 4078, 4076])).
% 1.05/1.25 tff(4080,plain,
% 1.05/1.25 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[3762])).
% 1.05/1.25 tff(4081,plain,
% 1.05/1.25 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.05/1.25 inference(transitivity,[status(thm)],[4080, 3716])).
% 1.05/1.25 tff(4082,plain,
% 1.05/1.25 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4081])).
% 1.05/1.25 tff(4083,plain,
% 1.05/1.25 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4082])).
% 1.05/1.25 tff(4084,plain,
% 1.05/1.25 (~(elem!1 = s(s(s(elem!1))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[821, 4083])).
% 1.05/1.25 tff(4085,plain,
% 1.05/1.25 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[804])).
% 1.05/1.25 tff(4086,plain,
% 1.05/1.25 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4085])).
% 1.05/1.25 tff(4087,plain,
% 1.05/1.25 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1291, 4086])).
% 1.05/1.25 tff(4088,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.25 tff(4089,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4088])).
% 1.05/1.25 tff(4090,plain,
% 1.05/1.25 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4077, 4089])).
% 1.05/1.25 tff(4091,plain,
% 1.05/1.25 (r(s(s(elem!1)), s(elem!1))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[169, 4090])).
% 1.05/1.25 tff(4092,plain,
% 1.05/1.25 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.25 tff(4093,plain,
% 1.05/1.25 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4092])).
% 1.05/1.25 tff(4094,plain,
% 1.05/1.25 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4093])).
% 1.05/1.25 tff(4095,plain,
% 1.05/1.25 (~b(elem!1, s(elem!1))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1400, 4094])).
% 1.05/1.25 tff(4096,plain,
% 1.05/1.25 (r(elem!1, s(elem!1))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[629, 4095, 391])).
% 1.05/1.25 tff(4097,plain,
% 1.05/1.25 (~r(elem!1, s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[599, 4096, 4091])).
% 1.05/1.25 tff(4098,plain,
% 1.05/1.25 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.25 tff(4099,plain,
% 1.05/1.25 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4098, 3730])).
% 1.05/1.25 tff(4100,plain,
% 1.05/1.25 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4099])).
% 1.05/1.25 tff(4101,plain,
% 1.05/1.25 (~(elem!1 = s(s(elem!1)))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[92, 4100])).
% 1.05/1.25 tff(4102,plain,
% 1.05/1.25 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.05/1.25 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.25 tff(4103,plain,
% 1.05/1.25 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.05/1.25 inference(symmetry,[status(thm)],[4102])).
% 1.05/1.25 tff(4104,plain,
% 1.05/1.25 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4103])).
% 1.05/1.25 tff(4105,plain,
% 1.05/1.25 (~r(s(s(elem!1)), z)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4079, 4104])).
% 1.05/1.25 tff(4106,plain,
% 1.05/1.25 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4030, 51, 92])).
% 1.05/1.25 tff(4107,plain,
% 1.05/1.25 (b(s(s(elem!1)), z)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4106, 4105])).
% 1.05/1.25 tff(4108,plain,
% 1.05/1.25 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.05/1.25 inference(symmetry,[status(thm)],[3730])).
% 1.05/1.25 tff(4109,plain,
% 1.05/1.25 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.05/1.25 inference(transitivity,[status(thm)],[4099, 4108])).
% 1.05/1.25 tff(4110,plain,
% 1.05/1.25 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4109])).
% 1.05/1.25 tff(4111,plain,
% 1.05/1.25 (~(s(s(elem!1)) = elem!1)),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[92, 4110])).
% 1.05/1.25 tff(4112,plain,
% 1.05/1.25 (b(s(s(elem!1)), elem!1)),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[255, 4111, 4079])).
% 1.05/1.25 tff(4113,plain,
% 1.05/1.25 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1083, 804, 1081])).
% 1.05/1.25 tff(4114,plain,
% 1.05/1.25 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1101, 4113])).
% 1.05/1.25 tff(4115,plain,
% 1.05/1.25 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.25 tff(4116,plain,
% 1.05/1.25 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.05/1.25 inference(symmetry,[status(thm)],[4115])).
% 1.05/1.25 tff(4117,plain,
% 1.05/1.25 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4116])).
% 1.05/1.25 tff(4118,plain,
% 1.05/1.25 (~b(z, s(z))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[1400, 4117])).
% 1.05/1.25 tff(4119,plain,
% 1.05/1.25 (r(z, s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1542, 4118])).
% 1.05/1.25 tff(4120,plain,
% 1.05/1.25 (~r(s(s(s(s(z)))), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4056, 353, 4107, 4119, 169])).
% 1.05/1.25 tff(4121,plain,
% 1.05/1.25 (b(s(s(s(s(z)))), s(z))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1623, 4120, 1619])).
% 1.05/1.25 tff(4122,assumption,(b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.05/1.25 tff(4123,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4124,plain,
% 1.05/1.25 (((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4125,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.05/1.25 inference(monotonicity,[status(thm)],[4124])).
% 1.05/1.25 tff(4126,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.05/1.25 inference(transitivity,[status(thm)],[4125, 4123])).
% 1.05/1.25 tff(4127,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4128,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4127, 4126])).
% 1.05/1.25 tff(4129,plain,
% 1.05/1.25 ($false),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4128, 238, 1137, 4047, 1783, 4122])).
% 1.05/1.25 tff(4130,plain,((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.25 tff(4131,plain,
% 1.05/1.25 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4130, 1137, 4047, 1783])).
% 1.05/1.25 tff(4132,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4133,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4134,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 1.05/1.25 tff(4135,plain,
% 1.05/1.25 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4134, 238, 1137, 1784, 1783])).
% 1.05/1.25 tff(4136,plain,
% 1.05/1.25 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1904, 4135])).
% 1.05/1.25 tff(4137,plain,
% 1.05/1.25 (~r(s(z), s(s(s(elem!1))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[2241, 4136, 1651, 1818])).
% 1.05/1.25 tff(4138,plain,
% 1.05/1.25 (b(s(z), s(s(s(elem!1))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[101, 4137])).
% 1.05/1.25 tff(4139,plain,
% 1.05/1.25 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[3152, 4138, 228, 1137])).
% 1.05/1.25 tff(4140,plain,
% 1.05/1.25 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[223, 4139, 3708])).
% 1.05/1.25 tff(4141,plain,
% 1.05/1.25 (r(s(s(s(z))), s(s(elem!1)))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4140, 3857])).
% 1.05/1.25 tff(4142,plain,
% 1.05/1.25 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[3867, 4141, 3495])).
% 1.05/1.25 tff(4143,plain,
% 1.05/1.25 ($false),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[2420, 51, 4142, 3851, 4131])).
% 1.05/1.25 tff(4144,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.25 tff(4145,plain,
% 1.05/1.25 (~b(s(z), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4144, 4121, 1783, 4114, 804, 4112, 1651, 1818, 4107])).
% 1.05/1.25 tff(4146,plain,
% 1.05/1.25 (r(s(z), s(s(elem!1)))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[56, 4145])).
% 1.05/1.25 tff(4147,plain,
% 1.05/1.25 (~r(s(z), s(s(s(elem!1))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[2484, 4146, 4101, 4097, 4087, 4084, 4079, 4076])).
% 1.05/1.25 tff(4148,plain,
% 1.05/1.25 (b(s(z), s(s(s(elem!1))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[101, 4147])).
% 1.05/1.25 tff(4149,plain,
% 1.05/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.25 inference(rewrite,[status(thm)],[])).
% 1.05/1.25 tff(4150,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.05/1.25 inference(quant_inst,[status(thm)],[])).
% 1.05/1.25 tff(4151,plain,
% 1.05/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.05/1.25 inference(modus_ponens,[status(thm)],[4150, 4149])).
% 1.05/1.25 tff(4152,plain,
% 1.05/1.25 ($false),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4151, 238, 546, 1786, 1784, 1783])).
% 1.05/1.25 tff(4153,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.25 tff(4154,plain,
% 1.05/1.25 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[4153, 4148, 4121, 1783])).
% 1.05/1.25 tff(4155,plain,
% 1.05/1.25 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1904, 4154])).
% 1.05/1.25 tff(4156,plain,
% 1.05/1.25 (~r(s(z), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1660, 4155, 1651])).
% 1.05/1.25 tff(4157,plain,
% 1.05/1.25 (b(s(z), s(s(s(s(z)))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[893, 4156, 3140])).
% 1.05/1.25 tff(4158,plain,
% 1.05/1.25 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[3711, 804])).
% 1.05/1.25 tff(4159,plain,
% 1.05/1.25 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[2788, 238, 4157, 4121, 1783])).
% 1.05/1.25 tff(4160,plain,
% 1.05/1.25 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.05/1.25 inference(unit_resolution,[status(thm)],[1051, 51, 4159, 2782])).
% 1.05/1.25 tff(4161,plain,
% 1.05/1.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[3504, 4160, 4114])).
% 1.05/1.26 tff(4162,plain,
% 1.05/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4163,plain,
% 1.05/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.05/1.26 inference(quant_inst,[status(thm)],[])).
% 1.05/1.26 tff(4164,plain,
% 1.05/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 1.05/1.26 tff(4165,plain,
% 1.05/1.26 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4164, 51])).
% 1.05/1.26 tff(4166,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4165, 4161, 4158])).
% 1.05/1.26 tff(4167,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[1076])).
% 1.05/1.26 tff(4168,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4167])).
% 1.05/1.26 tff(4169,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[2389, 4168])).
% 1.05/1.26 tff(4170,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4171,plain,
% 1.05/1.26 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4172,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4171])).
% 1.05/1.26 tff(4173,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4172, 4170])).
% 1.05/1.26 tff(4174,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.05/1.26 inference(quant_inst,[status(thm)],[])).
% 1.05/1.26 tff(4175,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4174, 4173])).
% 1.05/1.26 tff(4176,plain,
% 1.05/1.26 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4175, 238, 564, 546, 2765])).
% 1.05/1.26 tff(4177,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4176, 4169])).
% 1.05/1.26 tff(4178,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4179,plain,
% 1.05/1.26 (~b(s(s(s(elem!1))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4178, 4166, 804, 4157, 4148])).
% 1.05/1.26 tff(4180,plain,
% 1.05/1.26 (~b(s(s(s(z))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[3886, 4179, 804])).
% 1.05/1.26 tff(4181,plain,
% 1.05/1.26 (r(s(s(s(z))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2344, 4180, 4072])).
% 1.05/1.26 tff(4182,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), s(z))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4181, 4068])).
% 1.05/1.26 tff(4183,plain,
% 1.05/1.26 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4085, 2528])).
% 1.05/1.26 tff(4184,plain,
% 1.05/1.26 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4183])).
% 1.05/1.26 tff(4185,plain,
% 1.05/1.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[1291, 4184])).
% 1.05/1.26 tff(4186,plain,
% 1.05/1.26 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[804, 805])).
% 1.05/1.26 tff(4187,plain,
% 1.05/1.26 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4186])).
% 1.05/1.26 tff(4188,plain,
% 1.05/1.26 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[804])).
% 1.05/1.26 tff(4189,plain,
% 1.05/1.26 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4188])).
% 1.05/1.26 tff(4190,plain,
% 1.05/1.26 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3762])).
% 1.05/1.26 tff(4191,plain,
% 1.05/1.26 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4190, 4189])).
% 1.05/1.26 tff(4192,plain,
% 1.05/1.26 (b(elem!1, s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[606, 4097, 4101])).
% 1.05/1.26 tff(4193,plain,
% 1.05/1.26 (b(z, s(s(z)))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4192, 4191])).
% 1.05/1.26 tff(4194,plain,
% 1.05/1.26 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.05/1.26 inference(monotonicity,[status(thm)],[804])).
% 1.05/1.26 tff(4195,plain,
% 1.05/1.26 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.05/1.26 inference(symmetry,[status(thm)],[4194])).
% 1.05/1.26 tff(4196,plain,
% 1.05/1.26 (b(s(s(z)), z)),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4107, 4195])).
% 1.05/1.26 tff(4197,plain,
% 1.05/1.26 (~r(s(s(s(z))), z)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2827, 4181, 4119])).
% 1.05/1.26 tff(4198,plain,
% 1.05/1.26 (b(s(s(s(z))), z)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[1524, 4197])).
% 1.05/1.26 tff(4199,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.05/1.26 tff(4200,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.05/1.26 tff(4201,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.05/1.26 tff(4202,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4203,plain,
% 1.05/1.26 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4204,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4203])).
% 1.05/1.26 tff(4205,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4204, 4202])).
% 1.05/1.26 tff(4206,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.05/1.26 inference(quant_inst,[status(thm)],[])).
% 1.05/1.26 tff(4207,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4206, 4205])).
% 1.05/1.26 tff(4208,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4207, 238, 4201, 2388, 4200, 4199])).
% 1.05/1.26 tff(4209,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4210,plain,
% 1.05/1.26 (~b(s(s(z)), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4209, 4198, 4196, 4193])).
% 1.05/1.26 tff(4211,plain,
% 1.05/1.26 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4210, 4187])).
% 1.05/1.26 tff(4212,plain,
% 1.05/1.26 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2549, 51, 4211, 4185])).
% 1.05/1.26 tff(4213,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2545, 124, 4078, 4212, 4182])).
% 1.05/1.26 tff(4214,plain,((~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (elem!1 = s(elem!1)) | b(elem!1, s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4215,plain,
% 1.05/1.26 (~r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4214, 1783, 3717, 1818, 169, 4067, 1400, 1081])).
% 1.05/1.26 tff(4216,plain,
% 1.05/1.26 (b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[1709, 4215])).
% 1.05/1.26 tff(4217,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.26 tff(4218,plain,
% 1.05/1.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[3504, 3639, 3495])).
% 1.05/1.26 tff(4219,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4165, 4218, 3712])).
% 1.05/1.26 tff(4220,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4219, 4217])).
% 1.05/1.26 tff(4221,assumption,(~b(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.05/1.26 tff(4222,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4221, 4220])).
% 1.05/1.26 tff(4223,plain,(b(s(s(s(s(z)))), s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4224,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4223, 4216, 4060, 13, 4058, 1783])).
% 1.05/1.26 tff(4225,plain,
% 1.05/1.26 (b(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[101, 63])).
% 1.05/1.26 tff(4226,plain,
% 1.05/1.26 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), z)),
% 1.05/1.26 inference(monotonicity,[status(thm)],[1075])).
% 1.05/1.26 tff(4227,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 1.05/1.26 inference(symmetry,[status(thm)],[4226])).
% 1.05/1.26 tff(4228,plain,
% 1.05/1.26 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.05/1.26 inference(transitivity,[status(thm)],[3722, 641])).
% 1.05/1.26 tff(4229,plain,
% 1.05/1.26 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4228])).
% 1.05/1.26 tff(4230,plain,
% 1.05/1.26 (~(s(s(s(elem!1))) = elem!1)),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[821, 4229])).
% 1.05/1.26 tff(4231,plain,
% 1.05/1.26 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3701])).
% 1.05/1.26 tff(4232,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4231])).
% 1.05/1.26 tff(4233,plain,
% 1.05/1.26 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[1041, 4232])).
% 1.05/1.26 tff(4234,plain,
% 1.05/1.26 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(z))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3701, 3717])).
% 1.05/1.26 tff(4235,plain,
% 1.05/1.26 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4234])).
% 1.05/1.26 tff(4236,plain,
% 1.05/1.26 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[1784, 4235])).
% 1.05/1.26 tff(4237,plain,
% 1.05/1.26 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.05/1.26 inference(commutativity,[status(thm)],[])).
% 1.05/1.26 tff(4238,plain,
% 1.05/1.26 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.26 tff(4239,plain,
% 1.05/1.26 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4238, 4237])).
% 1.05/1.26 tff(4240,plain,
% 1.05/1.26 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4239])).
% 1.05/1.26 tff(4241,plain,
% 1.05/1.26 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4240])).
% 1.05/1.26 tff(4242,plain,
% 1.05/1.26 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[94, 4241])).
% 1.05/1.26 tff(4243,plain,
% 1.05/1.26 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[353])).
% 1.05/1.26 tff(4244,plain,
% 1.05/1.26 (r(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[542, 4243])).
% 1.05/1.26 tff(4245,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[63, 4244])).
% 1.05/1.26 tff(4246,plain,((~r(s(elem!1), s(s(s(elem!1))))) | r(s(z), s(s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4247,plain,
% 1.05/1.26 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4246, 63, 3717])).
% 1.05/1.26 tff(4248,plain,
% 1.05/1.26 (b(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[539, 4247, 4242])).
% 1.05/1.26 tff(4249,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.05/1.26 tff(4250,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.05/1.26 tff(4251,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4252,plain,
% 1.05/1.26 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4253,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4252])).
% 1.05/1.26 tff(4254,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4253, 4251])).
% 1.05/1.26 tff(4255,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.05/1.26 inference(quant_inst,[status(thm)],[])).
% 1.05/1.26 tff(4256,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4255, 4254])).
% 1.05/1.26 tff(4257,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4256, 238, 4250, 290, 781, 4249])).
% 1.05/1.26 tff(4258,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4259,plain,
% 1.05/1.26 (~b(s(s(s(elem!1))), elem!1)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4258, 4248, 4236, 4233])).
% 1.05/1.26 tff(4260,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), elem!1)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[647, 4259, 4230])).
% 1.05/1.26 tff(4261,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.05/1.26 inference(monotonicity,[status(thm)],[815])).
% 1.05/1.26 tff(4262,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.05/1.26 inference(symmetry,[status(thm)],[4261])).
% 1.05/1.26 tff(4263,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), z)),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[649, 4262])).
% 1.05/1.26 tff(4264,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.05/1.26 tff(4265,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4264, 4263])).
% 1.05/1.26 tff(4266,plain,(r(s(s(s(elem!1))), z) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4267,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), z)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4266, 4260, 3717])).
% 1.05/1.26 tff(4268,plain,
% 1.05/1.26 (r(s(s(s(z))), z)),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4267, 4227])).
% 1.05/1.26 tff(4269,plain,
% 1.05/1.26 (~r(s(s(s(z))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2827, 4268, 1545])).
% 1.05/1.26 tff(4270,plain,
% 1.05/1.26 (b(s(s(s(z))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2344, 4269, 3739])).
% 1.05/1.26 tff(4271,plain,
% 1.05/1.26 (b(s(s(s(elem!1))), s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[3886, 4270, 13])).
% 1.05/1.26 tff(4272,plain,
% 1.05/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.26 inference(rewrite,[status(thm)],[])).
% 1.05/1.26 tff(4273,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.05/1.26 inference(quant_inst,[status(thm)],[])).
% 1.05/1.26 tff(4274,plain,
% 1.05/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 1.05/1.26 tff(4275,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4274, 238, 4271, 4225, 1784, 1041])).
% 1.05/1.26 tff(4276,plain,(r(s(z), s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4277,plain,
% 1.05/1.26 (r(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4276, 4224, 4058, 13, 4018])).
% 1.05/1.26 tff(4278,assumption,(r(s(z), z)), introduced(assumption)).
% 1.05/1.26 tff(4279,plain,
% 1.05/1.26 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.05/1.26 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.26 tff(4280,plain,
% 1.05/1.26 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 1.05/1.26 inference(symmetry,[status(thm)],[4279])).
% 1.05/1.26 tff(4281,plain,
% 1.05/1.26 (b(s(s(z)), z)),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4031, 4280])).
% 1.05/1.26 tff(4282,plain,
% 1.05/1.26 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.26 tff(4283,plain,
% 1.05/1.26 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4282])).
% 1.05/1.26 tff(4284,plain,
% 1.05/1.26 (~r(z, s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2057, 124, 4020, 4018])).
% 1.05/1.26 tff(4285,plain,
% 1.05/1.26 (b(z, s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2071, 4284])).
% 1.05/1.26 tff(4286,plain,
% 1.05/1.26 (b(z, s(s(z)))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[4285, 4283])).
% 1.05/1.26 tff(4287,plain,
% 1.05/1.26 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.26 tff(4288,plain,
% 1.05/1.26 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4287])).
% 1.05/1.26 tff(4289,plain,
% 1.05/1.26 ((~b(elem!1, s(z))) <=> (~b(elem!1, s(elem!1)))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4288])).
% 1.05/1.26 tff(4290,plain,
% 1.05/1.26 (~b(elem!1, s(elem!1))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[1400, 4289])).
% 1.05/1.26 tff(4291,plain,
% 1.05/1.26 (r(elem!1, s(elem!1))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[629, 4290, 4067])).
% 1.05/1.26 tff(4292,plain,
% 1.05/1.26 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[3717])).
% 1.05/1.26 tff(4293,plain,
% 1.05/1.26 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.26 inference(symmetry,[status(thm)],[4292])).
% 1.05/1.26 tff(4294,plain,
% 1.05/1.26 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.05/1.26 inference(transitivity,[status(thm)],[4019, 4293])).
% 1.05/1.26 tff(4295,plain,
% 1.05/1.26 (r(s(s(elem!1)), s(elem!1))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[169, 4294])).
% 1.05/1.26 tff(4296,plain,
% 1.05/1.26 (~r(elem!1, s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[599, 4295, 4291])).
% 1.05/1.26 tff(4297,plain,
% 1.05/1.26 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.05/1.26 inference(monotonicity,[status(thm)],[4064])).
% 1.05/1.26 tff(4298,plain,
% 1.05/1.26 (~(elem!1 = s(z))),
% 1.05/1.26 inference(modus_ponens,[status(thm)],[72, 4297])).
% 1.05/1.26 tff(4299,plain,
% 1.05/1.26 (r(elem!1, s(z))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[363, 4298, 1400])).
% 1.05/1.26 tff(4300,plain,
% 1.05/1.26 (~r(s(s(elem!1)), elem!1)),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[263, 4020, 4299])).
% 1.05/1.26 tff(4301,plain,
% 1.05/1.26 (~b(elem!1, s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[615, 226, 150, 250, 602])).
% 1.05/1.26 tff(4302,plain,
% 1.05/1.26 (r(elem!1, s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[1319, 4301, 514])).
% 1.05/1.26 tff(4303,plain,
% 1.05/1.26 (~b(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[2991, 226, 1784, 1041])).
% 1.05/1.26 tff(4304,plain,
% 1.05/1.26 (r(s(z), s(s(s(elem!1))))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[101, 4303])).
% 1.05/1.26 tff(4305,plain,
% 1.05/1.26 ($false),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[1378, 4304, 4302, 1370])).
% 1.05/1.26 tff(4306,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.26 tff(4307,plain,
% 1.05/1.26 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[4306, 4224, 3724, 4058, 4299, 150, 4300, 4296])).
% 1.05/1.26 tff(4308,plain,
% 1.05/1.26 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[223, 4307, 3708])).
% 1.05/1.26 tff(4309,plain,
% 1.05/1.26 (~r(s(z), s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[218, 4277, 4308])).
% 1.05/1.26 tff(4310,plain,
% 1.05/1.26 (b(s(z), s(s(elem!1)))),
% 1.05/1.26 inference(unit_resolution,[status(thm)],[56, 4309])).
% 1.05/1.26 tff(4311,plain,
% 1.05/1.26 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4130, 4310, 4031, 1783])).
% 1.05/1.27 tff(4312,plain,
% 1.05/1.27 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[13])).
% 1.05/1.27 tff(4313,plain,
% 1.05/1.27 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(symmetry,[status(thm)],[4312])).
% 1.05/1.27 tff(4314,plain,
% 1.05/1.27 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4313])).
% 1.05/1.27 tff(4315,assumption,(~b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.05/1.27 tff(4316,plain,
% 1.05/1.27 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4315, 4314])).
% 1.05/1.27 tff(4317,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1906, 4316])).
% 1.05/1.27 tff(4318,plain,(b(s(s(s(s(s(z))))), s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4319,plain,
% 1.05/1.27 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4318, 4311, 13])).
% 1.05/1.27 tff(4320,plain,
% 1.05/1.27 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1738, 4319])).
% 1.05/1.27 tff(4321,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.05/1.27 tff(4322,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4323,plain,
% 1.05/1.27 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4324,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4323])).
% 1.05/1.27 tff(4325,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4324, 4322])).
% 1.05/1.27 tff(4326,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.27 tff(4327,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 1.05/1.27 tff(4328,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4327, 124, 1717, 3495, 4321])).
% 1.05/1.27 tff(4329,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4330,plain,
% 1.05/1.27 (~r(s(s(z)), s(s(s(z))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4329, 4320, 4060])).
% 1.05/1.27 tff(4331,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.05/1.27 tff(4332,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.05/1.27 tff(4333,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[3624, 51, 4332, 147, 4331])).
% 1.05/1.27 tff(4334,plain,(b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4335,plain,
% 1.05/1.27 (b(s(s(z)), s(s(s(z))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4334, 4330])).
% 1.05/1.27 tff(4336,plain,
% 1.05/1.27 (~b(s(s(s(z))), z)),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4209, 4335, 4286, 4281])).
% 1.05/1.27 tff(4337,plain,
% 1.05/1.27 (r(s(s(s(z))), z)),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1524, 4336])).
% 1.05/1.27 tff(4338,plain,
% 1.05/1.27 (r(s(s(s(elem!1))), z)),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4337, 4226])).
% 1.05/1.27 tff(4339,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4340,plain,
% 1.05/1.27 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4341,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4340])).
% 1.05/1.27 tff(4342,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4341, 4339])).
% 1.05/1.27 tff(4343,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.27 tff(4344,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4343, 4342])).
% 1.05/1.27 tff(4345,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4344, 124, 4338, 4278, 4277])).
% 1.05/1.27 tff(4346,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~(s(s(z)) = s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | b(elem!1, s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4347,plain,
% 1.05/1.27 (~b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4346, 4013, 3660, 4010, 1815, 3998, 1400, 1081])).
% 1.05/1.27 tff(4348,plain,
% 1.05/1.27 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4347, 4006])).
% 1.05/1.27 tff(4349,assumption,(~b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.05/1.27 tff(4350,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1118, 51, 2685, 2684, 4349])).
% 1.05/1.27 tff(4351,plain,(b(s(s(s(s(s(z))))), s(elem!1)) | (s(s(s(s(s(z))))) = s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4352,plain,
% 1.05/1.27 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4351, 4348, 4003])).
% 1.05/1.27 tff(4353,assumption,(r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.05/1.27 tff(4354,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4355,plain,
% 1.05/1.27 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4356,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4355])).
% 1.05/1.27 tff(4357,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4356, 4354])).
% 1.05/1.27 tff(4358,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.27 tff(4359,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4358, 4357])).
% 1.05/1.27 tff(4360,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4359, 124, 307, 3824, 4353])).
% 1.05/1.27 tff(4361,plain,((~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)))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4362,plain,
% 1.05/1.27 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4361, 4352, 3999])).
% 1.05/1.27 tff(4363,plain,
% 1.05/1.27 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4362, 3663])).
% 1.05/1.27 tff(4364,plain,
% 1.05/1.27 (r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1781, 4347])).
% 1.05/1.27 tff(4365,plain,
% 1.05/1.27 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1759, 4364, 3697, 3998])).
% 1.05/1.27 tff(4366,plain,
% 1.05/1.27 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1764, 4365])).
% 1.05/1.27 tff(4367,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4366, 4363])).
% 1.05/1.27 tff(4368,plain,((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(elem!1, s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | b(s(z), elem!1) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4369,plain,
% 1.05/1.27 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4368, 1807, 1380, 1400, 1803])).
% 1.05/1.27 tff(4370,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4369, 1796])).
% 1.05/1.27 tff(4371,plain,(b(elem!1, s(z)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = elem!1) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | b(s(s(z)), s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4372,plain,
% 1.05/1.27 (b(elem!1, s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4371, 307, 167, 692, 1380, 161, 210, 1137, 64, 1399, 359])).
% 1.05/1.27 tff(4373,plain,
% 1.05/1.27 (~r(elem!1, s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1149, 4372, 1137, 307, 150])).
% 1.05/1.27 tff(4374,plain,
% 1.05/1.27 (b(elem!1, s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[629, 4373, 387])).
% 1.05/1.27 tff(4375,plain,
% 1.05/1.27 (~b(s(elem!1), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1160, 4374, 1137, 4372])).
% 1.05/1.27 tff(4376,plain,
% 1.05/1.27 (r(s(elem!1), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[473, 4375, 1])).
% 1.05/1.27 tff(4377,plain,
% 1.05/1.27 (~r(s(elem!1), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[483, 4376, 80])).
% 1.05/1.27 tff(4378,plain,
% 1.05/1.27 (~r(s(s(z)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1256, 124, 80, 4376])).
% 1.05/1.27 tff(4379,assumption,(~r(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.05/1.27 tff(4380,plain,
% 1.05/1.27 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1260, 51, 4379])).
% 1.05/1.27 tff(4381,plain,
% 1.05/1.27 (b(s(s(z)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4380, 1250])).
% 1.05/1.27 tff(4382,plain,
% 1.05/1.27 (b(s(elem!1), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[488, 278, 2222])).
% 1.05/1.27 tff(4383,plain,
% 1.05/1.27 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[499, 4382, 225, 491])).
% 1.05/1.27 tff(4384,plain,
% 1.05/1.27 (r(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[539, 4383, 415])).
% 1.05/1.27 tff(4385,plain,
% 1.05/1.27 (s(s(s(elem!1))) = elem!1),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1203, 4384, 210, 150, 491, 631])).
% 1.05/1.27 tff(4386,plain,
% 1.05/1.27 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4385])).
% 1.05/1.27 tff(4387,plain,
% 1.05/1.27 (b(s(s(z)), elem!1)),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[225, 4386])).
% 1.05/1.27 tff(4388,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4389,plain,
% 1.05/1.27 (((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4390,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4389])).
% 1.05/1.27 tff(4391,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4390, 4388])).
% 1.05/1.27 tff(4392,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.27 tff(4393,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4392, 4391])).
% 1.05/1.27 tff(4394,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4393, 238, 631, 4382, 4387, 4381])).
% 1.05/1.27 tff(4395,plain,((s(elem!1) = s(s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | r(s(s(z)), s(elem!1)) | r(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4396,plain,
% 1.05/1.27 (s(elem!1) = s(s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4395, 4374, 266, 210, 150, 1399, 4378, 4377])).
% 1.05/1.27 tff(4397,plain,
% 1.05/1.27 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4396])).
% 1.05/1.27 tff(4398,plain,
% 1.05/1.27 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.05/1.27 inference(symmetry,[status(thm)],[4397])).
% 1.05/1.27 tff(4399,plain,
% 1.05/1.27 (s(z) = elem!1),
% 1.05/1.27 inference(transitivity,[status(thm)],[69, 4398, 154])).
% 1.05/1.27 tff(4400,plain,
% 1.05/1.27 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4399])).
% 1.05/1.27 tff(4401,plain,
% 1.05/1.27 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.05/1.27 inference(symmetry,[status(thm)],[4400])).
% 1.05/1.27 tff(4402,plain,
% 1.05/1.27 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4401])).
% 1.05/1.27 tff(4403,plain,
% 1.05/1.27 (~b(elem!1, s(z))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[839, 4402])).
% 1.05/1.27 tff(4404,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4372, 4403])).
% 1.05/1.27 tff(4405,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4406,plain,
% 1.05/1.27 (~r(s(s(elem!1)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4405, 210, 150, 358, 1389, 1380, 161, 64, 359])).
% 1.05/1.27 tff(4407,plain,
% 1.05/1.27 (b(s(s(elem!1)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[323, 4406, 272])).
% 1.05/1.27 tff(4408,plain,
% 1.05/1.27 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.05/1.27 inference(commutativity,[status(thm)],[])).
% 1.05/1.27 tff(4409,plain,
% 1.05/1.27 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.05/1.27 inference(symmetry,[status(thm)],[4408])).
% 1.05/1.27 tff(4410,plain,
% 1.05/1.27 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4409])).
% 1.05/1.27 tff(4411,plain,
% 1.05/1.27 (~(s(z) = s(s(z)))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[74, 4410])).
% 1.05/1.27 tff(4412,plain,
% 1.05/1.27 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.05/1.27 inference(symmetry,[status(thm)],[3617])).
% 1.05/1.27 tff(4413,plain,
% 1.05/1.27 (r(s(elem!1), s(s(elem!1)))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[192, 4412])).
% 1.05/1.27 tff(4414,plain,
% 1.05/1.27 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.05/1.27 inference(transitivity,[status(thm)],[304, 2668])).
% 1.05/1.27 tff(4415,plain,
% 1.05/1.27 (r(s(elem!1), elem!1)),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[169, 4414])).
% 1.05/1.27 tff(4416,plain,
% 1.05/1.27 (~r(s(s(elem!1)), elem!1)),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[700, 4415, 4413])).
% 1.05/1.27 tff(4417,plain,
% 1.05/1.27 (b(s(s(elem!1)), elem!1)),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[255, 4416, 248])).
% 1.05/1.27 tff(4418,plain,
% 1.05/1.27 (b(s(s(s(z))), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1428, 4417, 276])).
% 1.05/1.27 tff(4419,plain,
% 1.05/1.27 (b(s(s(z)), s(s(s(s(z)))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[462, 3331])).
% 1.05/1.27 tff(4420,plain,
% 1.05/1.27 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[2268])).
% 1.05/1.27 tff(4421,plain,
% 1.05/1.27 (r(s(z), s(s(s(s(z)))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[161, 4420])).
% 1.05/1.27 tff(4422,plain,
% 1.05/1.27 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[3229, 124, 192, 210])).
% 1.05/1.27 tff(4423,plain,
% 1.05/1.27 (b(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[3233, 4422])).
% 1.05/1.27 tff(4424,plain,
% 1.05/1.27 (b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4423, 2269])).
% 1.05/1.27 tff(4425,plain,
% 1.05/1.27 (~r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1697, 4424, 169, 281, 4421, 4419, 777])).
% 1.05/1.27 tff(4426,plain,
% 1.05/1.27 (b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1709, 4425])).
% 1.05/1.27 tff(4427,plain,
% 1.05/1.27 (r(s(s(z)), s(s(s(z))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[192, 3616])).
% 1.05/1.27 tff(4428,plain,
% 1.05/1.27 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4329, 3495, 4321])).
% 1.05/1.27 tff(4429,plain,
% 1.05/1.27 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1738, 4428])).
% 1.05/1.27 tff(4430,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4431,plain,
% 1.05/1.27 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4432,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4431])).
% 1.05/1.27 tff(4433,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4432, 4430])).
% 1.05/1.27 tff(4434,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.27 tff(4435,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.05/1.27 inference(modus_ponens,[status(thm)],[4434, 4433])).
% 1.05/1.27 tff(4436,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4435, 238, 1587, 1501, 1906, 1786])).
% 1.05/1.27 tff(4437,plain,((~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(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4438,plain,
% 1.05/1.27 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4437, 4429, 1587, 1501])).
% 1.05/1.27 tff(4439,plain,
% 1.05/1.27 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1904, 4438])).
% 1.05/1.27 tff(4440,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[3657, 124, 4439, 1477, 3495])).
% 1.05/1.27 tff(4441,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4442,plain,
% 1.05/1.27 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4441, 3422, 4424, 4419, 4427])).
% 1.05/1.27 tff(4443,plain,
% 1.05/1.27 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1101, 4442])).
% 1.05/1.27 tff(4444,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[3606, 238, 4443, 4426, 4418, 3288])).
% 1.05/1.27 tff(4445,plain,((~(elem!1 = s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(z)), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4446,plain,
% 1.05/1.27 (~(elem!1 = s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4445, 192, 80, 692, 161, 210, 167, 1137])).
% 1.05/1.27 tff(4447,plain,
% 1.05/1.27 (b(elem!1, s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[363, 4446, 359])).
% 1.05/1.27 tff(4448,plain,
% 1.05/1.27 (~(s(elem!1) = s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[379, 4446])).
% 1.05/1.27 tff(4449,plain,
% 1.05/1.27 (~r(elem!1, s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1149, 307, 1137, 370, 150])).
% 1.05/1.27 tff(4450,plain,
% 1.05/1.27 (b(elem!1, s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[629, 4449, 387])).
% 1.05/1.27 tff(4451,plain,
% 1.05/1.27 (~b(s(elem!1), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1160, 4450, 1137, 370])).
% 1.05/1.27 tff(4452,plain,
% 1.05/1.27 (r(s(elem!1), s(z))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[473, 4451, 1])).
% 1.05/1.27 tff(4453,plain,
% 1.05/1.27 (~b(s(elem!1), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[1243, 1399, 225, 1235])).
% 1.05/1.27 tff(4454,plain,
% 1.05/1.27 (r(s(elem!1), s(s(z)))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[488, 4453, 278])).
% 1.05/1.27 tff(4455,plain,
% 1.05/1.27 ($false),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[483, 4454, 4452, 169])).
% 1.05/1.27 tff(4456,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(s(z))) | (s(elem!1) = s(z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.27 tff(4457,plain,
% 1.05/1.27 (~r(s(s(elem!1)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[4456, 4448, 80, 1, 266, 4423, 1137, 4447, 210, 150])).
% 1.05/1.27 tff(4458,plain,
% 1.05/1.27 (b(s(s(elem!1)), s(elem!1))),
% 1.05/1.27 inference(unit_resolution,[status(thm)],[323, 4457, 272])).
% 1.05/1.27 tff(4459,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4460,plain,
% 1.05/1.27 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.05/1.27 inference(rewrite,[status(thm)],[])).
% 1.05/1.27 tff(4461,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))))),
% 1.05/1.27 inference(monotonicity,[status(thm)],[4460])).
% 1.05/1.27 tff(4462,plain,
% 1.05/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))))),
% 1.05/1.27 inference(transitivity,[status(thm)],[4461, 4459])).
% 1.05/1.27 tff(4463,plain,
% 1.05/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))))),
% 1.05/1.27 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4464,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1))))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 1.05/1.28 tff(4465,plain,
% 1.05/1.28 ($false),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4464, 238, 1185, 289, 1137, 370])).
% 1.05/1.28 tff(4466,plain,((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.28 tff(4467,plain,
% 1.05/1.28 (~b(elem!1, s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4466, 4458, 1137, 4447])).
% 1.05/1.28 tff(4468,plain,
% 1.05/1.28 (r(elem!1, s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[606, 4467, 150])).
% 1.05/1.28 tff(4469,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4470,plain,
% 1.05/1.28 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4471,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4470])).
% 1.05/1.28 tff(4472,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4471, 4469])).
% 1.05/1.28 tff(4473,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4474,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4473, 4472])).
% 1.05/1.28 tff(4475,plain,
% 1.05/1.28 (~r(elem!1, s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4474, 124, 4468, 210])).
% 1.05/1.28 tff(4476,plain,
% 1.05/1.28 (~(elem!1 = s(s(z)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[372, 4447, 64])).
% 1.05/1.28 tff(4477,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4478,plain,
% 1.05/1.28 (((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4479,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z))))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4478])).
% 1.05/1.28 tff(4480,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4479, 4477])).
% 1.05/1.28 tff(4481,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z)))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4482,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(z))))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4481, 4480])).
% 1.05/1.28 tff(4483,plain,
% 1.05/1.28 ($false),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4482, 124, 591, 192, 939])).
% 1.05/1.28 tff(4484,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.28 tff(4485,plain,
% 1.05/1.28 (~r(elem!1, s(s(z)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4484, 4468, 192])).
% 1.05/1.28 tff(4486,plain,
% 1.05/1.28 (b(elem!1, s(s(z)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[763, 4485, 4476])).
% 1.05/1.28 tff(4487,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4488,plain,
% 1.05/1.28 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4489,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4488])).
% 1.05/1.28 tff(4490,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4489, 4487])).
% 1.05/1.28 tff(4491,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4492,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4491, 4490])).
% 1.05/1.28 tff(4493,plain,
% 1.05/1.28 (~b(elem!1, s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4492, 238, 4486, 266, 4423])).
% 1.05/1.28 tff(4494,plain,
% 1.05/1.28 (elem!1 = s(s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[1319, 4493, 4475])).
% 1.05/1.28 tff(4495,plain,
% 1.05/1.28 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4494])).
% 1.05/1.28 tff(4496,plain,
% 1.05/1.28 (b(s(s(s(elem!1))), s(z))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4447, 4495])).
% 1.05/1.28 tff(4497,plain,
% 1.05/1.28 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[420, 418])).
% 1.05/1.28 tff(4498,plain,
% 1.05/1.28 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[1243, 490, 225, 1235])).
% 1.05/1.28 tff(4499,plain,
% 1.05/1.28 (r(s(s(s(elem!1))), s(elem!1))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[459, 4498, 4497])).
% 1.05/1.28 tff(4500,plain,
% 1.05/1.28 (~r(s(z), s(elem!1))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[450, 4499, 161])).
% 1.05/1.28 tff(4501,plain,
% 1.05/1.28 (b(s(z), s(elem!1))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[439, 4500, 433])).
% 1.05/1.28 tff(4502,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4503,plain,
% 1.05/1.28 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4504,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4503])).
% 1.05/1.28 tff(4505,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4504, 4502])).
% 1.05/1.28 tff(4506,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(elem!1)))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4507,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 1.05/1.28 tff(4508,plain,
% 1.05/1.28 ($false),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4507, 238, 289, 288, 1137, 660])).
% 1.05/1.28 tff(4509,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.28 tff(4510,plain,
% 1.05/1.28 (~b(s(elem!1), s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4509, 4501, 1137, 289])).
% 1.05/1.28 tff(4511,plain,
% 1.05/1.28 (r(s(elem!1), s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[534, 4510, 206])).
% 1.05/1.28 tff(4512,plain,
% 1.05/1.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[1169, 4511, 210])).
% 1.05/1.28 tff(4513,plain,
% 1.05/1.28 (b(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[539, 4512, 418])).
% 1.05/1.28 tff(4514,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4515,plain,
% 1.05/1.28 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4516,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4515])).
% 1.05/1.28 tff(4517,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4516, 4514])).
% 1.05/1.28 tff(4518,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4519,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4518, 4517])).
% 1.05/1.28 tff(4520,plain,
% 1.05/1.28 ($false),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4519, 238, 4513, 490, 225, 1235])).
% 1.05/1.28 tff(4521,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.28 tff(4522,plain,
% 1.05/1.28 (~b(s(elem!1), s(s(z)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4521, 4423, 266, 415, 210, 159, 1137, 4458, 426, 161])).
% 1.05/1.28 tff(4523,plain,
% 1.05/1.28 (r(s(elem!1), s(s(z)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[488, 4522, 4448])).
% 1.05/1.28 tff(4524,plain,
% 1.05/1.28 (~r(s(elem!1), s(z))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[483, 4523, 80])).
% 1.05/1.28 tff(4525,plain,
% 1.05/1.28 (b(s(elem!1), s(z))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[473, 4524, 1])).
% 1.05/1.28 tff(4526,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4527,plain,
% 1.05/1.28 (((~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(elem!1), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4528,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.05/1.28 inference(monotonicity,[status(thm)],[4527])).
% 1.05/1.28 tff(4529,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.28 inference(transitivity,[status(thm)],[4528, 4526])).
% 1.05/1.28 tff(4530,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(z))))),
% 1.05/1.28 inference(quant_inst,[status(thm)],[])).
% 1.05/1.28 tff(4531,plain,
% 1.05/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.05/1.28 inference(modus_ponens,[status(thm)],[4530, 4529])).
% 1.05/1.28 tff(4532,plain,
% 1.05/1.28 ($false),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4531, 238, 289, 288, 1137, 1152])).
% 1.05/1.28 tff(4533,plain,((~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(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.28 tff(4534,plain,
% 1.05/1.28 (~b(s(elem!1), s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[4533, 4525, 1137, 4458])).
% 1.05/1.28 tff(4535,plain,
% 1.05/1.28 (r(s(elem!1), s(s(elem!1)))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[534, 4534, 159])).
% 1.05/1.28 tff(4536,plain,
% 1.05/1.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[1169, 4535, 210])).
% 1.05/1.28 tff(4537,plain,
% 1.05/1.28 (b(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.28 inference(unit_resolution,[status(thm)],[539, 4536, 415])).
% 1.05/1.28 tff(4538,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4539,plain,
% 1.05/1.28 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.28 inference(rewrite,[status(thm)],[])).
% 1.05/1.28 tff(4540,plain,
% 1.05/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4539])).
% 1.05/1.29 tff(4541,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4540, 4538])).
% 1.05/1.29 tff(4542,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4543,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4542, 4541])).
% 1.05/1.29 tff(4544,plain,
% 1.05/1.29 ($false),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4543, 238, 4537, 1137, 4525, 4496])).
% 1.05/1.29 tff(4545,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(s(s(z)), s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.29 tff(4546,plain,
% 1.05/1.29 (~r(s(s(z)), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4545, 210, 1389, 358, 161, 150, 64, 359])).
% 1.05/1.29 tff(4547,plain,
% 1.05/1.29 (b(s(s(z)), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[135, 4546, 114])).
% 1.05/1.29 tff(4548,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4549,plain,
% 1.05/1.29 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4550,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4549])).
% 1.05/1.29 tff(4551,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4550, 4548])).
% 1.05/1.29 tff(4552,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4553,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4552, 4551])).
% 1.05/1.29 tff(4554,plain,
% 1.05/1.29 (~b(s(z), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4553, 238, 4407, 1389, 4547])).
% 1.05/1.29 tff(4555,plain,
% 1.05/1.29 (((~![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))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4556,plain,
% 1.05/1.29 ((~![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))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4557,plain,
% 1.05/1.29 ((~![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)))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4556, 4555])).
% 1.05/1.29 tff(4558,plain,
% 1.05/1.29 ((s(z) = s(s(z))) | r(s(z), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4557, 51, 4554])).
% 1.05/1.29 tff(4559,plain,
% 1.05/1.29 (r(s(z), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4558, 4411])).
% 1.05/1.29 tff(4560,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.05/1.29 tff(4561,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4562,plain,
% 1.05/1.29 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4563,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4562])).
% 1.05/1.29 tff(4564,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4563, 4561])).
% 1.05/1.29 tff(4565,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4566,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4565, 4564])).
% 1.05/1.29 tff(4567,plain,
% 1.05/1.29 ($false),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4566, 124, 161, 3002, 4560])).
% 1.05/1.29 tff(4568,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.29 tff(4569,plain,
% 1.05/1.29 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4568, 4559, 161])).
% 1.05/1.29 tff(4570,plain,
% 1.05/1.29 (b(s(s(s(elem!1))), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[3233, 4569])).
% 1.05/1.29 tff(4571,plain,
% 1.05/1.29 (~b(s(elem!1), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4521, 4570, 266, 415, 210, 159, 1389, 4407, 1387, 161])).
% 1.05/1.29 tff(4572,assumption,(~b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.05/1.29 tff(4573,plain,
% 1.05/1.29 (r(s(elem!1), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[488, 278, 4572])).
% 1.05/1.29 tff(4574,plain,
% 1.05/1.29 (~r(s(elem!1), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[483, 4573, 169])).
% 1.05/1.29 tff(4575,plain,
% 1.05/1.29 (b(s(elem!1), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[473, 4574, 1])).
% 1.05/1.29 tff(4576,plain,
% 1.05/1.29 (~(elem!1 = s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[280, 278])).
% 1.05/1.29 tff(4577,plain,
% 1.05/1.29 (b(elem!1, s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[363, 4576, 359])).
% 1.05/1.29 tff(4578,plain,
% 1.05/1.29 (~b(s(elem!1), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4533, 4575, 1137, 289])).
% 1.05/1.29 tff(4579,plain,
% 1.05/1.29 (r(s(elem!1), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[534, 4578, 159])).
% 1.05/1.29 tff(4580,plain,
% 1.05/1.29 (~b(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4466, 4577, 1137, 289])).
% 1.05/1.29 tff(4581,plain,
% 1.05/1.29 (r(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[606, 4580, 150])).
% 1.05/1.29 tff(4582,plain,
% 1.05/1.29 (~b(elem!1, s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1160, 4575, 1137, 4577])).
% 1.05/1.29 tff(4583,plain,
% 1.05/1.29 (r(elem!1, s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[629, 4582, 387])).
% 1.05/1.29 tff(4584,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4585,plain,
% 1.05/1.29 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4586,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4585])).
% 1.05/1.29 tff(4587,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4586, 4584])).
% 1.05/1.29 tff(4588,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(elem!1))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4589,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4588, 4587])).
% 1.05/1.29 tff(4590,plain,
% 1.05/1.29 ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4589, 124])).
% 1.05/1.29 tff(4591,plain,
% 1.05/1.29 (~r(s(elem!1), elem!1)),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4590, 4583, 4581, 4579])).
% 1.05/1.29 tff(4592,plain,
% 1.05/1.29 (b(s(elem!1), elem!1)),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[408, 4591, 394])).
% 1.05/1.29 tff(4593,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4594,plain,
% 1.05/1.29 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4595,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4594])).
% 1.05/1.29 tff(4596,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4595, 4593])).
% 1.05/1.29 tff(4597,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4598,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4597, 4596])).
% 1.05/1.29 tff(4599,plain,
% 1.05/1.29 ($false),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4598, 238, 4592, 1137, 4577, 4575])).
% 1.05/1.29 tff(4600,plain,((s(elem!1) = s(s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(z))) | r(elem!1, s(z)) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.29 tff(4601,plain,
% 1.05/1.29 (s(elem!1) = s(s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4600, 4407, 1389, 150, 358, 80, 359, 4571])).
% 1.05/1.29 tff(4602,plain,
% 1.05/1.29 (s(s(elem!1)) = s(s(s(z)))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4601])).
% 1.05/1.29 tff(4603,plain,
% 1.05/1.29 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4602])).
% 1.05/1.29 tff(4604,plain,
% 1.05/1.29 (b(s(z), s(s(s(z))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[1389, 4603])).
% 1.05/1.29 tff(4605,plain,
% 1.05/1.29 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4602])).
% 1.05/1.29 tff(4606,plain,
% 1.05/1.29 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4605])).
% 1.05/1.29 tff(4607,plain,
% 1.05/1.29 (b(s(s(z)), s(s(s(s(z)))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[266, 4606])).
% 1.05/1.29 tff(4608,plain,
% 1.05/1.29 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4605])).
% 1.05/1.29 tff(4609,plain,
% 1.05/1.29 (b(s(s(s(s(z)))), s(s(z)))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4570, 4608])).
% 1.05/1.29 tff(4610,plain,
% 1.05/1.29 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4605])).
% 1.05/1.29 tff(4611,plain,
% 1.05/1.29 (r(s(z), s(s(s(s(z)))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[161, 4610])).
% 1.05/1.29 tff(4612,plain,
% 1.05/1.29 (~r(s(z), s(s(s(s(s(z))))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1697, 4611, 80, 4601, 4609, 4607, 692])).
% 1.05/1.29 tff(4613,plain,
% 1.05/1.29 (b(s(z), s(s(s(s(s(z))))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1709, 4612])).
% 1.05/1.29 tff(4614,plain,
% 1.05/1.29 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4605])).
% 1.05/1.29 tff(4615,plain,
% 1.05/1.29 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4614, 4602])).
% 1.05/1.29 tff(4616,plain,
% 1.05/1.29 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4615])).
% 1.05/1.29 tff(4617,plain,
% 1.05/1.29 (elem!1 = s(z)),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[379, 4601])).
% 1.05/1.29 tff(4618,plain,
% 1.05/1.29 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4617])).
% 1.05/1.29 tff(4619,plain,
% 1.05/1.29 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(symmetry,[status(thm)],[4618])).
% 1.05/1.29 tff(4620,plain,
% 1.05/1.29 (b(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[1389, 4619])).
% 1.05/1.29 tff(4621,plain,
% 1.05/1.29 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4617, 4614])).
% 1.05/1.29 tff(4622,plain,
% 1.05/1.29 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4621, 3384])).
% 1.05/1.29 tff(4623,plain,
% 1.05/1.29 ((s(s(s(s(s(z))))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.05/1.29 inference(symmetry,[status(thm)],[4622])).
% 1.05/1.29 tff(4624,plain,
% 1.05/1.29 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4623])).
% 1.05/1.29 tff(4625,plain,
% 1.05/1.29 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[728, 4624])).
% 1.05/1.29 tff(4626,plain,
% 1.05/1.29 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[3552, 4612, 4601, 4625])).
% 1.05/1.29 tff(4627,plain,
% 1.05/1.29 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[3567, 4626, 4407, 4620])).
% 1.05/1.29 tff(4628,plain,
% 1.05/1.29 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4627, 4616])).
% 1.05/1.29 tff(4629,plain,
% 1.05/1.29 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1099, 51, 4628, 1094])).
% 1.05/1.29 tff(4630,plain,
% 1.05/1.29 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4605, 4602])).
% 1.05/1.29 tff(4631,plain,
% 1.05/1.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[210, 4630])).
% 1.05/1.29 tff(4632,plain,
% 1.05/1.29 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[3657, 124, 4631, 4629])).
% 1.05/1.29 tff(4633,plain,
% 1.05/1.29 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1904, 4632])).
% 1.05/1.29 tff(4634,plain,
% 1.05/1.29 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4437, 4633, 4609, 4607])).
% 1.05/1.29 tff(4635,plain,
% 1.05/1.29 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1738, 4634])).
% 1.05/1.29 tff(4636,plain,
% 1.05/1.29 (~r(s(s(s(s(s(z))))), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1725, 4635, 80])).
% 1.05/1.29 tff(4637,plain,
% 1.05/1.29 (b(s(s(s(s(s(z))))), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1781, 4636])).
% 1.05/1.29 tff(4638,plain,
% 1.05/1.29 (~r(s(s(s(s(z)))), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[3369, 4637, 4601, 4613, 4609, 4607, 80, 4604, 114])).
% 1.05/1.29 tff(4639,plain,
% 1.05/1.29 (~b(s(s(s(s(z)))), s(z))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1794, 4637, 4613, 4633])).
% 1.05/1.29 tff(4640,plain,
% 1.05/1.29 ($false),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1624, 4639, 4638])).
% 1.05/1.29 tff(4641,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.29 tff(4642,plain,
% 1.05/1.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4641, 64, 161, 150, 359, 1380, 114])).
% 1.05/1.29 tff(4643,plain,
% 1.05/1.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[223, 4642, 209])).
% 1.05/1.29 tff(4644,plain,
% 1.05/1.29 (~r(s(z), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[1345, 64, 150, 161, 374, 359, 114])).
% 1.05/1.29 tff(4645,plain,
% 1.05/1.29 (b(s(z), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[56, 4644])).
% 1.05/1.29 tff(4646,plain,
% 1.05/1.29 (~(elem!1 = s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[372, 4577, 64])).
% 1.05/1.29 tff(4647,plain,
% 1.05/1.29 (b(s(elem!1), s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4600, 289, 1137, 150, 358, 169, 359, 278])).
% 1.05/1.29 tff(4648,plain,
% 1.05/1.29 (~b(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4466, 289, 1137, 4577])).
% 1.05/1.29 tff(4649,plain,
% 1.05/1.29 (r(elem!1, s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[606, 4648, 150])).
% 1.05/1.29 tff(4650,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4651,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4652,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.05/1.29 tff(4653,plain,
% 1.05/1.29 (~b(s(s(z)), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4652, 238, 289, 490, 2180])).
% 1.05/1.29 tff(4654,plain,
% 1.05/1.29 (r(s(s(z)), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[135, 4653, 114])).
% 1.05/1.29 tff(4655,plain,
% 1.05/1.29 (~r(elem!1, s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4484, 4654, 591])).
% 1.05/1.29 tff(4656,plain,
% 1.05/1.29 (b(elem!1, s(s(z)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[763, 4655, 541])).
% 1.05/1.29 tff(4657,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4658,plain,
% 1.05/1.29 (((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4659,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4658])).
% 1.05/1.29 tff(4660,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4659, 4657])).
% 1.05/1.29 tff(4661,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4662,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4661, 4660])).
% 1.05/1.29 tff(4663,plain,
% 1.05/1.29 (~b(elem!1, s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4662, 238, 490, 4656, 2180])).
% 1.05/1.29 tff(4664,plain,
% 1.05/1.29 (r(elem!1, s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[629, 4663, 1212])).
% 1.05/1.29 tff(4665,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4666,plain,
% 1.05/1.29 (((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(rewrite,[status(thm)],[])).
% 1.05/1.29 tff(4667,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.05/1.29 inference(monotonicity,[status(thm)],[4666])).
% 1.05/1.29 tff(4668,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.05/1.29 inference(transitivity,[status(thm)],[4667, 4665])).
% 1.05/1.29 tff(4669,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 1.05/1.29 inference(quant_inst,[status(thm)],[])).
% 1.05/1.29 tff(4670,plain,
% 1.05/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.05/1.29 inference(modus_ponens,[status(thm)],[4669, 4668])).
% 1.05/1.29 tff(4671,plain,
% 1.05/1.29 (~b(s(elem!1), elem!1)),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4670, 238, 490, 4656, 2180])).
% 1.05/1.29 tff(4672,plain,
% 1.05/1.29 (r(s(elem!1), elem!1)),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[408, 4671, 1213])).
% 1.05/1.29 tff(4673,plain,
% 1.05/1.29 (~r(s(elem!1), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4590, 4672, 591, 4664])).
% 1.05/1.29 tff(4674,plain,
% 1.05/1.29 (b(s(elem!1), s(s(elem!1)))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[534, 4673, 206])).
% 1.05/1.29 tff(4675,plain,
% 1.05/1.29 (~b(s(z), s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[4509, 4674, 1137, 289])).
% 1.05/1.29 tff(4676,plain,
% 1.05/1.29 (r(s(z), s(elem!1))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[439, 4675, 1387])).
% 1.05/1.29 tff(4677,plain,
% 1.05/1.29 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[298, 4674, 226, 289])).
% 1.05/1.29 tff(4678,plain,
% 1.05/1.29 (r(s(elem!1), s(s(s(elem!1))))),
% 1.05/1.29 inference(unit_resolution,[status(thm)],[539, 4677, 418])).
% 1.05/1.29 tff(4679,plain,
% 1.05/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4680,plain,
% 1.15/1.30 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4681,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4680])).
% 1.15/1.30 tff(4682,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4681, 4679])).
% 1.15/1.30 tff(4683,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4684,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4683, 4682])).
% 1.15/1.30 tff(4685,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4684, 124, 4672, 4678, 161, 4676])).
% 1.15/1.30 tff(4686,plain,((~b(s(s(z)), s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (elem!1 = s(s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.30 tff(4687,plain,
% 1.15/1.30 (~b(s(s(z)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4686, 289, 415, 226, 161, 1137, 159, 4649, 4647, 541, 114])).
% 1.15/1.30 tff(4688,plain,
% 1.15/1.30 (r(s(s(z)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1260, 51, 4687, 1250])).
% 1.15/1.30 tff(4689,assumption,(r(s(s(z)), s(elem!1))), introduced(assumption)).
% 1.15/1.30 tff(4690,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4691,plain,
% 1.15/1.30 (((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4692,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4691])).
% 1.15/1.30 tff(4693,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4692, 4690])).
% 1.15/1.30 tff(4694,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), elem!1)))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4695,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), elem!1))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4694, 4693])).
% 1.15/1.30 tff(4696,plain,
% 1.15/1.30 (~r(s(s(z)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4695, 124, 590, 4689])).
% 1.15/1.30 tff(4697,plain,
% 1.15/1.30 (b(s(s(z)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1275, 4696, 374])).
% 1.15/1.30 tff(4698,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4699,plain,
% 1.15/1.30 (((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4700,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z))))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4699])).
% 1.15/1.30 tff(4701,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z)))))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4700, 4698])).
% 1.15/1.30 tff(4702,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4703,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1))) | (~r(elem!1, s(s(z))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4702, 4701])).
% 1.15/1.30 tff(4704,plain,
% 1.15/1.30 (~r(elem!1, s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4703, 124, 590, 169, 4689])).
% 1.15/1.30 tff(4705,plain,
% 1.15/1.30 (b(elem!1, s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[763, 4704, 541])).
% 1.15/1.30 tff(4706,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4707,plain,
% 1.15/1.30 (((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4708,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4707])).
% 1.15/1.30 tff(4709,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4708, 4706])).
% 1.15/1.30 tff(4710,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4711,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 1.15/1.30 tff(4712,plain,
% 1.15/1.30 (~b(s(elem!1), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4711, 238, 490, 4705, 4697])).
% 1.15/1.30 tff(4713,plain,
% 1.15/1.30 (r(s(elem!1), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[408, 4712, 1213])).
% 1.15/1.30 tff(4714,plain,
% 1.15/1.30 (~r(s(elem!1), s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4590, 4713, 591, 590])).
% 1.15/1.30 tff(4715,plain,
% 1.15/1.30 (b(s(elem!1), s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[534, 4714, 206])).
% 1.15/1.30 tff(4716,plain,
% 1.15/1.30 (~b(s(z), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4509, 4715, 1137, 289])).
% 1.15/1.30 tff(4717,plain,
% 1.15/1.30 (r(s(z), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[439, 4716, 433])).
% 1.15/1.30 tff(4718,plain,
% 1.15/1.30 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[298, 4715, 226, 289])).
% 1.15/1.30 tff(4719,plain,
% 1.15/1.30 (r(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[539, 4718, 418])).
% 1.15/1.30 tff(4720,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4684, 124, 4713, 4719, 161, 4717])).
% 1.15/1.30 tff(4721,plain,((~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (elem!1 = s(s(z))) | (s(s(z)) = elem!1) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.30 tff(4722,plain,
% 1.15/1.30 (~r(elem!1, s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4721, 289, 415, 1387, 226, 161, 1137, 159, 4649, 4647, 541, 374, 169, 4688])).
% 1.15/1.30 tff(4723,plain,
% 1.15/1.30 (b(elem!1, s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[629, 4722, 387])).
% 1.15/1.30 tff(4724,plain,
% 1.15/1.30 (~b(s(elem!1), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1160, 4723, 1137, 4577])).
% 1.15/1.30 tff(4725,plain,
% 1.15/1.30 (r(s(elem!1), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[473, 4724, 358])).
% 1.15/1.30 tff(4726,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1256, 124, 169, 4725, 4688])).
% 1.15/1.30 tff(4727,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(z))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(z)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.30 tff(4728,plain,
% 1.15/1.30 (~b(s(s(elem!1)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4727, 4646, 4645, 226, 161, 80, 374, 114, 150, 359, 278])).
% 1.15/1.30 tff(4729,plain,
% 1.15/1.30 (r(s(s(elem!1)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[323, 4728, 272])).
% 1.15/1.30 tff(4730,plain,
% 1.15/1.30 (~r(elem!1, s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1149, 4729, 4645, 4577, 150])).
% 1.15/1.30 tff(4731,plain,
% 1.15/1.30 (b(elem!1, s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[629, 4730, 387])).
% 1.15/1.30 tff(4732,plain,
% 1.15/1.30 (~b(s(elem!1), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1160, 4731, 4645, 4577])).
% 1.15/1.30 tff(4733,plain,
% 1.15/1.30 (r(s(elem!1), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[473, 4732, 358])).
% 1.15/1.30 tff(4734,plain,
% 1.15/1.30 (~r(s(elem!1), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[483, 4733, 80])).
% 1.15/1.30 tff(4735,plain,
% 1.15/1.30 (b(s(elem!1), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[488, 4734, 278])).
% 1.15/1.30 tff(4736,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4737,plain,
% 1.15/1.30 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4738,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4737])).
% 1.15/1.30 tff(4739,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4738, 4736])).
% 1.15/1.30 tff(4740,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4741,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4740, 4739])).
% 1.15/1.30 tff(4742,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4741, 124, 542, 306, 161])).
% 1.15/1.30 tff(4743,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.30 tff(4744,plain,
% 1.15/1.30 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4743, 4733, 161])).
% 1.15/1.30 tff(4745,plain,
% 1.15/1.30 (b(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[539, 4744, 415])).
% 1.15/1.30 tff(4746,plain,
% 1.15/1.30 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[499, 4745, 266, 4735])).
% 1.15/1.30 tff(4747,plain,
% 1.15/1.30 (r(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[459, 4746, 421])).
% 1.15/1.30 tff(4748,plain,
% 1.15/1.30 (~r(s(z), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[450, 4747, 161])).
% 1.15/1.30 tff(4749,plain,
% 1.15/1.30 (b(s(z), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[439, 4748, 1387])).
% 1.15/1.30 tff(4750,plain,
% 1.15/1.30 (~b(s(elem!1), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[668, 4749, 4577, 4731])).
% 1.15/1.30 tff(4751,plain,
% 1.15/1.30 (r(s(elem!1), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[408, 4750, 394])).
% 1.15/1.30 tff(4752,plain,
% 1.15/1.30 (~r(s(s(elem!1)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[403, 4751, 4729])).
% 1.15/1.30 tff(4753,plain,
% 1.15/1.30 (b(s(s(elem!1)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[255, 4752, 167])).
% 1.15/1.30 tff(4754,plain,
% 1.15/1.30 (~r(s(s(z)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1256, 124, 80, 4733])).
% 1.15/1.30 tff(4755,plain,
% 1.15/1.30 (b(s(s(z)), s(elem!1))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1260, 51, 4754, 1250])).
% 1.15/1.30 tff(4756,plain,
% 1.15/1.30 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.15/1.30 inference(rewrite,[status(thm)],[])).
% 1.15/1.30 tff(4757,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4756])).
% 1.15/1.30 tff(4758,plain,
% 1.15/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))))),
% 1.15/1.30 inference(transitivity,[status(thm)],[4757, 4657])).
% 1.15/1.30 tff(4759,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.15/1.30 inference(quant_inst,[status(thm)],[])).
% 1.15/1.30 tff(4760,plain,
% 1.15/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 1.15/1.30 tff(4761,plain,
% 1.15/1.30 (~b(elem!1, s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4760, 238, 4731, 4735, 4755])).
% 1.15/1.30 tff(4762,plain,
% 1.15/1.30 (r(elem!1, s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[763, 4761, 4646])).
% 1.15/1.30 tff(4763,plain,
% 1.15/1.30 (~b(s(s(z)), s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[246, 4753, 226, 266])).
% 1.15/1.30 tff(4764,plain,
% 1.15/1.30 (r(s(s(z)), s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[135, 4763, 114])).
% 1.15/1.30 tff(4765,plain,
% 1.15/1.30 (~r(elem!1, s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4484, 4764, 4762])).
% 1.15/1.30 tff(4766,plain,
% 1.15/1.30 (b(elem!1, s(s(elem!1)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[606, 4765, 150])).
% 1.15/1.30 tff(4767,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1147, 238, 4766, 4753, 4645, 4577])).
% 1.15/1.30 tff(4768,plain,((s(elem!1) = s(s(z))) | (elem!1 = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(z)) = elem!1) | r(elem!1, s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.30 tff(4769,plain,
% 1.15/1.30 (s(elem!1) = s(s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4768, 4643, 114, 150, 161, 1386, 359, 64])).
% 1.15/1.30 tff(4770,plain,
% 1.15/1.30 (s(s(elem!1)) = s(s(s(z)))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4769])).
% 1.15/1.30 tff(4771,plain,
% 1.15/1.30 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4770])).
% 1.15/1.30 tff(4772,plain,
% 1.15/1.30 (b(s(z), s(s(s(z))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[1389, 4771])).
% 1.15/1.30 tff(4773,plain,
% 1.15/1.30 (elem!1 = s(z)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[379, 4769])).
% 1.15/1.30 tff(4774,plain,
% 1.15/1.30 (~(elem!1 = s(s(s(elem!1))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1364, 4773])).
% 1.15/1.30 tff(4775,plain,
% 1.15/1.30 (r(s(elem!1), elem!1) <=> r(s(s(z)), elem!1)),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4769])).
% 1.15/1.30 tff(4776,plain,
% 1.15/1.30 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 1.15/1.30 inference(symmetry,[status(thm)],[4775])).
% 1.15/1.30 tff(4777,plain,
% 1.15/1.30 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(z))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4773])).
% 1.15/1.30 tff(4778,plain,
% 1.15/1.30 (r(s(s(z)), s(z)) <=> r(s(s(z)), elem!1)),
% 1.15/1.30 inference(symmetry,[status(thm)],[4777])).
% 1.15/1.30 tff(4779,plain,
% 1.15/1.30 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 1.15/1.30 inference(transitivity,[status(thm)],[4778, 4776])).
% 1.15/1.30 tff(4780,plain,
% 1.15/1.30 (r(s(elem!1), elem!1)),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[80, 4779])).
% 1.15/1.30 tff(4781,plain,
% 1.15/1.30 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4773])).
% 1.15/1.30 tff(4782,plain,
% 1.15/1.30 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.15/1.30 inference(symmetry,[status(thm)],[4781])).
% 1.15/1.30 tff(4783,plain,
% 1.15/1.30 (b(elem!1, s(s(elem!1)))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[1389, 4782])).
% 1.15/1.30 tff(4784,plain,
% 1.15/1.30 (~r(s(s(elem!1)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[3317, 4783, 4643, 415, 4780, 4774, 159])).
% 1.15/1.30 tff(4785,plain,
% 1.15/1.30 (b(s(s(elem!1)), elem!1)),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[255, 4784, 167])).
% 1.15/1.30 tff(4786,plain,
% 1.15/1.30 (b(s(s(s(z))), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1428, 4785, 4773])).
% 1.15/1.30 tff(4787,plain,
% 1.15/1.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[2405, 4769, 4643])).
% 1.15/1.30 tff(4788,plain,
% 1.15/1.30 (~b(s(s(s(s(z)))), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[3327, 238, 4787, 4786, 4772])).
% 1.15/1.30 tff(4789,plain,
% 1.15/1.30 (r(s(s(s(s(z)))), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1624, 4788])).
% 1.15/1.30 tff(4790,plain,
% 1.15/1.30 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4770])).
% 1.15/1.30 tff(4791,plain,
% 1.15/1.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4790])).
% 1.15/1.30 tff(4792,plain,
% 1.15/1.30 (b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[266, 4791])).
% 1.15/1.30 tff(4793,plain,
% 1.15/1.30 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1554, 4789, 80])).
% 1.15/1.30 tff(4794,plain,
% 1.15/1.30 (b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1564, 4793])).
% 1.15/1.30 tff(4795,plain,
% 1.15/1.30 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.15/1.30 inference(monotonicity,[status(thm)],[4790])).
% 1.15/1.30 tff(4796,plain,
% 1.15/1.30 (r(s(z), s(s(s(s(z)))))),
% 1.15/1.30 inference(modus_ponens,[status(thm)],[161, 4795])).
% 1.15/1.30 tff(4797,plain,
% 1.15/1.30 (~r(s(z), s(s(s(s(s(z))))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1697, 4794, 80, 4769, 4796, 4792, 692])).
% 1.15/1.30 tff(4798,plain,
% 1.15/1.30 (b(s(z), s(s(s(s(s(z))))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1709, 4797])).
% 1.15/1.30 tff(4799,plain,
% 1.15/1.30 (~b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[3369, 4798, 4769, 4789, 4794, 4792, 80, 4772, 114])).
% 1.15/1.30 tff(4800,plain,
% 1.15/1.30 (r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1781, 4799])).
% 1.15/1.30 tff(4801,plain,
% 1.15/1.30 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1725, 4800, 80])).
% 1.15/1.30 tff(4802,plain,
% 1.15/1.30 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1738, 4801])).
% 1.15/1.30 tff(4803,plain,
% 1.15/1.30 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[4437, 4802, 4794, 4792])).
% 1.15/1.30 tff(4804,plain,
% 1.15/1.30 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[1904, 4803])).
% 1.15/1.30 tff(4805,plain,
% 1.15/1.30 ($false),
% 1.15/1.30 inference(unit_resolution,[status(thm)],[3963, 124, 4800, 4804, 4789])).
% 1.15/1.30 tff(4806,plain,(b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4807,plain,
% 1.15/1.31 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4806, 1379, 114, 64, 161, 150])).
% 1.15/1.31 tff(4808,assumption,(s(s(s(s(s(z))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.15/1.31 tff(4809,plain,
% 1.15/1.31 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4808])).
% 1.15/1.31 tff(4810,plain,
% 1.15/1.31 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.15/1.31 inference(transitivity,[status(thm)],[723, 4809, 88])).
% 1.15/1.31 tff(4811,plain,
% 1.15/1.31 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4810])).
% 1.15/1.31 tff(4812,plain,
% 1.15/1.31 (s(s(s(z))) = s(elem!1)),
% 1.15/1.31 inference(transitivity,[status(thm)],[716, 4811, 17])).
% 1.15/1.31 tff(4813,plain,
% 1.15/1.31 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4812])).
% 1.15/1.31 tff(4814,plain,
% 1.15/1.31 (s(s(z)) = elem!1),
% 1.15/1.31 inference(transitivity,[status(thm)],[144, 4813, 154])).
% 1.15/1.31 tff(4815,plain,
% 1.15/1.31 (b(s(s(z)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4814])).
% 1.15/1.31 tff(4816,plain,
% 1.15/1.31 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.15/1.31 inference(symmetry,[status(thm)],[4815])).
% 1.15/1.31 tff(4817,plain,
% 1.15/1.31 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4816])).
% 1.15/1.31 tff(4818,plain,
% 1.15/1.31 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[1314, 4817])).
% 1.15/1.31 tff(4819,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[225, 4818])).
% 1.15/1.31 tff(4820,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4821,plain,
% 1.15/1.31 (b(elem!1, s(s(s(elem!1))))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4820, 4807, 191])).
% 1.15/1.31 tff(4822,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4821, 1357])).
% 1.15/1.31 tff(4823,plain,((~(elem!1 = s(z))) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(z)) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4824,plain,
% 1.15/1.31 (~(elem!1 = s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4823, 150, 81, 114, 102, 64])).
% 1.15/1.31 tff(4825,plain,
% 1.15/1.31 (~(s(elem!1) = s(s(z)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[379, 4824])).
% 1.15/1.31 tff(4826,plain,
% 1.15/1.31 (~r(s(s(z)), elem!1)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[3252, 124, 169, 1370])).
% 1.15/1.31 tff(4827,assumption,(elem!1 = z), introduced(assumption)).
% 1.15/1.31 tff(4828,plain,
% 1.15/1.31 (s(elem!1) = s(z)),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4827])).
% 1.15/1.31 tff(4829,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1, 4828])).
% 1.15/1.31 tff(4830,plain,((~(elem!1 = z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4831,plain,
% 1.15/1.31 (~(elem!1 = z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4830, 1])).
% 1.15/1.31 tff(4832,plain,
% 1.15/1.31 (b(s(s(z)), z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[2839, 51, 1449, 2810])).
% 1.15/1.31 tff(4833,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4834,plain,
% 1.15/1.31 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4835,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4834])).
% 1.15/1.31 tff(4836,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4835, 4833])).
% 1.15/1.31 tff(4837,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4838,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 1.15/1.31 tff(4839,plain,
% 1.15/1.31 (~r(elem!1, z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4838, 124, 1370, 1545])).
% 1.15/1.31 tff(4840,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.15/1.31 tff(4841,plain,
% 1.15/1.31 (((~![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))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4842,plain,
% 1.15/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4843,plain,
% 1.15/1.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4842, 4841])).
% 1.15/1.31 tff(4844,plain,
% 1.15/1.31 (b(elem!1, z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4843, 51, 4840, 4839])).
% 1.15/1.31 tff(4845,assumption,(z = s(s(z))), introduced(assumption)).
% 1.15/1.31 tff(4846,plain,
% 1.15/1.31 (s(s(z)) = z),
% 1.15/1.31 inference(symmetry,[status(thm)],[4845])).
% 1.15/1.31 tff(4847,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1449, 4846])).
% 1.15/1.31 tff(4848,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4849,plain,
% 1.15/1.31 (b(z, s(s(z)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1511, 51, 1584, 4848])).
% 1.15/1.31 tff(4850,plain,
% 1.15/1.31 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1613, 1545, 169])).
% 1.15/1.31 tff(4851,plain,
% 1.15/1.31 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1624, 4850])).
% 1.15/1.31 tff(4852,plain,
% 1.15/1.31 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[1382])).
% 1.15/1.31 tff(4853,plain,
% 1.15/1.31 (b(s(s(elem!1)), s(z))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[1784, 4852])).
% 1.15/1.31 tff(4854,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[82, 4853])).
% 1.15/1.31 tff(4855,plain,((~b(s(s(s(s(z)))), s(z))) | b(s(s(elem!1)), s(z)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4856,plain,
% 1.15/1.31 (~(s(s(z)) = elem!1)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4855, 4851, 82])).
% 1.15/1.31 tff(4857,plain,
% 1.15/1.31 (b(s(s(z)), elem!1)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1275, 4856, 4826])).
% 1.15/1.31 tff(4858,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4859,plain,
% 1.15/1.31 (((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4860,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4859])).
% 1.15/1.31 tff(4861,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4860, 4858])).
% 1.15/1.31 tff(4862,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4863,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 1.15/1.31 tff(4864,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4863, 238, 4857, 4849, 4844, 4832])).
% 1.15/1.31 tff(4865,plain,((~r(z, s(z))) | (elem!1 = z) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4866,plain,
% 1.15/1.31 (~r(z, s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4865, 1370, 4831, 169, 82])).
% 1.15/1.31 tff(4867,plain,
% 1.15/1.31 (b(z, s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[1542, 4866])).
% 1.15/1.31 tff(4868,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4869,plain,
% 1.15/1.31 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4870,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4869])).
% 1.15/1.31 tff(4871,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4870, 4868])).
% 1.15/1.31 tff(4872,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4873,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 1.15/1.31 tff(4874,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4873, 238, 1137, 2078, 23, 1457])).
% 1.15/1.31 tff(4875,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4876,plain,
% 1.15/1.31 (~b(s(s(elem!1)), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4875, 2078, 1137, 1457])).
% 1.15/1.31 tff(4877,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4878,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4879,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4878, 4877])).
% 1.15/1.31 tff(4880,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4879, 238, 289, 1137, 2078, 1457])).
% 1.15/1.31 tff(4881,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4882,plain,
% 1.15/1.31 (~b(s(s(elem!1)), s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4881, 2078, 1137, 1457])).
% 1.15/1.31 tff(4883,plain,
% 1.15/1.31 (r(s(s(elem!1)), s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[323, 4882, 275])).
% 1.15/1.31 tff(4884,plain,
% 1.15/1.31 (~r(s(s(elem!1)), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[315, 4883, 306])).
% 1.15/1.31 tff(4885,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[110, 51, 4884, 4876, 106])).
% 1.15/1.31 tff(4886,plain,((~b(z, s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4887,plain,
% 1.15/1.31 (~r(s(elem!1), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4886, 2078, 275, 1137, 1457])).
% 1.15/1.31 tff(4888,plain,
% 1.15/1.31 (b(s(elem!1), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[473, 4887, 1])).
% 1.15/1.31 tff(4889,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4890,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4891,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4890, 4889])).
% 1.15/1.31 tff(4892,plain,
% 1.15/1.31 (~b(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4891, 238, 1137, 4888, 1457])).
% 1.15/1.31 tff(4893,plain,
% 1.15/1.31 ((z = s(elem!1)) | r(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[3115, 51, 4892])).
% 1.15/1.31 tff(4894,plain,
% 1.15/1.31 (r(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4893, 3105])).
% 1.15/1.31 tff(4895,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4896,plain,
% 1.15/1.31 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4897,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4896])).
% 1.15/1.31 tff(4898,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4897, 4895])).
% 1.15/1.31 tff(4899,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4900,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(elem!1)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4899, 4898])).
% 1.15/1.31 tff(4901,plain,
% 1.15/1.31 (~r(s(s(elem!1)), z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4900, 124, 4883, 4894])).
% 1.15/1.31 tff(4902,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.15/1.31 tff(4903,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.15/1.31 tff(4904,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4030, 51, 92, 4903, 4902])).
% 1.15/1.31 tff(4905,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4906,plain,
% 1.15/1.31 (b(s(s(elem!1)), z)),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4905, 4901])).
% 1.15/1.31 tff(4907,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4908,plain,
% 1.15/1.31 (((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4909,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4908])).
% 1.15/1.31 tff(4910,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4909, 4907])).
% 1.15/1.31 tff(4911,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4912,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 1.15/1.31 tff(4913,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4912, 238, 1137, 2078, 4906, 1457])).
% 1.15/1.31 tff(4914,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4915,plain,
% 1.15/1.31 (~b(z, s(s(elem!1)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4914, 4867, 1, 3294, 1137])).
% 1.15/1.31 tff(4916,plain,
% 1.15/1.31 (r(z, s(s(elem!1)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[2071, 4915])).
% 1.15/1.31 tff(4917,plain,
% 1.15/1.31 (~r(s(elem!1), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[315, 307, 162])).
% 1.15/1.31 tff(4918,plain,
% 1.15/1.31 (b(s(elem!1), s(z))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[473, 4917, 1])).
% 1.15/1.31 tff(4919,plain,
% 1.15/1.31 (~b(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4891, 238, 1137, 4918, 1457])).
% 1.15/1.31 tff(4920,assumption,(z = s(elem!1)), introduced(assumption)).
% 1.15/1.31 tff(4921,plain,
% 1.15/1.31 (s(elem!1) = z),
% 1.15/1.31 inference(symmetry,[status(thm)],[4920])).
% 1.15/1.31 tff(4922,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[39, 4921])).
% 1.15/1.31 tff(4923,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4924,plain,
% 1.15/1.31 (r(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[3115, 51, 4923, 4919])).
% 1.15/1.31 tff(4925,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4926,plain,
% 1.15/1.31 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(rewrite,[status(thm)],[])).
% 1.15/1.31 tff(4927,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 1.15/1.31 inference(monotonicity,[status(thm)],[4926])).
% 1.15/1.31 tff(4928,plain,
% 1.15/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.31 inference(transitivity,[status(thm)],[4927, 4925])).
% 1.15/1.31 tff(4929,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.15/1.31 inference(quant_inst,[status(thm)],[])).
% 1.15/1.31 tff(4930,plain,
% 1.15/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 1.15/1.31 inference(modus_ponens,[status(thm)],[4929, 4928])).
% 1.15/1.31 tff(4931,plain,
% 1.15/1.31 ($false),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4930, 124, 307, 2026, 4924])).
% 1.15/1.31 tff(4932,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.31 tff(4933,plain,
% 1.15/1.31 (~r(s(s(elem!1)), s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4932, 4916, 1137, 4867, 1, 113])).
% 1.15/1.31 tff(4934,plain,
% 1.15/1.31 (b(s(s(elem!1)), s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[323, 4933, 3294])).
% 1.15/1.31 tff(4935,plain,
% 1.15/1.31 (~b(z, s(elem!1))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4891, 238, 1137, 1152, 1457])).
% 1.15/1.31 tff(4936,plain,
% 1.15/1.31 (~b(s(elem!1), s(s(elem!1)))),
% 1.15/1.31 inference(unit_resolution,[status(thm)],[4533, 1152, 289, 1137])).
% 1.15/1.32 tff(4937,plain,
% 1.15/1.32 (r(s(elem!1), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[534, 4936, 206])).
% 1.15/1.32 tff(4938,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.15/1.32 tff(4939,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(4940,plain,
% 1.15/1.32 (((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(4941,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4940])).
% 1.15/1.32 tff(4942,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[4941, 4939])).
% 1.15/1.32 tff(4943,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(elem!1))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(4944,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[4943, 4942])).
% 1.15/1.32 tff(4945,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4944, 124, 518, 2026, 4938])).
% 1.15/1.32 tff(4946,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4947,plain,
% 1.15/1.32 (~r(z, s(elem!1))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4946, 4937, 2026])).
% 1.15/1.32 tff(4948,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[3115, 51, 4947, 4923, 4935])).
% 1.15/1.32 tff(4949,plain,((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4950,plain,
% 1.15/1.32 (~b(s(elem!1), s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4949, 4934, 1137, 4867, 206, 4916])).
% 1.15/1.32 tff(4951,plain,
% 1.15/1.32 (r(s(elem!1), s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[473, 4950, 1])).
% 1.15/1.32 tff(4952,plain,
% 1.15/1.32 (~r(elem!1, s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[2461, 124, 169, 1370])).
% 1.15/1.32 tff(4953,plain,
% 1.15/1.32 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4810])).
% 1.15/1.32 tff(4954,plain,
% 1.15/1.32 (r(s(s(elem!1)), s(z))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[1544, 4953])).
% 1.15/1.32 tff(4955,plain,
% 1.15/1.32 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4814])).
% 1.15/1.32 tff(4956,plain,
% 1.15/1.32 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4955])).
% 1.15/1.32 tff(4957,plain,
% 1.15/1.32 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.15/1.32 inference(symmetry,[status(thm)],[4808])).
% 1.15/1.32 tff(4958,plain,
% 1.15/1.32 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[1075, 4957])).
% 1.15/1.32 tff(4959,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1092, 4958])).
% 1.15/1.32 tff(4960,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4961,plain,
% 1.15/1.32 (~(s(s(z)) = s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4960, 4808])).
% 1.15/1.32 tff(4962,plain,
% 1.15/1.32 (~(elem!1 = s(s(elem!1)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[4961, 4956])).
% 1.15/1.32 tff(4963,plain,
% 1.15/1.32 (~(s(elem!1) = s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[158, 4962])).
% 1.15/1.32 tff(4964,plain,
% 1.15/1.32 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4814])).
% 1.15/1.32 tff(4965,plain,
% 1.15/1.32 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 1.15/1.32 inference(transitivity,[status(thm)],[4964, 388])).
% 1.15/1.32 tff(4966,plain,
% 1.15/1.32 ((~(s(elem!1) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4965])).
% 1.15/1.32 tff(4967,plain,
% 1.15/1.32 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(elem!1))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4812])).
% 1.15/1.32 tff(4968,plain,
% 1.15/1.32 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 1.15/1.32 inference(transitivity,[status(thm)],[4967, 1245])).
% 1.15/1.32 tff(4969,plain,
% 1.15/1.32 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4968])).
% 1.15/1.32 tff(4970,plain,
% 1.15/1.32 (~(s(elem!1) = s(s(z)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[147, 4969])).
% 1.15/1.32 tff(4971,plain,
% 1.15/1.32 (~(elem!1 = s(elem!1))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[4970, 4966])).
% 1.15/1.32 tff(4972,plain,
% 1.15/1.32 (elem!1 = s(s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1231, 4814])).
% 1.15/1.32 tff(4973,plain,
% 1.15/1.32 (s(elem!1) = s(s(s(z)))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[365])).
% 1.15/1.32 tff(4974,plain,
% 1.15/1.32 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4973])).
% 1.15/1.32 tff(4975,plain,
% 1.15/1.32 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4974, 365])).
% 1.15/1.32 tff(4976,plain,
% 1.15/1.32 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4975])).
% 1.15/1.32 tff(4977,plain,
% 1.15/1.32 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[249, 4976])).
% 1.15/1.32 tff(4978,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1587, 4977])).
% 1.15/1.32 tff(4979,plain,(b(s(s(elem!1)), elem!1) | (~b(s(s(s(s(z)))), s(s(z)))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4980,plain,
% 1.15/1.32 (b(s(s(elem!1)), elem!1)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4979, 1565, 4972])).
% 1.15/1.32 tff(4981,plain,
% 1.15/1.32 (~b(s(elem!1), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[2644, 4980, 306, 1370, 4971])).
% 1.15/1.32 tff(4982,plain,
% 1.15/1.32 (r(s(elem!1), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[534, 4981, 4963])).
% 1.15/1.32 tff(4983,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(4984,plain,
% 1.15/1.32 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(4985,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[4984])).
% 1.15/1.32 tff(4986,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[4985, 4983])).
% 1.15/1.32 tff(4987,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(4988,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 1.15/1.32 tff(4989,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4988, 124, 4982, 306, 4954])).
% 1.15/1.32 tff(4990,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4991,plain,
% 1.15/1.32 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4990, 306, 169, 1544, 1370])).
% 1.15/1.32 tff(4992,plain,
% 1.15/1.32 (~(s(s(z)) = elem!1)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1385, 4991])).
% 1.15/1.32 tff(4993,plain,
% 1.15/1.32 (s(s(z)) = elem!1),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[365, 1971])).
% 1.15/1.32 tff(4994,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[374, 4993])).
% 1.15/1.32 tff(4995,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(4996,plain,
% 1.15/1.32 (~(elem!1 = s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4995, 4992])).
% 1.15/1.32 tff(4997,plain,
% 1.15/1.32 (b(elem!1, s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[763, 4996, 4952])).
% 1.15/1.32 tff(4998,plain,
% 1.15/1.32 (b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1604, 2280])).
% 1.15/1.32 tff(4999,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[2634, 124, 590, 1370, 306])).
% 1.15/1.32 tff(5000,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5001,plain,
% 1.15/1.32 (~r(elem!1, s(elem!1))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5000, 306, 1370])).
% 1.15/1.32 tff(5002,plain,
% 1.15/1.32 (b(elem!1, s(elem!1))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[629, 5001, 391])).
% 1.15/1.32 tff(5003,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5004,plain,
% 1.15/1.32 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5005,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5004])).
% 1.15/1.32 tff(5006,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[5005, 5003])).
% 1.15/1.32 tff(5007,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(elem!1))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(5008,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 1.15/1.32 tff(5009,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5008, 238, 5002, 1234, 4998, 4997])).
% 1.15/1.32 tff(5010,plain,((~r(s(elem!1), s(z))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5011,plain,
% 1.15/1.32 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5010, 4951, 278, 169, 1370, 1212])).
% 1.15/1.32 tff(5012,plain,
% 1.15/1.32 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1624, 5011])).
% 1.15/1.32 tff(5013,plain,
% 1.15/1.32 (~(s(s(z)) = elem!1)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4855, 5012, 82])).
% 1.15/1.32 tff(5014,plain,
% 1.15/1.32 (b(s(s(z)), elem!1)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1275, 5013, 4826])).
% 1.15/1.32 tff(5015,plain,
% 1.15/1.32 (~(elem!1 = s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4995, 5013])).
% 1.15/1.32 tff(5016,plain,
% 1.15/1.32 (b(elem!1, s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[763, 5015, 4952])).
% 1.15/1.32 tff(5017,plain,
% 1.15/1.32 (~r(s(elem!1), s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[483, 4951, 169])).
% 1.15/1.32 tff(5018,plain,
% 1.15/1.32 (b(s(elem!1), s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[488, 5017, 278])).
% 1.15/1.32 tff(5019,plain,
% 1.15/1.32 (~r(elem!1, s(elem!1))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5000, 4951, 1370])).
% 1.15/1.32 tff(5020,plain,
% 1.15/1.32 (b(elem!1, s(elem!1))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[629, 5019, 1212])).
% 1.15/1.32 tff(5021,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[3268, 238, 5020, 5018, 5016, 5014])).
% 1.15/1.32 tff(5022,plain,((~r(elem!1, s(z))) | b(s(s(elem!1)), s(z)) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5023,plain,
% 1.15/1.32 (~r(elem!1, s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5022, 4825, 82, 80, 358, 1353, 159])).
% 1.15/1.32 tff(5024,plain,
% 1.15/1.32 (s(s(z)) = elem!1),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4768, 359, 64, 161, 114, 150, 3258, 226])).
% 1.15/1.32 tff(5025,plain,
% 1.15/1.32 (b(elem!1, s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[363, 359, 330])).
% 1.15/1.32 tff(5026,plain,
% 1.15/1.32 (~(elem!1 = s(s(z)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[372, 5025, 64])).
% 1.15/1.32 tff(5027,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1231, 5026, 5024])).
% 1.15/1.32 tff(5028,plain,(r(elem!1, s(z)) | b(s(s(z)), s(z)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5029,plain,
% 1.15/1.32 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5028, 5023, 102, 114, 150, 64, 4824])).
% 1.15/1.32 tff(5030,plain,
% 1.15/1.32 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[223, 5029, 209])).
% 1.15/1.32 tff(5031,plain,
% 1.15/1.32 (~r(s(s(z)), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4545, 5030, 64, 102, 150, 358, 1353, 5023])).
% 1.15/1.32 tff(5032,plain,
% 1.15/1.32 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[135, 5031, 114])).
% 1.15/1.32 tff(5033,plain,
% 1.15/1.32 (~r(s(s(elem!1)), z)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4026, 124, 162, 1545])).
% 1.15/1.32 tff(5034,plain,
% 1.15/1.32 (b(s(s(elem!1)), z)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4030, 51, 92, 5033])).
% 1.15/1.32 tff(5035,plain,
% 1.15/1.32 (~r(z, s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[2057, 124, 162, 1545])).
% 1.15/1.32 tff(5036,plain,
% 1.15/1.32 (b(z, s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[2071, 5035])).
% 1.15/1.32 tff(5037,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5038,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(5039,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[5038, 5037])).
% 1.15/1.32 tff(5040,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5039, 238, 227, 5036, 5034, 4832])).
% 1.15/1.32 tff(5041,plain,((~r(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5042,plain,
% 1.15/1.32 (~r(z, s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5041, 5032, 113, 80])).
% 1.15/1.32 tff(5043,plain,
% 1.15/1.32 (b(z, s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[1542, 5042])).
% 1.15/1.32 tff(5044,plain,
% 1.15/1.32 (b(elem!1, s(z))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[363, 5023, 4824])).
% 1.15/1.32 tff(5045,plain,
% 1.15/1.32 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4806, 5023, 114, 64, 102, 150])).
% 1.15/1.32 tff(5046,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.15/1.32 tff(5047,plain,
% 1.15/1.32 (s(elem!1) = s(s(s(s(z))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5046])).
% 1.15/1.32 tff(5048,plain,
% 1.15/1.32 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5047])).
% 1.15/1.32 tff(5049,plain,
% 1.15/1.32 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.15/1.32 inference(symmetry,[status(thm)],[5048])).
% 1.15/1.32 tff(5050,plain,
% 1.15/1.32 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5049])).
% 1.15/1.32 tff(5051,plain,
% 1.15/1.32 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.32 inference(transitivity,[status(thm)],[5050, 2301])).
% 1.15/1.32 tff(5052,plain,
% 1.15/1.32 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.15/1.32 inference(symmetry,[status(thm)],[5051])).
% 1.15/1.32 tff(5053,plain,
% 1.15/1.32 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5052])).
% 1.15/1.32 tff(5054,plain,
% 1.15/1.32 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[545, 5053])).
% 1.15/1.32 tff(5055,plain,
% 1.15/1.32 ($false),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4808, 5054])).
% 1.15/1.32 tff(5056,plain,((~(elem!1 = s(s(s(z))))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.32 tff(5057,plain,
% 1.15/1.32 (~(elem!1 = s(s(s(z))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5056, 5045, 209])).
% 1.15/1.32 tff(5058,plain,
% 1.15/1.32 (~(elem!1 = z)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4830, 358])).
% 1.15/1.32 tff(5059,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5060,plain,
% 1.15/1.32 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5061,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z)))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5060])).
% 1.15/1.32 tff(5062,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[5061, 5059])).
% 1.15/1.32 tff(5063,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(5064,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(z, s(z)))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 1.15/1.32 tff(5065,plain,
% 1.15/1.32 (~b(elem!1, z)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5064, 238, 1353, 5044, 5043])).
% 1.15/1.32 tff(5066,plain,
% 1.15/1.32 (r(elem!1, z)),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[4843, 51, 5065, 5058])).
% 1.15/1.32 tff(5067,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.15/1.32 tff(5068,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.15/1.32 tff(5069,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5070,plain,
% 1.15/1.32 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.15/1.32 inference(rewrite,[status(thm)],[])).
% 1.15/1.32 tff(5071,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.15/1.32 inference(monotonicity,[status(thm)],[5070])).
% 1.15/1.32 tff(5072,plain,
% 1.15/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.15/1.32 inference(transitivity,[status(thm)],[5071, 5069])).
% 1.15/1.32 tff(5073,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.15/1.32 inference(quant_inst,[status(thm)],[])).
% 1.15/1.32 tff(5074,plain,
% 1.15/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.15/1.32 inference(modus_ponens,[status(thm)],[5073, 5072])).
% 1.15/1.32 tff(5075,plain,
% 1.15/1.32 (~b(elem!1, s(s(s(z))))),
% 1.15/1.32 inference(unit_resolution,[status(thm)],[5074, 238, 1137, 370, 1456])).
% 1.15/1.32 tff(5076,plain,
% 1.15/1.32 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5077,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5078,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5077, 5076])).
% 1.15/1.33 tff(5079,plain,
% 1.15/1.33 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5078, 51])).
% 1.15/1.33 tff(5080,plain,
% 1.15/1.33 (r(elem!1, s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5079, 5075, 5068])).
% 1.15/1.33 tff(5081,plain,
% 1.15/1.33 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.15/1.33 inference(commutativity,[status(thm)],[])).
% 1.15/1.33 tff(5082,plain,
% 1.15/1.33 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5081])).
% 1.15/1.33 tff(5083,plain,
% 1.15/1.33 (~(s(s(s(z))) = elem!1)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5068, 5082])).
% 1.15/1.33 tff(5084,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5085,plain,
% 1.15/1.33 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5086,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5085])).
% 1.15/1.33 tff(5087,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5086, 5084])).
% 1.15/1.33 tff(5088,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5089,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5088, 5087])).
% 1.15/1.33 tff(5090,plain,
% 1.15/1.33 (~b(s(s(s(z))), elem!1)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5089, 238, 1137, 370, 1456])).
% 1.15/1.33 tff(5091,plain,
% 1.15/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5092,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5093,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5092, 5091])).
% 1.15/1.33 tff(5094,plain,
% 1.15/1.33 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5093, 51])).
% 1.15/1.33 tff(5095,plain,
% 1.15/1.33 (r(s(s(s(z))), elem!1)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5094, 5090, 5083])).
% 1.15/1.33 tff(5096,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5097,plain,
% 1.15/1.33 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5098,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5097])).
% 1.15/1.33 tff(5099,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5098, 5096])).
% 1.15/1.33 tff(5100,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5101,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5100, 5099])).
% 1.15/1.33 tff(5102,plain,
% 1.15/1.33 (~b(s(s(s(z))), z)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5101, 238, 1137, 1457, 1456])).
% 1.15/1.33 tff(5103,plain,
% 1.15/1.33 (r(s(s(s(z))), z)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[1524, 5102])).
% 1.15/1.33 tff(5104,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5105,plain,
% 1.15/1.33 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5106,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5105])).
% 1.15/1.33 tff(5107,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5106, 5104])).
% 1.15/1.33 tff(5108,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5109,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5108, 5107])).
% 1.15/1.33 tff(5110,plain,
% 1.15/1.33 ($false),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5109, 124, 5103, 5095, 5080, 5067])).
% 1.15/1.33 tff(5111,plain,((~b(s(s(s(z))), s(z))) | (~r(elem!1, z)) | (elem!1 = s(s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.33 tff(5112,plain,
% 1.15/1.33 (~b(s(s(s(z))), s(z))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5111, 5066, 5057, 1353, 5044, 5043])).
% 1.15/1.33 tff(5113,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.15/1.33 tff(5114,plain,
% 1.15/1.33 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5113])).
% 1.15/1.33 tff(5115,plain,
% 1.15/1.33 (s(s(z)) = z),
% 1.15/1.33 inference(transitivity,[status(thm)],[144, 5114, 26])).
% 1.15/1.33 tff(5116,plain,
% 1.15/1.33 ($false),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[1449, 5115])).
% 1.15/1.33 tff(5117,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.33 tff(5118,plain,
% 1.15/1.33 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2344, 5117])).
% 1.15/1.33 tff(5119,plain,
% 1.15/1.33 (r(s(s(s(z))), s(z))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5118, 5112])).
% 1.15/1.33 tff(5120,plain,
% 1.15/1.33 (~r(s(s(s(z))), s(s(z)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2294, 124, 80, 5119])).
% 1.15/1.33 tff(5121,plain,
% 1.15/1.33 (b(s(s(s(z))), s(s(z)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2298, 51, 5120, 149])).
% 1.15/1.33 tff(5122,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5123,plain,
% 1.15/1.33 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5124,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5123])).
% 1.15/1.33 tff(5125,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5124, 5122])).
% 1.15/1.33 tff(5126,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5127,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5126, 5125])).
% 1.15/1.33 tff(5128,plain,
% 1.15/1.33 (~r(s(s(z)), s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5127, 124, 80, 5119])).
% 1.15/1.33 tff(5129,plain,
% 1.15/1.33 (b(s(s(z)), s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4334, 5128])).
% 1.15/1.33 tff(5130,plain,
% 1.15/1.33 (~b(z, s(s(elem!1)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4914, 5043, 358, 272, 1353])).
% 1.15/1.33 tff(5131,plain,
% 1.15/1.33 (r(z, s(s(elem!1)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2071, 5130])).
% 1.15/1.33 tff(5132,plain,
% 1.15/1.33 (~r(s(s(elem!1)), s(elem!1))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4932, 5131, 1353, 5043, 358, 113])).
% 1.15/1.33 tff(5133,plain,
% 1.15/1.33 (b(s(s(elem!1)), s(elem!1))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[323, 5132, 272])).
% 1.15/1.33 tff(5134,plain,
% 1.15/1.33 (b(s(elem!1), s(s(z)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4600, 5133, 358, 80, 150, 1353, 4825, 5023])).
% 1.15/1.33 tff(5135,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5136,plain,
% 1.15/1.33 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5137,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5136])).
% 1.15/1.33 tff(5138,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5137, 5135])).
% 1.15/1.33 tff(5139,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5140,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5139, 5138])).
% 1.15/1.33 tff(5141,plain,
% 1.15/1.33 (~b(s(s(s(z))), s(elem!1))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5140, 238, 5134, 5129, 5121])).
% 1.15/1.33 tff(5142,plain,
% 1.15/1.33 (~b(s(elem!1), s(z))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4949, 5133, 1353, 5043, 159, 5131])).
% 1.15/1.33 tff(5143,plain,
% 1.15/1.33 (r(s(elem!1), s(z))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[473, 5142, 358])).
% 1.15/1.33 tff(5144,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5145,plain,
% 1.15/1.33 (((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5146,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5145])).
% 1.15/1.33 tff(5147,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5146, 5144])).
% 1.15/1.33 tff(5148,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5149,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5148, 5147])).
% 1.15/1.33 tff(5150,plain,
% 1.15/1.33 (~r(s(s(s(z))), s(elem!1))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5149, 124, 5143, 5119])).
% 1.15/1.33 tff(5151,plain,
% 1.15/1.33 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5152,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5153,plain,
% 1.15/1.33 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5152, 5151])).
% 1.15/1.33 tff(5154,plain,
% 1.15/1.33 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5153, 51, 5150])).
% 1.15/1.33 tff(5155,plain,
% 1.15/1.33 (s(s(s(z))) = s(elem!1)),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5154, 5141])).
% 1.15/1.33 tff(5156,plain,
% 1.15/1.33 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5155])).
% 1.15/1.33 tff(5157,plain,
% 1.15/1.33 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.15/1.33 inference(symmetry,[status(thm)],[5156])).
% 1.15/1.33 tff(5158,plain,
% 1.15/1.33 (b(s(s(s(z))), s(s(z)))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2298, 51, 2295, 149])).
% 1.15/1.33 tff(5159,plain,
% 1.15/1.33 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[2320, 124, 2288, 1544])).
% 1.15/1.33 tff(5160,plain,
% 1.15/1.33 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[3379])).
% 1.15/1.33 tff(5161,plain,
% 1.15/1.33 (s(s(s(z))) = s(s(s(s(z))))),
% 1.15/1.33 inference(symmetry,[status(thm)],[3704])).
% 1.15/1.33 tff(5162,plain,
% 1.15/1.33 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5161])).
% 1.15/1.33 tff(5163,plain,
% 1.15/1.33 (s(s(z)) = s(s(s(z)))),
% 1.15/1.33 inference(transitivity,[status(thm)],[144, 5162, 715])).
% 1.15/1.33 tff(5164,plain,
% 1.15/1.33 ($false),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[147, 5163])).
% 1.15/1.33 tff(5165,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.33 tff(5166,plain,
% 1.15/1.33 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5165, 5160])).
% 1.15/1.33 tff(5167,plain,
% 1.15/1.33 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[3591, 5166])).
% 1.15/1.33 tff(5168,plain,
% 1.15/1.33 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5167, 5159])).
% 1.15/1.33 tff(5169,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5170,plain,
% 1.15/1.33 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5171,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.15/1.33 inference(monotonicity,[status(thm)],[5170])).
% 1.15/1.33 tff(5172,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.15/1.33 inference(transitivity,[status(thm)],[5171, 5169])).
% 1.15/1.33 tff(5173,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.15/1.33 inference(quant_inst,[status(thm)],[])).
% 1.15/1.33 tff(5174,plain,
% 1.15/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.15/1.33 inference(modus_ponens,[status(thm)],[5173, 5172])).
% 1.15/1.33 tff(5175,plain,
% 1.15/1.33 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5174, 124, 2288, 1544])).
% 1.15/1.33 tff(5176,plain,
% 1.15/1.33 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[4165, 5165])).
% 1.15/1.33 tff(5177,plain,
% 1.15/1.33 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.15/1.33 inference(unit_resolution,[status(thm)],[5176, 5175])).
% 1.15/1.33 tff(5178,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5179,plain,
% 1.15/1.33 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.15/1.33 inference(rewrite,[status(thm)],[])).
% 1.15/1.33 tff(5180,plain,
% 1.15/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5179])).
% 1.15/1.34 tff(5181,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5180, 5178])).
% 1.15/1.34 tff(5182,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5183,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 1.15/1.34 tff(5184,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5183, 238, 5177, 4998, 5168, 5158])).
% 1.15/1.34 tff(5185,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5186,plain,
% 1.15/1.34 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5185, 5119, 80])).
% 1.15/1.34 tff(5187,plain,
% 1.15/1.34 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1624, 5186])).
% 1.15/1.34 tff(5188,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5189,plain,
% 1.15/1.34 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5190,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5189])).
% 1.15/1.34 tff(5191,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5190, 5188])).
% 1.15/1.34 tff(5192,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5193,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5192, 5191])).
% 1.15/1.34 tff(5194,plain,
% 1.15/1.34 (~b(elem!1, s(s(s(s(z)))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5193, 238, 1353, 5044, 5187])).
% 1.15/1.34 tff(5195,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5196,plain,
% 1.15/1.34 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5197,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5196])).
% 1.15/1.34 tff(5198,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5197, 5195])).
% 1.15/1.34 tff(5199,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5200,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5199, 5198])).
% 1.15/1.34 tff(5201,plain,
% 1.15/1.34 (~b(s(s(s(s(z)))), z)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5200, 238, 1353, 5043, 5187])).
% 1.15/1.34 tff(5202,plain,
% 1.15/1.34 (r(s(s(s(s(z)))), z)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1499, 51, 726, 5201])).
% 1.15/1.34 tff(5203,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5204,plain,
% 1.15/1.34 (((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5205,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5204])).
% 1.15/1.34 tff(5206,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z)))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5205, 5203])).
% 1.15/1.34 tff(5207,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5208,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, z))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5207, 5206])).
% 1.15/1.34 tff(5209,plain,
% 1.15/1.34 (~r(elem!1, s(s(s(s(z)))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5208, 124, 5066, 5202])).
% 1.15/1.34 tff(5210,plain,
% 1.15/1.34 (elem!1 = s(s(s(s(z))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[935, 5209, 5194])).
% 1.15/1.34 tff(5211,plain,
% 1.15/1.34 (s(s(s(s(z)))) = elem!1),
% 1.15/1.34 inference(symmetry,[status(thm)],[5210])).
% 1.15/1.34 tff(5212,plain,
% 1.15/1.34 (s(s(s(s(z)))) = s(s(z))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5211, 155, 5157, 138])).
% 1.15/1.34 tff(5213,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[730, 5212])).
% 1.15/1.34 tff(5214,plain,((elem!1 = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(z)) | b(s(s(elem!1)), s(z)) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5215,plain,
% 1.15/1.34 (elem!1 = s(s(elem!1))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5214, 64, 114, 82, 81])).
% 1.15/1.34 tff(5216,plain,
% 1.15/1.34 (s(elem!1) = s(s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[2097, 5215])).
% 1.15/1.34 tff(5217,plain,
% 1.15/1.34 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[2890])).
% 1.15/1.34 tff(5218,plain,
% 1.15/1.34 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.15/1.34 inference(transitivity,[status(thm)],[716, 5217, 17, 410])).
% 1.15/1.34 tff(5219,plain,
% 1.15/1.34 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5218])).
% 1.15/1.34 tff(5220,plain,
% 1.15/1.34 (s(s(z)) = s(s(elem!1))),
% 1.15/1.34 inference(transitivity,[status(thm)],[144, 5219, 88])).
% 1.15/1.34 tff(5221,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[114, 5220])).
% 1.15/1.34 tff(5222,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~(s(elem!1) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5223,plain,
% 1.15/1.34 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5222, 5216, 114])).
% 1.15/1.34 tff(5224,plain,
% 1.15/1.34 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.15/1.34 inference(symmetry,[status(thm)],[2282])).
% 1.15/1.34 tff(5225,plain,
% 1.15/1.34 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5224])).
% 1.15/1.34 tff(5226,plain,
% 1.15/1.34 (~(s(s(elem!1)) = s(s(z)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[114, 5225])).
% 1.15/1.34 tff(5227,plain,
% 1.15/1.34 (~r(s(s(elem!1)), s(s(z)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[2523, 124, 80, 113])).
% 1.15/1.34 tff(5228,plain,
% 1.15/1.34 (((~![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))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5229,plain,
% 1.15/1.34 ((~![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))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5230,plain,
% 1.15/1.34 ((~![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)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5229, 5228])).
% 1.15/1.34 tff(5231,plain,
% 1.15/1.34 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5230, 51, 5227])).
% 1.15/1.34 tff(5232,plain,
% 1.15/1.34 (b(s(s(elem!1)), s(s(z)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5231, 5226])).
% 1.15/1.34 tff(5233,assumption,(~(s(s(s(s(z)))) = s(s(elem!1)))), introduced(assumption)).
% 1.15/1.34 tff(5234,plain,
% 1.15/1.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(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(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5235,plain,
% 1.15/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5236,plain,
% 1.15/1.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5235, 5234])).
% 1.15/1.34 tff(5237,plain,
% 1.15/1.34 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5236, 51, 5233, 2959])).
% 1.15/1.34 tff(5238,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.15/1.34 tff(5239,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(s(elem!1)))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5240,plain,
% 1.15/1.34 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(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(z)))), s(s(elem!1)))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5241,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(elem!1))))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5240])).
% 1.15/1.34 tff(5242,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z)))), s(s(elem!1)))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5241, 5239])).
% 1.15/1.34 tff(5243,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5244,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 1.15/1.34 tff(5245,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5244, 238, 227, 1565, 5238, 5237])).
% 1.15/1.34 tff(5246,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5247,plain,
% 1.15/1.34 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5246, 5232, 80, 113, 5223, 136])).
% 1.15/1.34 tff(5248,plain,
% 1.15/1.34 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1624, 5247])).
% 1.15/1.34 tff(5249,plain,
% 1.15/1.34 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[2597])).
% 1.15/1.34 tff(5250,plain,
% 1.15/1.34 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.15/1.34 inference(symmetry,[status(thm)],[5249])).
% 1.15/1.34 tff(5251,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.34 tff(5252,plain,
% 1.15/1.34 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.34 tff(5253,plain,
% 1.15/1.34 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.15/1.34 inference(symmetry,[status(thm)],[5252])).
% 1.15/1.34 tff(5254,plain,
% 1.15/1.34 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5253])).
% 1.15/1.34 tff(5255,plain,
% 1.15/1.34 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[2106, 2597])).
% 1.15/1.34 tff(5256,plain,
% 1.15/1.34 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5255, 5254])).
% 1.15/1.34 tff(5257,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5258,plain,
% 1.15/1.34 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), 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(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5259,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5258])).
% 1.15/1.34 tff(5260,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.15/1.34 inference(transitivity,[status(thm)],[5259, 5257])).
% 1.15/1.34 tff(5261,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5262,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 1.15/1.34 tff(5263,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5262, 124, 162, 1711, 2008])).
% 1.15/1.34 tff(5264,plain,((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5265,plain,
% 1.15/1.34 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5264, 1711, 162])).
% 1.15/1.34 tff(5266,plain,
% 1.15/1.34 (elem!1 = s(elem!1)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[393, 389])).
% 1.15/1.34 tff(5267,plain,
% 1.15/1.34 (s(elem!1) = s(s(elem!1))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[386, 5266])).
% 1.15/1.34 tff(5268,plain,
% 1.15/1.34 (s(s(elem!1)) = s(elem!1)),
% 1.15/1.34 inference(symmetry,[status(thm)],[5267])).
% 1.15/1.34 tff(5269,plain,
% 1.15/1.34 (s(s(elem!1)) = elem!1),
% 1.15/1.34 inference(transitivity,[status(thm)],[5268, 389])).
% 1.15/1.34 tff(5270,plain,
% 1.15/1.34 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.15/1.34 inference(monotonicity,[status(thm)],[5269])).
% 1.15/1.34 tff(5271,plain,
% 1.15/1.34 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(symmetry,[status(thm)],[5270])).
% 1.15/1.34 tff(5272,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.15/1.34 tff(5273,plain,
% 1.15/1.34 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5272, 5271])).
% 1.15/1.34 tff(5274,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[2666, 5273])).
% 1.15/1.34 tff(5275,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), s(s(elem!1))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5276,plain,
% 1.15/1.34 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5275, 5265, 389])).
% 1.15/1.34 tff(5277,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), elem!1)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1064, 5276, 5256])).
% 1.15/1.34 tff(5278,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5277, 5251])).
% 1.15/1.34 tff(5279,plain,
% 1.15/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), 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(s(s(s(z))))), s(s(z)))))),
% 1.15/1.34 inference(rewrite,[status(thm)],[])).
% 1.15/1.34 tff(5280,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(s(s(s(z))))), s(s(z)))))),
% 1.15/1.34 inference(quant_inst,[status(thm)],[])).
% 1.15/1.34 tff(5281,plain,
% 1.15/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5280, 5279])).
% 1.15/1.34 tff(5282,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5281, 238, 227, 1739, 5278, 5238])).
% 1.15/1.34 tff(5283,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~(elem!1 = s(s(elem!1)))) | (~(s(elem!1) = elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.34 tff(5284,plain,
% 1.15/1.34 (~r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5283, 389, 162, 2073, 227, 5238, 169])).
% 1.15/1.34 tff(5285,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1781, 5284])).
% 1.15/1.34 tff(5286,plain,
% 1.15/1.34 (~b(s(z), s(s(s(s(s(z))))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1794, 5285, 1786, 1784])).
% 1.15/1.34 tff(5287,plain,
% 1.15/1.34 (r(s(z), s(s(s(s(s(z))))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1709, 5286])).
% 1.15/1.34 tff(5288,plain,
% 1.15/1.34 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1690, 5287, 169])).
% 1.15/1.34 tff(5289,plain,
% 1.15/1.34 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1764, 5288])).
% 1.15/1.34 tff(5290,plain,
% 1.15/1.34 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[2016, 5287, 160])).
% 1.15/1.34 tff(5291,plain,
% 1.15/1.34 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[5275, 5290, 389])).
% 1.15/1.34 tff(5292,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), elem!1)),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[1064, 5291, 5256])).
% 1.15/1.34 tff(5293,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.15/1.34 tff(5294,plain,
% 1.15/1.34 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.34 inference(modus_ponens,[status(thm)],[5293, 5251])).
% 1.15/1.34 tff(5295,plain,
% 1.15/1.34 ($false),
% 1.15/1.34 inference(unit_resolution,[status(thm)],[4315, 5294])).
% 1.15/1.34 tff(5296,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), s(s(elem!1))) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5297,plain,
% 1.15/1.35 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5296, 5292, 2073])).
% 1.15/1.35 tff(5298,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5299,plain,
% 1.15/1.35 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5300,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5299])).
% 1.15/1.35 tff(5301,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5300, 5298])).
% 1.15/1.35 tff(5302,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(5303,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5302, 5301])).
% 1.15/1.35 tff(5304,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5303, 238, 227, 5297, 5289, 5238])).
% 1.15/1.35 tff(5305,plain,((~(s(elem!1) = elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5306,plain,
% 1.15/1.35 (~(s(elem!1) = elem!1)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5305, 160, 5238, 2073, 227, 169, 1786, 1784, 162])).
% 1.15/1.35 tff(5307,plain,
% 1.15/1.35 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.35 tff(5308,plain,
% 1.15/1.35 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5307, 267])).
% 1.15/1.35 tff(5309,plain,
% 1.15/1.35 ((s(elem!1) = s(s(elem!1))) <=> (elem!1 = s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5308])).
% 1.15/1.35 tff(5310,plain,
% 1.15/1.35 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2597])).
% 1.15/1.35 tff(5311,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5310])).
% 1.15/1.35 tff(5312,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = elem!1)),
% 1.15/1.35 inference(transitivity,[status(thm)],[5311, 5309, 2902])).
% 1.15/1.35 tff(5313,plain,
% 1.15/1.35 (s(elem!1) = elem!1),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[58, 5312])).
% 1.15/1.35 tff(5314,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[632, 5313])).
% 1.15/1.35 tff(5315,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(elem!1) = elem!1) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5316,plain,
% 1.15/1.35 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5315, 5306, 2073])).
% 1.15/1.35 tff(5317,plain,
% 1.15/1.35 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[223, 5316, 219])).
% 1.15/1.35 tff(5318,plain,
% 1.15/1.35 (b(s(elem!1), s(s(elem!1)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5317, 5250])).
% 1.15/1.35 tff(5319,plain,
% 1.15/1.35 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2597])).
% 1.15/1.35 tff(5320,plain,
% 1.15/1.35 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5319])).
% 1.15/1.35 tff(5321,plain,
% 1.15/1.35 (b(s(s(z)), s(elem!1))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[462, 5320])).
% 1.15/1.35 tff(5322,plain,
% 1.15/1.35 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.35 tff(5323,plain,
% 1.15/1.35 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.15/1.35 inference(symmetry,[status(thm)],[5322])).
% 1.15/1.35 tff(5324,plain,
% 1.15/1.35 (b(s(s(z)), elem!1)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[227, 5323])).
% 1.15/1.35 tff(5325,plain,
% 1.15/1.35 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.35 tff(5326,plain,
% 1.15/1.35 (r(s(s(elem!1)), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5325])).
% 1.15/1.35 tff(5327,plain,
% 1.15/1.35 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2597])).
% 1.15/1.35 tff(5328,plain,
% 1.15/1.35 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5327])).
% 1.15/1.35 tff(5329,plain,
% 1.15/1.35 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2073])).
% 1.15/1.35 tff(5330,plain,
% 1.15/1.35 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5329, 5328, 5326])).
% 1.15/1.35 tff(5331,plain,
% 1.15/1.35 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5330])).
% 1.15/1.35 tff(5332,plain,
% 1.15/1.35 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[2580])).
% 1.15/1.35 tff(5333,plain,
% 1.15/1.35 (r(elem!1, s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[162, 5332])).
% 1.15/1.35 tff(5334,plain,
% 1.15/1.35 (~r(elem!1, s(s(s(elem!1))))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1378, 5333, 161])).
% 1.15/1.35 tff(5335,plain,
% 1.15/1.35 (~r(elem!1, s(elem!1))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5334, 5331])).
% 1.15/1.35 tff(5336,plain,
% 1.15/1.35 (elem!1 = s(s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[158, 151])).
% 1.15/1.35 tff(5337,plain,
% 1.15/1.35 (s(elem!1) = s(s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2097, 5336])).
% 1.15/1.35 tff(5338,plain,
% 1.15/1.35 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5337])).
% 1.15/1.35 tff(5339,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5338])).
% 1.15/1.35 tff(5340,plain,
% 1.15/1.35 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5339])).
% 1.15/1.35 tff(5341,plain,
% 1.15/1.35 (~(s(elem!1) = s(s(elem!1)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[545, 5340])).
% 1.15/1.35 tff(5342,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[151, 5341])).
% 1.15/1.35 tff(5343,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5344,plain,
% 1.15/1.35 (~(s(elem!1) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5343, 5316])).
% 1.15/1.35 tff(5345,plain,
% 1.15/1.35 (~(elem!1 = s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[386, 5344])).
% 1.15/1.35 tff(5346,plain,
% 1.15/1.35 (b(elem!1, s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[629, 5345, 5335])).
% 1.15/1.35 tff(5347,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.15/1.35 tff(5348,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5349,plain,
% 1.15/1.35 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5350,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5349])).
% 1.15/1.35 tff(5351,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5350, 5348])).
% 1.15/1.35 tff(5352,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(5353,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), elem!1))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5352, 5351])).
% 1.15/1.35 tff(5354,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5353, 238, 631, 288, 5347, 2180])).
% 1.15/1.35 tff(5355,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5356,plain,
% 1.15/1.35 (~b(s(elem!1), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5355, 5346, 5324, 5321])).
% 1.15/1.35 tff(5357,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5356, 5318])).
% 1.15/1.35 tff(5358,plain,((~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5359,plain,
% 1.15/1.35 (~r(s(z), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5358, 5215, 5232, 136, 80, 1786, 5248, 113, 102])).
% 1.15/1.35 tff(5360,plain,
% 1.15/1.35 (b(s(z), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[56, 5359])).
% 1.15/1.35 tff(5361,plain,
% 1.15/1.35 (b(s(z), s(s(s(elem!1))))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[1137, 2568])).
% 1.15/1.35 tff(5362,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[81, 5361])).
% 1.15/1.35 tff(5363,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5364,plain,
% 1.15/1.35 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5363, 5360, 81])).
% 1.15/1.35 tff(5365,plain,
% 1.15/1.35 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5216])).
% 1.15/1.35 tff(5366,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5365])).
% 1.15/1.35 tff(5367,plain,
% 1.15/1.35 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5366])).
% 1.15/1.35 tff(5368,plain,
% 1.15/1.35 (~(s(elem!1) = s(s(z)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[1291, 5367])).
% 1.15/1.35 tff(5369,plain,
% 1.15/1.35 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5215])).
% 1.15/1.35 tff(5370,plain,
% 1.15/1.35 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5369])).
% 1.15/1.35 tff(5371,plain,
% 1.15/1.35 (r(elem!1, s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[113, 5370])).
% 1.15/1.35 tff(5372,plain,
% 1.15/1.35 (s(elem!1) = s(s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5022, 5360, 82, 80, 358, 5371, 5368])).
% 1.15/1.35 tff(5373,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5343, 5372, 5364])).
% 1.15/1.35 tff(5374,plain,(b(s(s(z)), s(z)) | b(s(s(elem!1)), s(z)) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5375,plain,
% 1.15/1.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5374, 82, 64, 22, 81])).
% 1.15/1.35 tff(5376,plain,
% 1.15/1.35 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1904, 5375])).
% 1.15/1.35 tff(5377,plain,
% 1.15/1.35 (elem!1 = s(s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5214, 82, 64, 22, 81])).
% 1.15/1.35 tff(5378,plain,
% 1.15/1.35 (s(elem!1) = s(s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2097, 5377])).
% 1.15/1.35 tff(5379,plain,
% 1.15/1.35 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5222, 5378, 22])).
% 1.15/1.35 tff(5380,plain,
% 1.15/1.35 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[135, 131, 22])).
% 1.15/1.35 tff(5381,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.15/1.35 tff(5382,plain,
% 1.15/1.35 (s(s(z)) = s(s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5381])).
% 1.15/1.35 tff(5383,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[114, 5382])).
% 1.15/1.35 tff(5384,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5385,plain,
% 1.15/1.35 (~(s(s(elem!1)) = s(s(z)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5384, 22])).
% 1.15/1.35 tff(5386,plain,
% 1.15/1.35 (b(s(s(elem!1)), s(s(z)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5230, 51, 5227, 5385])).
% 1.15/1.35 tff(5387,plain,
% 1.15/1.35 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5246, 5386, 80, 5380, 113, 5379])).
% 1.15/1.35 tff(5388,plain,
% 1.15/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1624, 5387])).
% 1.15/1.35 tff(5389,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.15/1.35 tff(5390,plain,
% 1.15/1.35 (r(z, s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1542, 5389])).
% 1.15/1.35 tff(5391,plain,
% 1.15/1.35 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1613, 5390, 80])).
% 1.15/1.35 tff(5392,plain,
% 1.15/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1624, 5391])).
% 1.15/1.35 tff(5393,plain,
% 1.15/1.35 (~r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1773, 5390, 80])).
% 1.15/1.35 tff(5394,plain,
% 1.15/1.35 (b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1781, 5393])).
% 1.15/1.35 tff(5395,plain,
% 1.15/1.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4153, 5394, 4225, 5392])).
% 1.15/1.35 tff(5396,plain,
% 1.15/1.35 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[3727])).
% 1.15/1.35 tff(5397,plain,
% 1.15/1.35 (b(s(s(z)), s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[23, 5396])).
% 1.15/1.35 tff(5398,plain,
% 1.15/1.35 ($false),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[64, 5397])).
% 1.15/1.35 tff(5399,plain,((~(s(s(z)) = s(s(elem!1)))) | b(s(s(z)), s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.35 tff(5400,plain,
% 1.15/1.35 (~(s(s(z)) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5399, 23, 64])).
% 1.15/1.35 tff(5401,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5402,plain,
% 1.15/1.35 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.35 inference(rewrite,[status(thm)],[])).
% 1.15/1.35 tff(5403,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5402])).
% 1.15/1.35 tff(5404,plain,
% 1.15/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5403, 5401])).
% 1.15/1.35 tff(5405,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))))),
% 1.15/1.35 inference(quant_inst,[status(thm)],[])).
% 1.15/1.35 tff(5406,plain,
% 1.15/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5405, 5404])).
% 1.15/1.35 tff(5407,plain,
% 1.15/1.35 (~b(s(z), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[5406, 238, 1137, 23])).
% 1.15/1.35 tff(5408,plain,
% 1.15/1.35 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1613, 1545, 80])).
% 1.15/1.35 tff(5409,plain,
% 1.15/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1624, 5408])).
% 1.15/1.35 tff(5410,plain,
% 1.15/1.35 (~r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1773, 1545, 80])).
% 1.15/1.35 tff(5411,plain,
% 1.15/1.35 (b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1781, 5410])).
% 1.15/1.35 tff(5412,plain,
% 1.15/1.35 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4153, 5411, 546, 5409])).
% 1.15/1.35 tff(5413,plain,
% 1.15/1.35 (~(s(elem!1) = s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[357, 5400])).
% 1.15/1.35 tff(5414,plain,
% 1.15/1.35 (r(s(elem!1), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[473, 1808, 1])).
% 1.15/1.35 tff(5415,plain,
% 1.15/1.35 (~r(z, s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[3111, 124, 5414, 1545])).
% 1.15/1.35 tff(5416,plain,
% 1.15/1.35 (b(z, s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[3115, 51, 5415, 4923])).
% 1.15/1.35 tff(5417,assumption,(~b(s(z), s(z))), introduced(assumption)).
% 1.15/1.35 tff(5418,plain,
% 1.15/1.35 (~b(s(z), elem!1)),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1802, 2359])).
% 1.15/1.35 tff(5419,plain,
% 1.15/1.35 (b(elem!1, s(z)) <=> b(s(z), s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2359])).
% 1.15/1.35 tff(5420,plain,
% 1.15/1.35 (b(s(z), s(z)) <=> b(elem!1, s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5419])).
% 1.15/1.35 tff(5421,plain,
% 1.15/1.35 ((~b(s(z), s(z))) <=> (~b(elem!1, s(z)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5420])).
% 1.15/1.35 tff(5422,plain,
% 1.15/1.35 (~b(elem!1, s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5417, 5421])).
% 1.15/1.35 tff(5423,plain,
% 1.15/1.35 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[2228])).
% 1.15/1.35 tff(5424,plain,
% 1.15/1.35 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[1899, 5423])).
% 1.15/1.35 tff(5425,plain,
% 1.15/1.35 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4368, 345, 1081, 1400, 1808])).
% 1.15/1.35 tff(5426,plain,
% 1.15/1.35 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5425])).
% 1.15/1.35 tff(5427,plain,
% 1.15/1.35 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.15/1.35 inference(transitivity,[status(thm)],[723, 5426, 88])).
% 1.15/1.35 tff(5428,plain,
% 1.15/1.35 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5427])).
% 1.15/1.35 tff(5429,plain,
% 1.15/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5427])).
% 1.15/1.35 tff(5430,plain,
% 1.15/1.35 (s(s(s(z))) = s(elem!1)),
% 1.15/1.35 inference(transitivity,[status(thm)],[716, 5429, 17])).
% 1.15/1.35 tff(5431,plain,
% 1.15/1.35 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5430])).
% 1.15/1.35 tff(5432,plain,
% 1.15/1.35 (s(s(z)) = elem!1),
% 1.15/1.35 inference(transitivity,[status(thm)],[144, 5431, 154])).
% 1.15/1.35 tff(5433,plain,
% 1.15/1.35 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5434,plain,
% 1.15/1.35 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5433])).
% 1.15/1.35 tff(5435,plain,
% 1.15/1.35 ((~b(elem!1, s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5434])).
% 1.15/1.35 tff(5436,plain,
% 1.15/1.35 (~b(s(s(z)), s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[1400, 5435])).
% 1.15/1.35 tff(5437,plain,
% 1.15/1.35 (r(s(s(z)), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[79, 5436])).
% 1.15/1.35 tff(5438,plain,
% 1.15/1.35 ((s(s(z)) = s(z)) <=> (elem!1 = s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5439,plain,
% 1.15/1.35 ((~(s(s(z)) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5438])).
% 1.15/1.35 tff(5440,plain,
% 1.15/1.35 (~(elem!1 = s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[74, 5439])).
% 1.15/1.35 tff(5441,plain,
% 1.15/1.35 (r(elem!1, s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[363, 5440, 1400])).
% 1.15/1.35 tff(5442,plain,
% 1.15/1.35 (~(s(s(z)) = s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4960, 5425])).
% 1.15/1.35 tff(5443,plain,
% 1.15/1.35 (~(s(elem!1) = s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[357, 5442])).
% 1.15/1.35 tff(5444,plain,
% 1.15/1.35 (r(s(elem!1), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[473, 5443, 1808])).
% 1.15/1.35 tff(5445,plain,
% 1.15/1.35 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4990, 5444, 5425, 5441, 5437])).
% 1.15/1.35 tff(5446,plain,
% 1.15/1.35 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1623, 5445, 1619])).
% 1.15/1.35 tff(5447,plain,
% 1.15/1.35 (b(s(s(elem!1)), s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5446, 5428])).
% 1.15/1.35 tff(5448,plain,
% 1.15/1.35 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5449,plain,
% 1.15/1.35 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5448])).
% 1.15/1.35 tff(5450,plain,
% 1.15/1.35 (~(elem!1 = s(s(elem!1)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5442, 5449])).
% 1.15/1.35 tff(5451,plain,
% 1.15/1.35 (~r(s(z), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2862, 5440, 345, 5444, 5450, 1400])).
% 1.15/1.35 tff(5452,plain,
% 1.15/1.35 (b(s(z), s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[56, 5451])).
% 1.15/1.35 tff(5453,plain,
% 1.15/1.35 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5427])).
% 1.15/1.35 tff(5454,plain,
% 1.15/1.35 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5453, 2301])).
% 1.15/1.35 tff(5455,plain,
% 1.15/1.35 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5454])).
% 1.15/1.35 tff(5456,plain,
% 1.15/1.35 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5425])).
% 1.15/1.35 tff(5457,plain,
% 1.15/1.35 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5456])).
% 1.15/1.35 tff(5458,plain,
% 1.15/1.35 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[2782, 5457])).
% 1.15/1.35 tff(5459,plain,
% 1.15/1.35 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5458, 5455])).
% 1.15/1.35 tff(5460,plain,
% 1.15/1.35 ((s(elem!1) = s(s(z))) <=> (s(elem!1) = elem!1)),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5461,plain,
% 1.15/1.35 ((s(elem!1) = s(s(z))) <=> (elem!1 = s(elem!1))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5460, 388])).
% 1.15/1.35 tff(5462,plain,
% 1.15/1.35 ((~(s(elem!1) = s(s(z)))) <=> (~(elem!1 = s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5461])).
% 1.15/1.35 tff(5463,plain,
% 1.15/1.35 ((s(s(z)) = s(s(s(z)))) <=> (s(s(z)) = s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5430])).
% 1.15/1.35 tff(5464,plain,
% 1.15/1.35 ((s(s(z)) = s(s(s(z)))) <=> (s(elem!1) = s(s(z)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5463, 1245])).
% 1.15/1.35 tff(5465,plain,
% 1.15/1.35 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(elem!1) = s(s(z))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5464])).
% 1.15/1.35 tff(5466,plain,
% 1.15/1.35 (~(s(elem!1) = s(s(z)))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[147, 5465])).
% 1.15/1.35 tff(5467,plain,
% 1.15/1.35 (~(elem!1 = s(elem!1))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5466, 5462])).
% 1.15/1.35 tff(5468,plain,
% 1.15/1.35 (~r(elem!1, s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2634, 124, 5441, 5444])).
% 1.15/1.35 tff(5469,plain,
% 1.15/1.35 (b(elem!1, s(elem!1))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[629, 5468, 5467])).
% 1.15/1.35 tff(5470,plain,
% 1.15/1.35 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5471,plain,
% 1.15/1.35 (~r(s(elem!1), s(s(z)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[483, 5437, 5444])).
% 1.15/1.35 tff(5472,plain,
% 1.15/1.35 (b(s(elem!1), s(s(z)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[488, 5471, 5466])).
% 1.15/1.35 tff(5473,plain,
% 1.15/1.35 (b(s(elem!1), elem!1)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5472, 5470])).
% 1.15/1.35 tff(5474,plain,
% 1.15/1.35 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5430])).
% 1.15/1.35 tff(5475,plain,
% 1.15/1.35 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5474])).
% 1.15/1.35 tff(5476,plain,
% 1.15/1.35 (r(s(s(s(z))), s(z))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5444, 5475])).
% 1.15/1.35 tff(5477,plain,
% 1.15/1.35 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5430])).
% 1.15/1.35 tff(5478,plain,
% 1.15/1.35 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5477])).
% 1.15/1.35 tff(5479,plain,
% 1.15/1.35 (b(s(s(z)), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5432])).
% 1.15/1.35 tff(5480,plain,
% 1.15/1.35 (b(elem!1, s(elem!1)) <=> b(s(s(z)), s(elem!1))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5479])).
% 1.15/1.35 tff(5481,plain,
% 1.15/1.35 (b(elem!1, s(elem!1)) <=> b(s(s(z)), s(s(s(z))))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5480, 5478])).
% 1.15/1.35 tff(5482,plain,
% 1.15/1.35 (b(s(s(z)), s(s(s(z))))),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[5469, 5481])).
% 1.15/1.35 tff(5483,plain,
% 1.15/1.35 (~r(z, s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2841, 5482, 5476, 5437])).
% 1.15/1.35 tff(5484,plain,
% 1.15/1.35 (b(z, s(z))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[1542, 5483])).
% 1.15/1.35 tff(5485,plain,
% 1.15/1.35 (~b(z, s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[4873, 238, 5452, 5447, 5484])).
% 1.15/1.35 tff(5486,plain,
% 1.15/1.35 (r(z, s(s(elem!1)))),
% 1.15/1.35 inference(unit_resolution,[status(thm)],[2071, 5485])).
% 1.15/1.35 tff(5487,plain,
% 1.15/1.35 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5431])).
% 1.15/1.35 tff(5488,plain,
% 1.15/1.35 (elem!1 = s(s(z))),
% 1.15/1.35 inference(transitivity,[status(thm)],[155, 5487, 138])).
% 1.15/1.35 tff(5489,plain,
% 1.15/1.35 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5488])).
% 1.15/1.35 tff(5490,plain,
% 1.15/1.35 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.15/1.35 inference(transitivity,[status(thm)],[5489, 1284])).
% 1.15/1.35 tff(5491,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5490])).
% 1.15/1.35 tff(5492,plain,
% 1.15/1.35 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.15/1.35 inference(transitivity,[status(thm)],[5491, 641])).
% 1.15/1.35 tff(5493,plain,
% 1.15/1.35 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5492])).
% 1.15/1.35 tff(5494,plain,
% 1.15/1.35 (~(s(s(s(elem!1))) = elem!1)),
% 1.15/1.35 inference(modus_ponens,[status(thm)],[1291, 5493])).
% 1.15/1.35 tff(5495,plain,
% 1.15/1.35 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.15/1.35 inference(monotonicity,[status(thm)],[5427])).
% 1.15/1.35 tff(5496,plain,
% 1.15/1.35 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.15/1.35 inference(symmetry,[status(thm)],[5495])).
% 1.15/1.35 tff(5497,plain,
% 1.15/1.35 (b(s(z), s(s(s(s(z)))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5452, 5496])).
% 1.15/1.36 tff(5498,plain,
% 1.15/1.36 (~b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[2798, 5446, 5497, 5484])).
% 1.15/1.36 tff(5499,plain,
% 1.15/1.36 (r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1781, 5498])).
% 1.15/1.36 tff(5500,plain,
% 1.15/1.36 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1725, 5499, 5437])).
% 1.15/1.36 tff(5501,plain,
% 1.15/1.36 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[4808])).
% 1.15/1.36 tff(5502,plain,
% 1.15/1.36 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.36 inference(symmetry,[status(thm)],[5501])).
% 1.15/1.36 tff(5503,plain,
% 1.15/1.36 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.15/1.36 inference(monotonicity,[status(thm)],[4814])).
% 1.15/1.36 tff(5504,plain,
% 1.15/1.36 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.15/1.36 inference(symmetry,[status(thm)],[5503])).
% 1.15/1.36 tff(5505,plain,
% 1.15/1.36 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5504, 5502])).
% 1.15/1.36 tff(5506,plain,
% 1.15/1.36 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[649, 5505])).
% 1.15/1.36 tff(5507,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1732, 5506])).
% 1.15/1.36 tff(5508,plain,((~r(s(s(s(elem!1))), elem!1)) | r(s(s(s(s(s(z))))), s(s(z))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5509,plain,
% 1.15/1.36 (~r(s(s(s(elem!1))), elem!1)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5508, 5500, 5425])).
% 1.15/1.36 tff(5510,plain,
% 1.15/1.36 (b(s(s(s(elem!1))), elem!1)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[647, 5509, 5494])).
% 1.15/1.36 tff(5511,plain,
% 1.15/1.36 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.15/1.36 inference(symmetry,[status(thm)],[4813])).
% 1.15/1.36 tff(5512,plain,
% 1.15/1.36 (elem!1 = s(s(z))),
% 1.15/1.36 inference(transitivity,[status(thm)],[155, 5511, 138])).
% 1.15/1.36 tff(5513,plain,
% 1.15/1.36 ((elem!1 = z) <=> (s(s(z)) = z)),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5512])).
% 1.15/1.36 tff(5514,plain,
% 1.15/1.36 ((s(s(z)) = z) <=> (elem!1 = z)),
% 1.15/1.36 inference(symmetry,[status(thm)],[5513])).
% 1.15/1.36 tff(5515,plain,
% 1.15/1.36 ((~(s(s(z)) = z)) <=> (~(elem!1 = z))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5514])).
% 1.15/1.36 tff(5516,plain,
% 1.15/1.36 (~(elem!1 = z)),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[1449, 5515])).
% 1.15/1.36 tff(5517,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.15/1.36 tff(5518,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5519,plain,
% 1.15/1.36 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5520,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5519])).
% 1.15/1.36 tff(5521,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5520, 5518])).
% 1.15/1.36 tff(5522,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5523,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5522, 5521])).
% 1.15/1.36 tff(5524,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5523, 124, 210, 2026, 5517])).
% 1.15/1.36 tff(5525,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5526,plain,
% 1.15/1.36 (~r(z, s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5525, 210, 2026])).
% 1.15/1.36 tff(5527,plain,
% 1.15/1.36 (b(z, s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[3795, 51, 5526, 3785])).
% 1.15/1.36 tff(5528,plain,
% 1.15/1.36 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5512])).
% 1.15/1.36 tff(5529,plain,
% 1.15/1.36 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5528, 1284])).
% 1.15/1.36 tff(5530,plain,
% 1.15/1.36 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.15/1.36 inference(symmetry,[status(thm)],[5529])).
% 1.15/1.36 tff(5531,plain,
% 1.15/1.36 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5530])).
% 1.15/1.36 tff(5532,plain,
% 1.15/1.36 (~(elem!1 = s(s(s(elem!1))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[1291, 5531])).
% 1.15/1.36 tff(5533,plain,
% 1.15/1.36 (~(s(s(elem!1)) = s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[271, 4963])).
% 1.15/1.36 tff(5534,plain,
% 1.15/1.36 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.15/1.36 inference(commutativity,[status(thm)],[])).
% 1.15/1.36 tff(5535,plain,
% 1.15/1.36 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.15/1.36 inference(symmetry,[status(thm)],[5534])).
% 1.15/1.36 tff(5536,plain,
% 1.15/1.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[4812, 4808])).
% 1.15/1.36 tff(5537,plain,
% 1.15/1.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5536, 5535])).
% 1.15/1.36 tff(5538,plain,
% 1.15/1.36 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5537])).
% 1.15/1.36 tff(5539,plain,
% 1.15/1.36 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[1092, 5538])).
% 1.15/1.36 tff(5540,plain,
% 1.15/1.36 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[786, 781, 507, 631])).
% 1.15/1.36 tff(5541,plain,
% 1.15/1.36 (r(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[459, 5540, 5539])).
% 1.15/1.36 tff(5542,plain,
% 1.15/1.36 (~r(s(s(elem!1)), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1397, 210, 5541])).
% 1.15/1.36 tff(5543,plain,
% 1.15/1.36 (b(s(s(elem!1)), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[323, 5542, 5533])).
% 1.15/1.36 tff(5544,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5545,plain,
% 1.15/1.36 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5546,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5545])).
% 1.15/1.36 tff(5547,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5546, 5544])).
% 1.15/1.36 tff(5548,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5549,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 1.15/1.36 tff(5550,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5549, 238, 631, 507, 1185, 289])).
% 1.15/1.36 tff(5551,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5552,plain,
% 1.15/1.36 (~b(elem!1, s(s(elem!1)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5551, 5543, 507, 631])).
% 1.15/1.36 tff(5553,plain,
% 1.15/1.36 (r(elem!1, s(s(elem!1)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[606, 5552, 4962])).
% 1.15/1.36 tff(5554,plain,
% 1.15/1.36 (~r(elem!1, s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[4474, 124, 5553, 210])).
% 1.15/1.36 tff(5555,plain,
% 1.15/1.36 (b(elem!1, s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1319, 5554, 5532])).
% 1.15/1.36 tff(5556,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5557,plain,
% 1.15/1.36 (((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5558,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5557])).
% 1.15/1.36 tff(5559,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5558, 5556])).
% 1.15/1.36 tff(5560,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, z)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5561,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5560, 5559])).
% 1.15/1.36 tff(5562,plain,
% 1.15/1.36 (~b(elem!1, z)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5561, 238, 5555, 781, 5527])).
% 1.15/1.36 tff(5563,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5564,plain,
% 1.15/1.36 (((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5565,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5564])).
% 1.15/1.36 tff(5566,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5565, 5563])).
% 1.15/1.36 tff(5567,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5568,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, z))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5567, 5566])).
% 1.15/1.36 tff(5569,plain,
% 1.15/1.36 (~r(elem!1, z)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5568, 124, 5553, 2026])).
% 1.15/1.36 tff(5570,plain,
% 1.15/1.36 ((elem!1 = z) | b(elem!1, z)),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[4843, 51, 5569])).
% 1.15/1.36 tff(5571,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5570, 5562, 5516])).
% 1.15/1.36 tff(5572,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5573,plain,
% 1.15/1.36 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5572, 5510, 5425, 5486, 5473, 5469])).
% 1.15/1.36 tff(5574,plain,
% 1.15/1.36 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[223, 5573, 5459])).
% 1.15/1.36 tff(5575,plain,
% 1.15/1.36 (~b(s(z), s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[3192, 5574, 5452, 5447])).
% 1.15/1.36 tff(5576,plain,
% 1.15/1.36 (r(s(z), s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[101, 5575])).
% 1.15/1.36 tff(5577,plain,
% 1.15/1.36 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5430, 5425])).
% 1.15/1.36 tff(5578,plain,
% 1.15/1.36 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5577])).
% 1.15/1.36 tff(5579,plain,
% 1.15/1.36 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[1092, 5578])).
% 1.15/1.36 tff(5580,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5581,plain,
% 1.15/1.36 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5582,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5581])).
% 1.15/1.36 tff(5583,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5582, 5580])).
% 1.15/1.36 tff(5584,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5585,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5584, 5583])).
% 1.15/1.36 tff(5586,plain,
% 1.15/1.36 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5585, 238, 5469, 5473, 5510])).
% 1.15/1.36 tff(5587,plain,
% 1.15/1.36 (r(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[539, 5586, 5579])).
% 1.15/1.36 tff(5588,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[4741, 124, 5587, 5444, 5576])).
% 1.15/1.36 tff(5589,plain,(b(s(z), elem!1) | b(elem!1, s(z)) | b(s(elem!1), s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5590,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5589, 5424, 5422, 1808, 5418])).
% 1.15/1.36 tff(5591,plain,((~(s(elem!1) = s(s(z)))) | b(s(elem!1), s(z)) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | b(s(z), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5592,plain,
% 1.15/1.36 (~(s(elem!1) = s(s(z)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5591, 1808, 1899, 5417])).
% 1.15/1.36 tff(5593,plain,
% 1.15/1.36 (~(s(s(z)) = s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1249, 5592])).
% 1.15/1.36 tff(5594,plain,
% 1.15/1.36 (~r(s(s(z)), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1256, 124, 169, 5414])).
% 1.15/1.36 tff(5595,plain,
% 1.15/1.36 (b(s(s(z)), s(elem!1))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[1260, 51, 5594, 5593])).
% 1.15/1.36 tff(5596,plain,
% 1.15/1.36 (~r(s(elem!1), s(s(z)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[483, 5414, 169])).
% 1.15/1.36 tff(5597,plain,
% 1.15/1.36 (b(s(elem!1), s(s(z)))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[488, 5596, 5592])).
% 1.15/1.36 tff(5598,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5599,plain,
% 1.15/1.36 (((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5600,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1)))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5599])).
% 1.15/1.36 tff(5601,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1))))),
% 1.15/1.36 inference(transitivity,[status(thm)],[5600, 5598])).
% 1.15/1.36 tff(5602,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), z)))),
% 1.15/1.36 inference(quant_inst,[status(thm)],[])).
% 1.15/1.36 tff(5603,plain,
% 1.15/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(elem!1)))),
% 1.15/1.36 inference(modus_ponens,[status(thm)],[5602, 5601])).
% 1.15/1.36 tff(5604,plain,
% 1.15/1.36 ($false),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5603, 238, 5597, 5595, 4832, 5416])).
% 1.15/1.36 tff(5605,plain,(b(s(elem!1), s(z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | b(s(z), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.36 tff(5606,plain,
% 1.15/1.36 (b(s(elem!1), s(z))),
% 1.15/1.36 inference(unit_resolution,[status(thm)],[5605, 5413, 80, 1545, 5412, 5407])).
% 1.15/1.36 tff(5607,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5608,plain,
% 1.15/1.36 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.36 inference(rewrite,[status(thm)],[])).
% 1.15/1.36 tff(5609,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.15/1.36 inference(monotonicity,[status(thm)],[5608])).
% 1.15/1.36 tff(5610,plain,
% 1.15/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5609, 5607])).
% 1.15/1.37 tff(5611,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5612,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 1.15/1.37 tff(5613,plain,
% 1.15/1.37 (~b(s(elem!1), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5612, 238, 1137, 5606, 23])).
% 1.15/1.37 tff(5614,plain,
% 1.15/1.37 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[3192, 23, 546, 1137])).
% 1.15/1.37 tff(5615,plain,
% 1.15/1.37 (r(s(elem!1), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[534, 159, 528])).
% 1.15/1.37 tff(5616,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.15/1.37 tff(5617,plain,
% 1.15/1.37 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[223, 209, 5616])).
% 1.15/1.37 tff(5618,plain,
% 1.15/1.37 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[1169, 518, 210])).
% 1.15/1.37 tff(5619,plain,
% 1.15/1.37 (b(s(elem!1), s(s(s(elem!1))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[539, 5618, 418])).
% 1.15/1.37 tff(5620,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(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)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5621,plain,
% 1.15/1.37 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5622,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(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))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5621])).
% 1.15/1.37 tff(5623,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(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)))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5622, 5620])).
% 1.15/1.37 tff(5624,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5625,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5624, 5623])).
% 1.15/1.37 tff(5626,plain,
% 1.15/1.37 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5625, 124, 518, 210])).
% 1.15/1.37 tff(5627,plain,
% 1.15/1.37 (b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[459, 5626, 4497])).
% 1.15/1.37 tff(5628,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5629,plain,
% 1.15/1.37 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5630,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5629])).
% 1.15/1.37 tff(5631,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5630, 5628])).
% 1.15/1.37 tff(5632,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5633,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5632, 5631])).
% 1.15/1.37 tff(5634,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5633, 238, 5627, 5619, 1152, 546])).
% 1.15/1.37 tff(5635,plain,((~r(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5636,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5635, 5617, 5615, 546, 1152, 415])).
% 1.15/1.37 tff(5637,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(elem!1), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5638,plain,
% 1.15/1.37 (elem!1 = s(s(elem!1))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5637, 5606, 546, 5614, 5613])).
% 1.15/1.37 tff(5639,plain,
% 1.15/1.37 (s(elem!1) = s(s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2097, 5638])).
% 1.15/1.37 tff(5640,plain,
% 1.15/1.37 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5222, 5639, 5400])).
% 1.15/1.37 tff(5641,assumption,(b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.15/1.37 tff(5642,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[3983, 238, 546, 23, 1784, 5641])).
% 1.15/1.37 tff(5643,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5644,plain,
% 1.15/1.37 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5643, 23, 5409, 546])).
% 1.15/1.37 tff(5645,plain,
% 1.15/1.37 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5236, 51, 5644])).
% 1.15/1.37 tff(5646,plain,
% 1.15/1.37 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5645, 5640])).
% 1.15/1.37 tff(5647,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5648,plain,
% 1.15/1.37 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5649,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5648])).
% 1.15/1.37 tff(5650,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5649, 5647])).
% 1.15/1.37 tff(5651,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5652,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5651, 5650])).
% 1.15/1.37 tff(5653,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5652, 238, 1137, 23, 1783, 4122])).
% 1.15/1.37 tff(5654,plain,((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5655,plain,
% 1.15/1.37 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5654, 23, 5411, 1137])).
% 1.15/1.37 tff(5656,plain,
% 1.15/1.37 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2106, 5639])).
% 1.15/1.37 tff(5657,plain,
% 1.15/1.37 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2420, 51, 5656, 5655])).
% 1.15/1.37 tff(5658,plain,
% 1.15/1.37 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2879, 5639])).
% 1.15/1.37 tff(5659,plain,
% 1.15/1.37 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[410])).
% 1.15/1.37 tff(5660,plain,
% 1.15/1.37 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.15/1.37 inference(symmetry,[status(thm)],[5659])).
% 1.15/1.37 tff(5661,plain,
% 1.15/1.37 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5660])).
% 1.15/1.37 tff(5662,plain,
% 1.15/1.37 (~b(s(elem!1), s(z))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[3884, 5661])).
% 1.15/1.37 tff(5663,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[1152, 5662])).
% 1.15/1.37 tff(5664,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5665,plain,
% 1.15/1.37 (b(s(s(s(elem!1))), s(z))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5664, 5639, 5606])).
% 1.15/1.37 tff(5666,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5667,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5668,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5667, 5666])).
% 1.15/1.37 tff(5669,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5668, 238, 1137, 564, 1784, 1041])).
% 1.15/1.37 tff(5670,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5671,plain,
% 1.15/1.37 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5670, 5665, 1137, 5409])).
% 1.15/1.37 tff(5672,plain,
% 1.15/1.37 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2974, 51, 5671, 5658])).
% 1.15/1.37 tff(5673,plain,
% 1.15/1.37 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[1904, 5412])).
% 1.15/1.37 tff(5674,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5675,plain,
% 1.15/1.37 (((~r(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(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), 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(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5676,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5675])).
% 1.15/1.37 tff(5677,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5676, 5674])).
% 1.15/1.37 tff(5678,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5679,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5678, 5677])).
% 1.15/1.37 tff(5680,plain,
% 1.15/1.37 ($false),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5679, 124, 5673, 5672, 5657, 5646])).
% 1.15/1.37 tff(5681,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.37 tff(5682,plain,
% 1.15/1.37 (~b(s(s(elem!1)), s(z))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5681, 1137, 546, 5390, 64])).
% 1.15/1.37 tff(5683,plain,
% 1.15/1.37 (r(s(s(elem!1)), s(z))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[112, 5682])).
% 1.15/1.37 tff(5684,plain,
% 1.15/1.37 (~r(s(s(elem!1)), z)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[4026, 124, 5683, 5390])).
% 1.15/1.37 tff(5685,plain,
% 1.15/1.37 (b(s(s(elem!1)), z)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[4905, 5684])).
% 1.15/1.37 tff(5686,plain,
% 1.15/1.37 (~r(z, s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2057, 124, 5683, 5390])).
% 1.15/1.37 tff(5687,plain,
% 1.15/1.37 (b(z, s(s(elem!1)))),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[2071, 5686])).
% 1.15/1.37 tff(5688,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5689,plain,
% 1.15/1.37 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.15/1.37 inference(rewrite,[status(thm)],[])).
% 1.15/1.37 tff(5690,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1))))))),
% 1.15/1.37 inference(monotonicity,[status(thm)],[5689])).
% 1.15/1.37 tff(5691,plain,
% 1.15/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))))),
% 1.15/1.37 inference(transitivity,[status(thm)],[5690, 5688])).
% 1.15/1.37 tff(5692,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.15/1.37 inference(quant_inst,[status(thm)],[])).
% 1.15/1.37 tff(5693,plain,
% 1.15/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1))))),
% 1.15/1.37 inference(modus_ponens,[status(thm)],[5692, 5691])).
% 1.15/1.37 tff(5694,plain,
% 1.15/1.37 (~b(s(z), z)),
% 1.15/1.37 inference(unit_resolution,[status(thm)],[5693, 238, 1137, 5687, 5685])).
% 1.15/1.37 tff(5695,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.15/1.37 tff(5696,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.15/1.37 tff(5697,plain,
% 1.15/1.37 (((~![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))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5698,plain,
% 1.15/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5699,plain,
% 1.15/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 1.15/1.38 tff(5700,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5699, 51, 72, 5696, 5695])).
% 1.15/1.38 tff(5701,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5702,plain,
% 1.15/1.38 (r(s(z), z)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5701, 5694])).
% 1.15/1.38 tff(5703,plain,
% 1.15/1.38 (~b(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5041, 5683, 80, 5390])).
% 1.15/1.38 tff(5704,plain,
% 1.15/1.38 (~r(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[130, 124, 80, 5683])).
% 1.15/1.38 tff(5705,plain,
% 1.15/1.38 (s(s(z)) = s(s(elem!1))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[135, 5704, 5703])).
% 1.15/1.38 tff(5706,plain,
% 1.15/1.38 (s(elem!1) = s(z)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[21, 5705])).
% 1.15/1.38 tff(5707,plain,
% 1.15/1.38 (b(z, s(z))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[370, 4116])).
% 1.15/1.38 tff(5708,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5389, 5707])).
% 1.15/1.38 tff(5709,plain,((~(s(elem!1) = s(z))) | b(z, s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5710,plain,
% 1.15/1.38 (~b(elem!1, s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5709, 5706, 5389])).
% 1.15/1.38 tff(5711,plain,
% 1.15/1.38 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5705])).
% 1.15/1.38 tff(5712,plain,
% 1.15/1.38 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5711, 3730])).
% 1.15/1.38 tff(5713,plain,
% 1.15/1.38 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5712])).
% 1.15/1.38 tff(5714,plain,
% 1.15/1.38 (~(s(s(z)) = elem!1)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4855, 5682, 5392])).
% 1.15/1.38 tff(5715,plain,
% 1.15/1.38 (~(elem!1 = s(s(elem!1)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5714, 5713])).
% 1.15/1.38 tff(5716,plain,
% 1.15/1.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5705])).
% 1.15/1.38 tff(5717,plain,
% 1.15/1.38 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5716])).
% 1.15/1.38 tff(5718,plain,
% 1.15/1.38 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.15/1.38 inference(symmetry,[status(thm)],[5717])).
% 1.15/1.38 tff(5719,plain,
% 1.15/1.38 (b(s(z), s(s(s(z))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[546, 5718])).
% 1.15/1.38 tff(5720,plain,
% 1.15/1.38 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.15/1.38 inference(commutativity,[status(thm)],[])).
% 1.15/1.38 tff(5721,plain,
% 1.15/1.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5705])).
% 1.15/1.38 tff(5722,plain,
% 1.15/1.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5721, 5720])).
% 1.15/1.38 tff(5723,plain,
% 1.15/1.38 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5722])).
% 1.15/1.38 tff(5724,plain,
% 1.15/1.38 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[147, 5723])).
% 1.15/1.38 tff(5725,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5726,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5727,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5726, 5725])).
% 1.15/1.38 tff(5728,plain,
% 1.15/1.38 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5727, 238, 3818, 2078, 4047])).
% 1.15/1.38 tff(5729,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 1.15/1.38 tff(5730,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5731,plain,
% 1.15/1.38 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5732,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5731])).
% 1.15/1.38 tff(5733,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5732, 5730])).
% 1.15/1.38 tff(5734,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5735,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5734, 5733])).
% 1.15/1.38 tff(5736,plain,
% 1.15/1.38 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5735, 124, 162, 2288])).
% 1.15/1.38 tff(5737,plain,
% 1.15/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5738,plain,
% 1.15/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5739,plain,
% 1.15/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5738, 5737])).
% 1.15/1.38 tff(5740,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5739, 51, 5736, 5729, 5728])).
% 1.15/1.38 tff(5741,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5742,plain,
% 1.15/1.38 (~r(s(s(s(z))), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5741, 5724, 5683, 5685, 5687, 5390])).
% 1.15/1.38 tff(5743,plain,
% 1.15/1.38 (b(s(s(s(z))), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5118, 5742])).
% 1.15/1.38 tff(5744,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[3362, 238, 1079, 1783, 1456, 1455])).
% 1.15/1.38 tff(5745,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5746,plain,
% 1.15/1.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5745, 5743, 5719, 5394])).
% 1.15/1.38 tff(5747,plain,
% 1.15/1.38 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[1075])).
% 1.15/1.38 tff(5748,plain,
% 1.15/1.38 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5747])).
% 1.15/1.38 tff(5749,plain,
% 1.15/1.38 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[1095, 5748])).
% 1.15/1.38 tff(5750,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1040, 5749])).
% 1.15/1.38 tff(5751,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5752,plain,
% 1.15/1.38 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5751, 5746, 5705])).
% 1.15/1.38 tff(5753,plain,
% 1.15/1.38 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4960, 5705])).
% 1.15/1.38 tff(5754,plain,
% 1.15/1.38 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1814, 5752, 5753])).
% 1.15/1.38 tff(5755,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4346, 5754, 5752, 80, 5715, 5394, 5705, 5710, 5702])).
% 1.15/1.38 tff(5756,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | b(z, s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5757,plain,
% 1.15/1.38 (~b(s(z), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5756, 5389, 4225, 64])).
% 1.15/1.38 tff(5758,plain,
% 1.15/1.38 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[2572, 5757, 4225])).
% 1.15/1.38 tff(5759,plain,
% 1.15/1.38 (~(s(elem!1) = s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5343, 5758])).
% 1.15/1.38 tff(5760,plain,
% 1.15/1.38 (r(s(z), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[56, 5757])).
% 1.15/1.38 tff(5761,plain,
% 1.15/1.38 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[805])).
% 1.15/1.38 tff(5762,plain,
% 1.15/1.38 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.15/1.38 inference(symmetry,[status(thm)],[5761])).
% 1.15/1.38 tff(5763,plain,
% 1.15/1.38 (b(s(z), s(s(s(z))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[4225, 5762])).
% 1.15/1.38 tff(5764,plain,
% 1.15/1.38 (~r(z, s(s(z)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1583, 5390, 80])).
% 1.15/1.38 tff(5765,plain,
% 1.15/1.38 (b(z, s(s(z)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1511, 51, 5764, 4848])).
% 1.15/1.38 tff(5766,plain,
% 1.15/1.38 (b(z, s(s(elem!1)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5765, 4188])).
% 1.15/1.38 tff(5767,plain,
% 1.15/1.38 (~r(s(s(z)), z)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[2809, 124, 80, 5390])).
% 1.15/1.38 tff(5768,plain,
% 1.15/1.38 (b(s(s(z)), z)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[2839, 51, 1449, 5767])).
% 1.15/1.38 tff(5769,plain,
% 1.15/1.38 (b(s(s(elem!1)), z)),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5768, 4194])).
% 1.15/1.38 tff(5770,plain,
% 1.15/1.38 (~b(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5399, 804, 64])).
% 1.15/1.38 tff(5771,plain,
% 1.15/1.38 (r(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[112, 5770])).
% 1.15/1.38 tff(5772,plain,
% 1.15/1.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[804])).
% 1.15/1.38 tff(5773,plain,
% 1.15/1.38 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5772, 5720])).
% 1.15/1.38 tff(5774,plain,
% 1.15/1.38 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5773])).
% 1.15/1.38 tff(5775,plain,
% 1.15/1.38 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[147, 5774])).
% 1.15/1.38 tff(5776,plain,
% 1.15/1.38 (~r(s(s(s(z))), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5741, 5775, 5771, 5769, 5766, 5390])).
% 1.15/1.38 tff(5777,plain,
% 1.15/1.38 (b(s(s(s(z))), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5118, 5776])).
% 1.15/1.38 tff(5778,plain,
% 1.15/1.38 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5745, 5777, 5763, 5394])).
% 1.15/1.38 tff(5779,plain,
% 1.15/1.38 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5751, 5778, 804])).
% 1.15/1.38 tff(5780,plain,
% 1.15/1.38 (~b(elem!1, s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5709, 353, 5389])).
% 1.15/1.38 tff(5781,plain,
% 1.15/1.38 (~(elem!1 = s(elem!1))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[386, 5759])).
% 1.15/1.38 tff(5782,plain,
% 1.15/1.38 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4960, 804])).
% 1.15/1.38 tff(5783,plain,
% 1.15/1.38 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1814, 5779, 5782])).
% 1.15/1.38 tff(5784,plain,
% 1.15/1.38 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4276, 804, 63, 5392, 5390])).
% 1.15/1.38 tff(5785,plain,
% 1.15/1.38 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1101, 5778])).
% 1.15/1.38 tff(5786,plain,
% 1.15/1.38 (~b(s(z), s(s(s(s(s(z))))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4223, 5785, 5392, 5394, 804, 5784])).
% 1.15/1.38 tff(5787,plain,
% 1.15/1.38 (r(s(z), s(s(s(s(s(z))))))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1709, 5786])).
% 1.15/1.38 tff(5788,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[4214, 5787, 5783, 80, 5394, 353, 5781, 5780, 5779])).
% 1.15/1.38 tff(5789,plain,((~(s(elem!1) = s(z))) | b(s(s(z)), s(z)) | r(s(z), s(s(s(elem!1)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5790,plain,
% 1.15/1.38 (~(s(elem!1) = s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5789, 5389, 63, 64])).
% 1.15/1.38 tff(5791,plain,
% 1.15/1.38 (r(s(elem!1), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[473, 1, 1808])).
% 1.15/1.38 tff(5792,plain,
% 1.15/1.38 (~r(s(elem!1), s(s(z)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[483, 5791, 169])).
% 1.15/1.38 tff(5793,plain,
% 1.15/1.38 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[135, 22, 2214])).
% 1.15/1.38 tff(5794,plain,
% 1.15/1.38 (~r(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5041, 5793, 169, 1545])).
% 1.15/1.38 tff(5795,plain,
% 1.15/1.38 (b(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[112, 5794])).
% 1.15/1.38 tff(5796,plain,
% 1.15/1.38 (~r(s(elem!1), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[526, 5791, 160])).
% 1.15/1.38 tff(5797,plain,
% 1.15/1.38 (b(s(elem!1), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[534, 5796, 206])).
% 1.15/1.38 tff(5798,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5799,plain,
% 1.15/1.38 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5800,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5799])).
% 1.15/1.38 tff(5801,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5800, 5798])).
% 1.15/1.38 tff(5802,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5803,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5802, 5801])).
% 1.15/1.38 tff(5804,plain,
% 1.15/1.38 (~b(s(elem!1), s(s(z)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5803, 238, 5797, 5793, 5795])).
% 1.15/1.38 tff(5805,plain,
% 1.15/1.38 (s(elem!1) = s(s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[488, 5804, 5792])).
% 1.15/1.38 tff(5806,plain,
% 1.15/1.38 (elem!1 = s(z)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[379, 5805])).
% 1.15/1.38 tff(5807,plain,
% 1.15/1.38 (b(elem!1, elem!1) <=> b(s(z), s(z))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5806, 5806])).
% 1.15/1.38 tff(5808,plain,
% 1.15/1.38 (b(s(z), s(z)) <=> b(elem!1, elem!1)),
% 1.15/1.38 inference(symmetry,[status(thm)],[5807])).
% 1.15/1.38 tff(5809,plain,
% 1.15/1.38 (b(s(z), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5605, 1, 169, 1808, 1899, 1545])).
% 1.15/1.38 tff(5810,plain,
% 1.15/1.38 (b(elem!1, elem!1)),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5809, 5808])).
% 1.15/1.38 tff(5811,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[839, 5810])).
% 1.15/1.38 tff(5812,plain,((s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | b(s(elem!1), s(z)) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5813,plain,
% 1.15/1.38 (b(s(elem!1), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5812, 5790, 80, 5390, 5760, 5759, 5395])).
% 1.15/1.38 tff(5814,plain,
% 1.15/1.38 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[2855])).
% 1.15/1.38 tff(5815,plain,
% 1.15/1.38 (~b(s(elem!1), s(z))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[64, 5814])).
% 1.15/1.38 tff(5816,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[1152, 5815])).
% 1.15/1.38 tff(5817,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), s(z))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5818,plain,
% 1.15/1.38 (~(s(elem!1) = s(s(z)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5817, 5813, 64])).
% 1.15/1.38 tff(5819,plain,
% 1.15/1.38 (~r(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[200, 5760, 80])).
% 1.15/1.38 tff(5820,plain,
% 1.15/1.38 (~(s(s(z)) = s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[21, 5790])).
% 1.15/1.38 tff(5821,plain,
% 1.15/1.38 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[135, 5820, 5819])).
% 1.15/1.38 tff(5822,plain,
% 1.15/1.38 (~r(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5041, 5821, 80, 5390])).
% 1.15/1.38 tff(5823,plain,
% 1.15/1.38 (b(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[112, 5822])).
% 1.15/1.38 tff(5824,plain,
% 1.15/1.38 (~(s(s(elem!1)) = s(elem!1))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[271, 5759])).
% 1.15/1.38 tff(5825,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5826,plain,
% 1.15/1.38 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5827,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5826])).
% 1.15/1.38 tff(5828,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5827, 5825])).
% 1.15/1.38 tff(5829,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5830,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 1.15/1.38 tff(5831,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5830, 238, 289, 1152, 546, 23])).
% 1.15/1.38 tff(5832,plain,((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5833,plain,
% 1.15/1.38 (~b(s(s(elem!1)), s(elem!1))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5832, 5823, 4225, 5813])).
% 1.15/1.38 tff(5834,plain,
% 1.15/1.38 (r(s(s(elem!1)), s(elem!1))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[323, 5833, 5824])).
% 1.15/1.38 tff(5835,plain,
% 1.15/1.38 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[135, 22, 2150])).
% 1.15/1.38 tff(5836,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5837,plain,
% 1.15/1.38 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5838,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5837])).
% 1.15/1.38 tff(5839,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5838, 5836])).
% 1.15/1.38 tff(5840,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5841,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5840, 5839])).
% 1.15/1.38 tff(5842,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5841, 124, 591, 160, 1370])).
% 1.15/1.38 tff(5843,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5844,plain,
% 1.15/1.38 (~r(elem!1, s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5843, 160, 1370])).
% 1.15/1.38 tff(5845,plain,
% 1.15/1.38 (b(elem!1, s(s(elem!1)))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[606, 150, 5844])).
% 1.15/1.38 tff(5846,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5847,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.15/1.38 inference(quant_inst,[status(thm)],[])).
% 1.15/1.38 tff(5848,plain,
% 1.15/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 1.15/1.38 inference(modus_ponens,[status(thm)],[5847, 5846])).
% 1.15/1.38 tff(5849,plain,
% 1.15/1.38 ($false),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5848, 238, 1185, 228, 227, 5347])).
% 1.15/1.38 tff(5850,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.38 tff(5851,plain,
% 1.15/1.38 (~b(s(s(elem!1)), elem!1)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[5850, 5347, 227, 1185])).
% 1.15/1.38 tff(5852,plain,
% 1.15/1.38 (r(s(s(elem!1)), elem!1)),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[255, 5851, 248])).
% 1.15/1.38 tff(5853,plain,
% 1.15/1.38 (~r(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[263, 5852, 1370])).
% 1.15/1.38 tff(5854,plain,
% 1.15/1.38 (b(s(s(elem!1)), s(z))),
% 1.15/1.38 inference(unit_resolution,[status(thm)],[110, 51, 5853, 106])).
% 1.15/1.38 tff(5855,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5856,plain,
% 1.15/1.38 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(rewrite,[status(thm)],[])).
% 1.15/1.38 tff(5857,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.15/1.38 inference(monotonicity,[status(thm)],[5856])).
% 1.15/1.38 tff(5858,plain,
% 1.15/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.38 inference(transitivity,[status(thm)],[5857, 5855])).
% 1.15/1.39 tff(5859,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), elem!1)))),
% 1.15/1.39 inference(quant_inst,[status(thm)],[])).
% 1.15/1.39 tff(5860,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5859, 5858])).
% 1.15/1.39 tff(5861,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5860, 238, 1185, 227, 5347, 5854])).
% 1.15/1.39 tff(5862,plain,((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(elem!1, s(z))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5863,plain,
% 1.15/1.39 (~b(s(s(z)), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5862, 5845, 5835, 1370, 167])).
% 1.15/1.39 tff(5864,plain,
% 1.15/1.39 (s(s(z)) = elem!1),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1275, 5863, 4826])).
% 1.15/1.39 tff(5865,plain,
% 1.15/1.39 (s(s(s(z))) = s(elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5864])).
% 1.15/1.39 tff(5866,plain,
% 1.15/1.39 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5865])).
% 1.15/1.39 tff(5867,plain,
% 1.15/1.39 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5866])).
% 1.15/1.39 tff(5868,plain,
% 1.15/1.39 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5867])).
% 1.15/1.39 tff(5869,plain,
% 1.15/1.39 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5868])).
% 1.15/1.39 tff(5870,plain,
% 1.15/1.39 (elem!1 = s(s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1231, 5864])).
% 1.15/1.39 tff(5871,plain,
% 1.15/1.39 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.15/1.39 inference(symmetry,[status(thm)],[4974])).
% 1.15/1.39 tff(5872,plain,
% 1.15/1.39 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5871])).
% 1.15/1.39 tff(5873,plain,
% 1.15/1.39 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5872])).
% 1.15/1.39 tff(5874,plain,
% 1.15/1.39 (b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[227, 5873])).
% 1.15/1.39 tff(5875,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.15/1.39 tff(5876,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5875, 5874])).
% 1.15/1.39 tff(5877,plain,((~(elem!1 = s(s(z)))) | b(s(s(z)), s(s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5878,plain,
% 1.15/1.39 (b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5877, 5870, 5835])).
% 1.15/1.39 tff(5879,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5864])).
% 1.15/1.39 tff(5880,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5879])).
% 1.15/1.39 tff(5881,plain,
% 1.15/1.39 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5866])).
% 1.15/1.39 tff(5882,plain,
% 1.15/1.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5881])).
% 1.15/1.39 tff(5883,plain,
% 1.15/1.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5882, 5880])).
% 1.15/1.39 tff(5884,plain,
% 1.15/1.39 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1228])).
% 1.15/1.39 tff(5885,plain,
% 1.15/1.39 (elem!1 = s(s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1231, 1228])).
% 1.15/1.39 tff(5886,plain,
% 1.15/1.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[4979, 249, 5885])).
% 1.15/1.39 tff(5887,plain,
% 1.15/1.39 (r(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1564, 5886])).
% 1.15/1.39 tff(5888,plain,
% 1.15/1.39 (~r(s(s(s(s(z)))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1554, 5887, 169])).
% 1.15/1.39 tff(5889,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1624, 5888])).
% 1.15/1.39 tff(5890,plain,
% 1.15/1.39 (b(s(s(elem!1)), s(z))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5889, 4852])).
% 1.15/1.39 tff(5891,plain,
% 1.15/1.39 (r(s(s(elem!1)), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[255, 249, 248])).
% 1.15/1.39 tff(5892,plain,
% 1.15/1.39 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1228])).
% 1.15/1.39 tff(5893,plain,
% 1.15/1.39 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5892, 511])).
% 1.15/1.39 tff(5894,plain,
% 1.15/1.39 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.15/1.39 inference(transitivity,[status(thm)],[5893, 641])).
% 1.15/1.39 tff(5895,plain,
% 1.15/1.39 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5894])).
% 1.15/1.39 tff(5896,plain,
% 1.15/1.39 (~(s(s(s(elem!1))) = elem!1)),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[1291, 5895])).
% 1.15/1.39 tff(5897,plain,
% 1.15/1.39 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1228])).
% 1.15/1.39 tff(5898,plain,
% 1.15/1.39 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5897])).
% 1.15/1.39 tff(5899,plain,
% 1.15/1.39 ((~r(s(elem!1), elem!1)) <=> (~r(s(elem!1), s(s(z))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5898])).
% 1.15/1.39 tff(5900,plain,
% 1.15/1.39 (~r(s(elem!1), s(s(z)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[404, 5899])).
% 1.15/1.39 tff(5901,plain,
% 1.15/1.39 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1385, 1228])).
% 1.15/1.39 tff(5902,plain,
% 1.15/1.39 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5901])).
% 1.15/1.39 tff(5903,plain,
% 1.15/1.39 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.15/1.39 inference(transitivity,[status(thm)],[723, 5902, 88])).
% 1.15/1.39 tff(5904,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5903])).
% 1.15/1.39 tff(5905,plain,
% 1.15/1.39 (b(s(s(elem!1)), s(z))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[1784, 5904])).
% 1.15/1.39 tff(5906,plain,
% 1.15/1.39 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[4974])).
% 1.15/1.39 tff(5907,plain,
% 1.15/1.39 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5906])).
% 1.15/1.39 tff(5908,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5907, 5871])).
% 1.15/1.39 tff(5909,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5908])).
% 1.15/1.39 tff(5910,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[226, 5909])).
% 1.15/1.39 tff(5911,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1899, 5910])).
% 1.15/1.39 tff(5912,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5913,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5912, 226, 365])).
% 1.15/1.39 tff(5914,plain,
% 1.15/1.39 (~b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[4153, 5913, 1784, 546])).
% 1.15/1.39 tff(5915,plain,
% 1.15/1.39 (r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1781, 5914])).
% 1.15/1.39 tff(5916,plain,
% 1.15/1.39 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1725, 5915, 169])).
% 1.15/1.39 tff(5917,plain,
% 1.15/1.39 (~r(s(s(s(elem!1))), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5508, 5916, 5901])).
% 1.15/1.39 tff(5918,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[647, 5917, 5896])).
% 1.15/1.39 tff(5919,plain,
% 1.15/1.39 (b(s(s(z)), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1228])).
% 1.15/1.39 tff(5920,plain,
% 1.15/1.39 (~b(s(z), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[3192, 226, 5905, 546])).
% 1.15/1.39 tff(5921,plain,
% 1.15/1.39 (r(s(z), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[56, 5920])).
% 1.15/1.39 tff(5922,plain,
% 1.15/1.39 (b(s(s(z)), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[2225, 5921, 169, 2222])).
% 1.15/1.39 tff(5923,plain,
% 1.15/1.39 (b(elem!1, s(s(elem!1)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5922, 5919])).
% 1.15/1.39 tff(5924,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(5925,plain,
% 1.15/1.39 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(5926,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5925])).
% 1.15/1.39 tff(5927,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5926, 5924])).
% 1.15/1.39 tff(5928,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.39 inference(quant_inst,[status(thm)],[])).
% 1.15/1.39 tff(5929,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5928, 5927])).
% 1.15/1.39 tff(5930,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5929, 238, 5923, 5918, 226, 5905])).
% 1.15/1.39 tff(5931,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = elem!1)) | (~r(s(s(z)), s(z))) | r(s(elem!1), s(s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5932,plain,
% 1.15/1.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5931, 5900, 546, 169, 1784, 1228, 5885])).
% 1.15/1.39 tff(5933,plain,
% 1.15/1.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[223, 5932, 545])).
% 1.15/1.39 tff(5934,plain,
% 1.15/1.39 (~r(s(s(s(elem!1))), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1182, 5933, 301])).
% 1.15/1.39 tff(5935,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[647, 5934, 5896])).
% 1.15/1.39 tff(5936,plain,
% 1.15/1.39 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1397, 5933, 307])).
% 1.15/1.39 tff(5937,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[459, 5936, 453])).
% 1.15/1.39 tff(5938,plain,
% 1.15/1.39 (b(s(elem!1), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[408, 404, 632])).
% 1.15/1.39 tff(5939,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(5940,plain,
% 1.15/1.39 (((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(5941,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5940])).
% 1.15/1.39 tff(5942,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5941, 5939])).
% 1.15/1.39 tff(5943,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.15/1.39 inference(quant_inst,[status(thm)],[])).
% 1.15/1.39 tff(5944,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5943, 5942])).
% 1.15/1.39 tff(5945,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5944, 238, 5938, 1185, 5937, 5935])).
% 1.15/1.39 tff(5946,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(z)) = elem!1)) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5947,plain,
% 1.15/1.39 (~r(s(s(elem!1)), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5946, 5891, 453, 1185, 545, 546, 169, 5889, 1228, 2620])).
% 1.15/1.39 tff(5948,plain,
% 1.15/1.39 (b(s(s(elem!1)), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[323, 5947, 275])).
% 1.15/1.39 tff(5949,plain,
% 1.15/1.39 (~b(s(elem!1), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5832, 5948, 546, 5890])).
% 1.15/1.39 tff(5950,plain,
% 1.15/1.39 (r(s(elem!1), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[473, 5949, 1])).
% 1.15/1.39 tff(5951,plain,
% 1.15/1.39 (~r(s(elem!1), s(s(z)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[483, 5950, 169])).
% 1.15/1.39 tff(5952,plain,
% 1.15/1.39 (b(s(elem!1), s(s(z)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[488, 5951, 278])).
% 1.15/1.39 tff(5953,plain,
% 1.15/1.39 (b(s(elem!1), elem!1)),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5952, 5884])).
% 1.15/1.39 tff(5954,plain,
% 1.15/1.39 (~r(elem!1, s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5000, 5950, 1370])).
% 1.15/1.39 tff(5955,plain,
% 1.15/1.39 (b(elem!1, s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[629, 5954, 391])).
% 1.15/1.39 tff(5956,plain,
% 1.15/1.39 (~b(s(elem!1), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5551, 5955, 5948, 1185])).
% 1.15/1.39 tff(5957,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5956, 5953])).
% 1.15/1.39 tff(5958,plain,(b(s(s(elem!1)), elem!1) | (~(s(s(z)) = elem!1)) | (~b(elem!1, s(s(elem!1)))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5959,plain,
% 1.15/1.39 (b(s(s(elem!1)), elem!1)),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5958, 5864, 5845, 387, 278, 1370, 169, 1, 546, 272, 421, 545, 167])).
% 1.15/1.39 tff(5960,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5959, 5883])).
% 1.15/1.39 tff(5961,plain,
% 1.15/1.39 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5864])).
% 1.15/1.39 tff(5962,plain,
% 1.15/1.39 (r(elem!1, s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5961])).
% 1.15/1.39 tff(5963,plain,
% 1.15/1.39 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5865])).
% 1.15/1.39 tff(5964,plain,
% 1.15/1.39 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5963])).
% 1.15/1.39 tff(5965,plain,
% 1.15/1.39 (r(elem!1, s(elem!1)) <=> r(s(s(z)), s(s(s(z))))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5964, 5962])).
% 1.15/1.39 tff(5966,plain,
% 1.15/1.39 (~r(s(elem!1), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[526, 306, 160])).
% 1.15/1.39 tff(5967,plain,
% 1.15/1.39 (~b(s(elem!1), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[2644, 306, 1370, 228, 1212])).
% 1.15/1.39 tff(5968,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[534, 5967, 5966, 206])).
% 1.15/1.39 tff(5969,plain,((~r(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5970,plain,
% 1.15/1.39 (~r(s(elem!1), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5969, 159, 1370, 5959, 160])).
% 1.15/1.39 tff(5971,plain,
% 1.15/1.39 (b(s(elem!1), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[473, 5970, 1])).
% 1.15/1.39 tff(5972,plain,
% 1.15/1.39 (s(elem!1) = s(s(s(z)))),
% 1.15/1.39 inference(symmetry,[status(thm)],[1381])).
% 1.15/1.39 tff(5973,plain,
% 1.15/1.39 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5972])).
% 1.15/1.39 tff(5974,plain,
% 1.15/1.39 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5973])).
% 1.15/1.39 tff(5975,plain,
% 1.15/1.39 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5972])).
% 1.15/1.39 tff(5976,plain,
% 1.15/1.39 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5975])).
% 1.15/1.39 tff(5977,plain,
% 1.15/1.39 (b(s(s(z)), s(s(s(s(z)))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5877, 5885, 227])).
% 1.15/1.39 tff(5978,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1228])).
% 1.15/1.39 tff(5979,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5978])).
% 1.15/1.39 tff(5980,plain,
% 1.15/1.39 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[1382])).
% 1.15/1.39 tff(5981,plain,
% 1.15/1.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5980])).
% 1.15/1.39 tff(5982,plain,
% 1.15/1.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5981, 5979])).
% 1.15/1.39 tff(5983,plain,
% 1.15/1.39 (b(s(s(s(s(z)))), s(s(z)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[228, 5982])).
% 1.15/1.39 tff(5984,plain,
% 1.15/1.39 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[1383])).
% 1.15/1.39 tff(5985,plain,
% 1.15/1.39 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5984])).
% 1.15/1.39 tff(5986,plain,
% 1.15/1.39 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[4437, 1739, 1587, 1501])).
% 1.15/1.39 tff(5987,plain,
% 1.15/1.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5912, 5986, 5885])).
% 1.15/1.39 tff(5988,plain,
% 1.15/1.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[223, 5987, 545])).
% 1.15/1.39 tff(5989,plain,
% 1.15/1.39 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5988, 5985])).
% 1.15/1.39 tff(5990,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[2665, 5989])).
% 1.15/1.39 tff(5991,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(z)) = elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(5992,plain,
% 1.15/1.39 (~r(s(s(s(s(s(z))))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5991, 1228, 545, 5983, 5977, 160, 169])).
% 1.15/1.39 tff(5993,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1781, 5992])).
% 1.15/1.39 tff(5994,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5984])).
% 1.15/1.39 tff(5995,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5994])).
% 1.15/1.39 tff(5996,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1381])).
% 1.15/1.39 tff(5997,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(transitivity,[status(thm)],[5996, 5995])).
% 1.15/1.39 tff(5998,plain,
% 1.15/1.39 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[5997])).
% 1.15/1.39 tff(5999,plain,
% 1.15/1.39 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1381])).
% 1.15/1.39 tff(6000,plain,
% 1.15/1.39 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.15/1.39 inference(symmetry,[status(thm)],[5999])).
% 1.15/1.39 tff(6001,plain,
% 1.15/1.39 (b(s(s(s(z))), s(z))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[1152, 6000])).
% 1.15/1.39 tff(6002,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(6003,plain,
% 1.15/1.39 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(6004,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[6003])).
% 1.15/1.39 tff(6005,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1))))),
% 1.15/1.39 inference(transitivity,[status(thm)],[6004, 6002])).
% 1.15/1.39 tff(6006,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.15/1.39 inference(quant_inst,[status(thm)],[])).
% 1.15/1.39 tff(6007,plain,
% 1.15/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(elem!1)))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 1.15/1.39 tff(6008,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6007, 124, 307, 160, 441])).
% 1.15/1.39 tff(6009,plain,((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(6010,plain,
% 1.15/1.39 (~r(s(z), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6009, 307, 160])).
% 1.15/1.39 tff(6011,plain,
% 1.15/1.39 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[1381])).
% 1.15/1.39 tff(6012,plain,
% 1.15/1.39 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[6011])).
% 1.15/1.39 tff(6013,plain,
% 1.15/1.39 ((~r(s(z), s(elem!1))) <=> (~r(s(z), s(s(s(z)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[6012])).
% 1.15/1.39 tff(6014,plain,
% 1.15/1.39 (~r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[434, 6013])).
% 1.15/1.39 tff(6015,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.15/1.39 tff(6016,plain,
% 1.15/1.39 ($false),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6015, 6014])).
% 1.15/1.39 tff(6017,plain,((~r(s(z), s(s(s(z))))) | r(s(z), s(elem!1)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.39 tff(6018,plain,
% 1.15/1.39 (~r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6017, 6010, 1228])).
% 1.15/1.39 tff(6019,plain,
% 1.15/1.39 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.15/1.39 inference(symmetry,[status(thm)],[2336])).
% 1.15/1.39 tff(6020,plain,
% 1.15/1.39 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.15/1.39 inference(monotonicity,[status(thm)],[6019])).
% 1.15/1.39 tff(6021,plain,
% 1.15/1.39 (~(s(z) = s(s(s(z))))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[5117, 6020])).
% 1.15/1.39 tff(6022,plain,
% 1.15/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(6023,plain,
% 1.15/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.15/1.39 inference(quant_inst,[status(thm)],[])).
% 1.15/1.39 tff(6024,plain,
% 1.15/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[6023, 6022])).
% 1.15/1.39 tff(6025,plain,
% 1.15/1.39 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6024, 51])).
% 1.15/1.39 tff(6026,plain,
% 1.15/1.39 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6025, 6021])).
% 1.15/1.39 tff(6027,plain,
% 1.15/1.39 (b(s(z), s(s(s(z))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[6026, 6018])).
% 1.15/1.39 tff(6028,plain,
% 1.15/1.39 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5745, 6027, 6001, 5993])).
% 1.15/1.39 tff(6029,plain,
% 1.15/1.39 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(modus_ponens,[status(thm)],[6028, 5998])).
% 1.15/1.39 tff(6030,plain,
% 1.15/1.39 (r(s(s(s(elem!1))), s(elem!1))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[457, 51, 6029, 453])).
% 1.15/1.39 tff(6031,plain,
% 1.15/1.39 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1397, 6030, 307])).
% 1.15/1.39 tff(6032,plain,
% 1.15/1.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[223, 6031, 545])).
% 1.15/1.39 tff(6033,plain,
% 1.15/1.39 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[5912, 6032, 5885])).
% 1.15/1.39 tff(6034,plain,
% 1.15/1.39 (~b(s(s(s(s(z)))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[4153, 6033, 546, 5993])).
% 1.15/1.39 tff(6035,plain,
% 1.15/1.39 (r(s(s(s(s(z)))), s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1624, 6034])).
% 1.15/1.39 tff(6036,plain,
% 1.15/1.39 (~r(z, s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1613, 6035, 169])).
% 1.15/1.39 tff(6037,plain,
% 1.15/1.39 (b(z, s(z))),
% 1.15/1.39 inference(unit_resolution,[status(thm)],[1542, 6036])).
% 1.15/1.39 tff(6038,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(6039,plain,
% 1.15/1.39 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.15/1.39 inference(rewrite,[status(thm)],[])).
% 1.15/1.39 tff(6040,plain,
% 1.15/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6039])).
% 1.25/1.40 tff(6041,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6040, 6038])).
% 1.25/1.40 tff(6042,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6043,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6042, 6041])).
% 1.25/1.40 tff(6044,plain,
% 1.25/1.40 (~b(z, s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6043, 238, 1152, 546, 6037])).
% 1.25/1.40 tff(6045,plain,
% 1.25/1.40 (~b(z, s(s(s(z))))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6044, 5976])).
% 1.25/1.40 tff(6046,plain,
% 1.25/1.40 (r(z, s(s(s(z))))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1475, 6045])).
% 1.25/1.40 tff(6047,plain,
% 1.25/1.40 (r(z, s(elem!1))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6046, 5974])).
% 1.25/1.40 tff(6048,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6049,plain,
% 1.25/1.40 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6050,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6049])).
% 1.25/1.40 tff(6051,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6050, 6048])).
% 1.25/1.40 tff(6052,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6053,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6052, 6051])).
% 1.25/1.40 tff(6054,plain,
% 1.25/1.40 ((~r(s(s(s(elem!1))), z)) | (~r(z, s(elem!1)))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6053, 124, 6030])).
% 1.25/1.40 tff(6055,plain,
% 1.25/1.40 (~r(s(s(s(elem!1))), z)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6054, 6047])).
% 1.25/1.40 tff(6056,plain,
% 1.25/1.40 (((~![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))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6057,plain,
% 1.25/1.40 ((~![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))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6058,plain,
% 1.25/1.40 ((~![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)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 1.25/1.40 tff(6059,plain,
% 1.25/1.40 (b(s(s(s(elem!1))), z)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6058, 51, 821, 6055])).
% 1.25/1.40 tff(6060,plain,
% 1.25/1.40 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[246, 6032, 227, 228])).
% 1.25/1.40 tff(6061,plain,
% 1.25/1.40 (r(s(s(z)), s(s(s(elem!1))))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[190, 6060])).
% 1.25/1.40 tff(6062,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6063,plain,
% 1.25/1.40 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6064,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6063])).
% 1.25/1.40 tff(6065,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6064, 6062])).
% 1.25/1.40 tff(6066,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6067,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6066, 6065])).
% 1.25/1.40 tff(6068,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6067, 124, 169, 168, 2964])).
% 1.25/1.40 tff(6069,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(6070,plain,
% 1.25/1.40 (~r(s(s(s(elem!1))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6069, 6061, 169])).
% 1.25/1.40 tff(6071,plain,
% 1.25/1.40 (b(s(s(s(elem!1))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[576, 51, 94, 6070])).
% 1.25/1.40 tff(6072,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6073,plain,
% 1.25/1.40 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6074,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6073])).
% 1.25/1.40 tff(6075,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6074, 6072])).
% 1.25/1.40 tff(6076,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6077,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6076, 6075])).
% 1.25/1.40 tff(6078,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6077, 238, 6071, 546, 6037, 6059])).
% 1.25/1.40 tff(6079,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~(s(s(z)) = elem!1)) | (~b(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(6080,plain,
% 1.25/1.40 (~r(s(s(elem!1)), s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6079, 5864, 546, 5971, 169, 5835, 5959, 545, 421, 160])).
% 1.25/1.40 tff(6081,plain,
% 1.25/1.40 (b(s(s(elem!1)), s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[323, 6080, 272])).
% 1.25/1.40 tff(6082,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6083,plain,
% 1.25/1.40 (((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6084,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6083])).
% 1.25/1.40 tff(6085,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6084, 6082])).
% 1.25/1.40 tff(6086,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6087,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6086, 6085])).
% 1.25/1.40 tff(6088,plain,
% 1.25/1.40 ($false),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6087, 238, 631, 1185, 289, 1152])).
% 1.25/1.40 tff(6089,plain,((~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.40 tff(6090,plain,
% 1.25/1.40 (~b(elem!1, s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6089, 5845, 6081, 5971])).
% 1.25/1.40 tff(6091,plain,
% 1.25/1.40 (r(elem!1, s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[629, 6090, 387])).
% 1.25/1.40 tff(6092,plain,
% 1.25/1.40 (r(s(s(z)), s(s(s(z))))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6091, 5965])).
% 1.25/1.40 tff(6093,plain,
% 1.25/1.40 (~r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[5991, 5864, 545, 5960, 5878, 160, 169])).
% 1.25/1.40 tff(6094,plain,
% 1.25/1.40 (b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1781, 6093])).
% 1.25/1.40 tff(6095,plain,
% 1.25/1.40 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[5865])).
% 1.25/1.40 tff(6096,plain,
% 1.25/1.40 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.25/1.40 inference(symmetry,[status(thm)],[6095])).
% 1.25/1.40 tff(6097,plain,
% 1.25/1.40 (b(s(s(s(z))), s(z))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[5971, 6096])).
% 1.25/1.40 tff(6098,plain,
% 1.25/1.40 (~(s(z) = elem!1)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[332, 4576])).
% 1.25/1.40 tff(6099,plain,
% 1.25/1.40 ((z = elem!1) <=> (elem!1 = z)),
% 1.25/1.40 inference(commutativity,[status(thm)],[])).
% 1.25/1.40 tff(6100,plain,
% 1.25/1.40 ((elem!1 = z) <=> (z = elem!1)),
% 1.25/1.40 inference(symmetry,[status(thm)],[6099])).
% 1.25/1.40 tff(6101,plain,
% 1.25/1.40 ((~(elem!1 = z)) <=> (~(z = elem!1))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6100])).
% 1.25/1.40 tff(6102,plain,
% 1.25/1.40 (~(z = elem!1)),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[4831, 6101])).
% 1.25/1.40 tff(6103,plain,
% 1.25/1.40 (s(elem!1) = s(s(s(z)))),
% 1.25/1.40 inference(symmetry,[status(thm)],[5865])).
% 1.25/1.40 tff(6104,plain,
% 1.25/1.40 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6103])).
% 1.25/1.40 tff(6105,plain,
% 1.25/1.40 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.25/1.40 inference(symmetry,[status(thm)],[6104])).
% 1.25/1.40 tff(6106,plain,
% 1.25/1.40 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6103])).
% 1.25/1.40 tff(6107,plain,
% 1.25/1.40 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6106])).
% 1.25/1.40 tff(6108,plain,
% 1.25/1.40 (~b(s(s(elem!1)), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[5832, 6081, 546, 5971])).
% 1.25/1.40 tff(6109,plain,
% 1.25/1.40 (~b(s(s(s(s(z)))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[4855, 6108, 5864])).
% 1.25/1.40 tff(6110,plain,
% 1.25/1.40 (r(s(s(s(s(z)))), s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1624, 6109])).
% 1.25/1.40 tff(6111,plain,
% 1.25/1.40 (~r(z, s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1613, 6110, 169])).
% 1.25/1.40 tff(6112,plain,
% 1.25/1.40 (b(z, s(z))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1542, 6111])).
% 1.25/1.40 tff(6113,plain,
% 1.25/1.40 (~b(z, s(elem!1))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6043, 238, 5971, 546, 6112])).
% 1.25/1.40 tff(6114,plain,
% 1.25/1.40 (~b(z, s(s(s(z))))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6113, 6107])).
% 1.25/1.40 tff(6115,plain,
% 1.25/1.40 (r(z, s(s(s(z))))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[1475, 6114])).
% 1.25/1.40 tff(6116,plain,
% 1.25/1.40 (r(z, s(elem!1))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6115, 6105])).
% 1.25/1.40 tff(6117,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6118,plain,
% 1.25/1.40 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6119,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 1.25/1.40 inference(monotonicity,[status(thm)],[6118])).
% 1.25/1.40 tff(6120,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.25/1.40 inference(transitivity,[status(thm)],[6119, 6117])).
% 1.25/1.40 tff(6121,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6122,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6121, 6120])).
% 1.25/1.40 tff(6123,plain,
% 1.25/1.40 (~r(z, elem!1)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6122, 124, 6091, 6116])).
% 1.25/1.40 tff(6124,plain,
% 1.25/1.40 ((z = elem!1) | b(z, elem!1)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[3134, 51, 6123])).
% 1.25/1.40 tff(6125,plain,
% 1.25/1.40 (b(z, elem!1)),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6124, 6102])).
% 1.25/1.40 tff(6126,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6127,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 1.25/1.40 inference(quant_inst,[status(thm)],[])).
% 1.25/1.40 tff(6128,plain,
% 1.25/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))),
% 1.25/1.40 inference(modus_ponens,[status(thm)],[6127, 6126])).
% 1.25/1.40 tff(6129,plain,
% 1.25/1.40 (~b(z, s(s(elem!1)))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[6128, 238, 5845, 5959, 6125])).
% 1.25/1.40 tff(6130,plain,
% 1.25/1.40 (r(z, s(s(elem!1)))),
% 1.25/1.40 inference(unit_resolution,[status(thm)],[2071, 6129])).
% 1.25/1.40 tff(6131,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6132,plain,
% 1.25/1.40 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.25/1.40 inference(rewrite,[status(thm)],[])).
% 1.25/1.40 tff(6133,plain,
% 1.25/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6132])).
% 1.25/1.41 tff(6134,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6133, 6131])).
% 1.25/1.41 tff(6135,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6136,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 1.25/1.41 tff(6137,plain,
% 1.25/1.41 (~r(s(z), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6136, 124, 160, 6130])).
% 1.25/1.41 tff(6138,plain,
% 1.25/1.41 (b(s(z), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[5699, 51, 72, 6137])).
% 1.25/1.41 tff(6139,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6140,plain,
% 1.25/1.41 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6141,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6140])).
% 1.25/1.41 tff(6142,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1))))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6141, 6139])).
% 1.25/1.41 tff(6143,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, z)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6144,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)) | (~r(z, s(elem!1)))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6143, 6142])).
% 1.25/1.41 tff(6145,plain,
% 1.25/1.41 (~r(elem!1, z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6144, 124, 6091, 6116])).
% 1.25/1.41 tff(6146,plain,
% 1.25/1.41 (b(elem!1, z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[4843, 51, 4831, 6145])).
% 1.25/1.41 tff(6147,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6148,plain,
% 1.25/1.41 (((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6149,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6148])).
% 1.25/1.41 tff(6150,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6149, 6147])).
% 1.25/1.41 tff(6151,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), elem!1)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6152,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 1.25/1.41 tff(6153,plain,
% 1.25/1.41 (~b(s(z), elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6152, 238, 6125, 6146, 6138])).
% 1.25/1.41 tff(6154,plain,
% 1.25/1.41 (r(s(z), elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[351, 6153, 6098])).
% 1.25/1.41 tff(6155,plain,
% 1.25/1.41 (r(s(elem!1), z) <=> r(s(s(s(z))), z)),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6103])).
% 1.25/1.41 tff(6156,plain,
% 1.25/1.41 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.25/1.41 inference(symmetry,[status(thm)],[6155])).
% 1.25/1.41 tff(6157,plain,
% 1.25/1.41 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6103])).
% 1.25/1.41 tff(6158,plain,
% 1.25/1.41 ((~b(s(elem!1), z)) <=> (~b(s(s(s(z))), z))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6157])).
% 1.25/1.41 tff(6159,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6160,plain,
% 1.25/1.41 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6161,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6160])).
% 1.25/1.41 tff(6162,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6161, 6159])).
% 1.25/1.41 tff(6163,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6164,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(elem!1), z))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6163, 6162])).
% 1.25/1.41 tff(6165,plain,
% 1.25/1.41 (~b(s(elem!1), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6164, 238, 5971, 546, 6112])).
% 1.25/1.41 tff(6166,plain,
% 1.25/1.41 (~b(s(s(s(z))), z)),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6165, 6158])).
% 1.25/1.41 tff(6167,plain,
% 1.25/1.41 (r(s(s(s(z))), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[1524, 6166])).
% 1.25/1.41 tff(6168,plain,
% 1.25/1.41 (r(s(elem!1), z)),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6167, 6156])).
% 1.25/1.41 tff(6169,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6170,plain,
% 1.25/1.41 (((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6171,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6170])).
% 1.25/1.41 tff(6172,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6171, 6169])).
% 1.25/1.41 tff(6173,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6174,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 1.25/1.41 tff(6175,plain,
% 1.25/1.41 (~b(s(s(elem!1)), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6174, 238, 5845, 5959, 6125])).
% 1.25/1.41 tff(6176,plain,
% 1.25/1.41 (r(s(s(elem!1)), z)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[4030, 51, 92, 6175])).
% 1.25/1.41 tff(6177,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6178,plain,
% 1.25/1.41 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6179,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6178])).
% 1.25/1.41 tff(6180,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6179, 6177])).
% 1.25/1.41 tff(6181,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6182,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 1.25/1.41 tff(6183,plain,
% 1.25/1.41 ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6182, 124, 6176])).
% 1.25/1.41 tff(6184,plain,
% 1.25/1.41 (~r(s(elem!1), s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6183, 6168])).
% 1.25/1.41 tff(6185,plain,
% 1.25/1.41 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[534, 6184, 159])).
% 1.25/1.41 tff(6186,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6187,plain,
% 1.25/1.41 (((~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(elem!1), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6188,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6187])).
% 1.25/1.41 tff(6189,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6188, 6186])).
% 1.25/1.41 tff(6190,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), elem!1)))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6191,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 1.25/1.41 tff(6192,plain,
% 1.25/1.41 (~b(s(elem!1), elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6191, 238, 5845, 6081, 6185])).
% 1.25/1.41 tff(6193,plain,
% 1.25/1.41 (r(s(elem!1), elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[408, 6192, 394])).
% 1.25/1.41 tff(6194,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6195,plain,
% 1.25/1.41 (((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6196,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6195])).
% 1.25/1.41 tff(6197,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.25/1.41 inference(transitivity,[status(thm)],[6196, 6194])).
% 1.25/1.41 tff(6198,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 1.25/1.41 inference(quant_inst,[status(thm)],[])).
% 1.25/1.41 tff(6199,plain,
% 1.25/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6198, 6197])).
% 1.25/1.41 tff(6200,plain,
% 1.25/1.41 (~r(s(z), s(elem!1))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6199, 124, 6193, 6154])).
% 1.25/1.41 tff(6201,plain,
% 1.25/1.41 (~r(s(z), s(s(s(z))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6017, 6200, 5864])).
% 1.25/1.41 tff(6202,plain,
% 1.25/1.41 (b(s(z), s(s(s(z))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6026, 6201])).
% 1.25/1.41 tff(6203,plain,
% 1.25/1.41 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[5745, 6202, 6097, 6094])).
% 1.25/1.41 tff(6204,plain,
% 1.25/1.41 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[1101, 6203])).
% 1.25/1.41 tff(6205,plain,
% 1.25/1.41 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[4329, 6204, 6092])).
% 1.25/1.41 tff(6206,plain,
% 1.25/1.41 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[1738, 6205])).
% 1.25/1.41 tff(6207,plain,
% 1.25/1.41 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[4437, 6206, 5960, 5878])).
% 1.25/1.41 tff(6208,plain,
% 1.25/1.41 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[5912, 6207, 5870])).
% 1.25/1.41 tff(6209,plain,
% 1.25/1.41 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[223, 6208, 545])).
% 1.25/1.41 tff(6210,plain,
% 1.25/1.41 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6209, 5869])).
% 1.25/1.41 tff(6211,plain,
% 1.25/1.41 (~(z = elem!1)),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[4840, 6101])).
% 1.25/1.41 tff(6212,plain,
% 1.25/1.41 (b(z, s(z))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[1542, 2040])).
% 1.25/1.41 tff(6213,plain,
% 1.25/1.41 (~b(z, s(elem!1))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6043, 238, 1152, 546, 6212])).
% 1.25/1.41 tff(6214,plain,
% 1.25/1.41 (~b(z, s(s(s(z))))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6213, 5976])).
% 1.25/1.41 tff(6215,plain,
% 1.25/1.41 (r(z, s(s(s(z))))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[1475, 6214])).
% 1.25/1.41 tff(6216,plain,
% 1.25/1.41 (r(z, s(elem!1))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[6215, 5974])).
% 1.25/1.41 tff(6217,plain,
% 1.25/1.41 ((~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6122, 124, 590])).
% 1.25/1.41 tff(6218,plain,
% 1.25/1.41 (~r(z, elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6217, 6216])).
% 1.25/1.41 tff(6219,plain,
% 1.25/1.41 ((z = elem!1) | b(z, elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[3134, 51, 6218])).
% 1.25/1.41 tff(6220,plain,
% 1.25/1.41 (b(z, elem!1)),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6219, 6211])).
% 1.25/1.41 tff(6221,plain,
% 1.25/1.41 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[1383])).
% 1.25/1.41 tff(6222,plain,
% 1.25/1.41 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.25/1.41 inference(symmetry,[status(thm)],[6221])).
% 1.25/1.41 tff(6223,plain,
% 1.25/1.41 (b(s(z), s(s(s(s(s(z))))))),
% 1.25/1.41 inference(modus_ponens,[status(thm)],[546, 6222])).
% 1.25/1.41 tff(6224,plain,
% 1.25/1.41 (~r(z, s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[2050, 2040, 1783, 6223, 2008])).
% 1.25/1.41 tff(6225,plain,
% 1.25/1.41 (b(z, s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[2071, 6224])).
% 1.25/1.41 tff(6226,plain,
% 1.25/1.41 ($false),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6128, 238, 1185, 228, 6225, 6220])).
% 1.25/1.41 tff(6227,plain,(r(z, s(z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(elem!1, s(elem!1))) | (~(s(s(z)) = elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.41 tff(6228,plain,
% 1.25/1.41 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6227, 6091, 5959, 4831, 5845, 5864, 5971, 546, 6094, 6111])).
% 1.25/1.41 tff(6229,plain,
% 1.25/1.41 ($false),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6228, 6210])).
% 1.25/1.41 tff(6230,plain,((elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.41 tff(6231,plain,
% 1.25/1.41 (~r(elem!1, s(z))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6230, 278, 546, 1, 169, 150, 209, 160])).
% 1.25/1.41 tff(6232,plain,
% 1.25/1.41 ($false),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[363, 6231, 4576, 1400])).
% 1.25/1.41 tff(6233,plain,((s(elem!1) = s(s(z))) | b(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.41 tff(6234,plain,
% 1.25/1.41 (b(elem!1, s(z))),
% 1.25/1.41 inference(unit_resolution,[status(thm)],[6233, 150, 546, 169, 160, 1, 278])).
% 1.25/1.41 tff(6235,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6236,plain,
% 1.25/1.41 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.41 inference(rewrite,[status(thm)],[])).
% 1.25/1.41 tff(6237,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.25/1.41 inference(monotonicity,[status(thm)],[6236])).
% 1.25/1.41 tff(6238,plain,
% 1.25/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6237, 6235])).
% 1.25/1.42 tff(6239,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6240,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6239, 6238])).
% 1.25/1.42 tff(6241,plain,
% 1.25/1.42 (~b(elem!1, s(elem!1))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6240, 238, 6234, 1152, 546])).
% 1.25/1.42 tff(6242,plain,
% 1.25/1.42 (r(elem!1, s(elem!1))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[629, 6241, 391])).
% 1.25/1.42 tff(6243,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6244,plain,
% 1.25/1.42 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6245,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6244])).
% 1.25/1.42 tff(6246,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6245, 6243])).
% 1.25/1.42 tff(6247,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6248,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6247, 6246])).
% 1.25/1.42 tff(6249,plain,
% 1.25/1.42 (~b(elem!1, s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6248, 238, 6234, 546, 23])).
% 1.25/1.42 tff(6250,plain,
% 1.25/1.42 (r(elem!1, s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[606, 6249, 150])).
% 1.25/1.42 tff(6251,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[599, 6250, 6242, 307])).
% 1.25/1.42 tff(6252,plain,((elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6253,plain,
% 1.25/1.42 (elem!1 = s(s(elem!1))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6252, 5834, 5781, 4225, 5823, 5813, 80, 5760, 5790, 5818])).
% 1.25/1.42 tff(6254,plain,
% 1.25/1.42 (s(elem!1) = s(s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[2097, 6253])).
% 1.25/1.42 tff(6255,plain,
% 1.25/1.42 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[2879, 6254])).
% 1.25/1.42 tff(6256,plain,
% 1.25/1.42 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6254])).
% 1.25/1.42 tff(6257,plain,
% 1.25/1.42 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6256])).
% 1.25/1.42 tff(6258,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6259,plain,
% 1.25/1.42 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6260,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6259])).
% 1.25/1.42 tff(6261,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6260, 6258])).
% 1.25/1.42 tff(6262,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6263,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6262, 6261])).
% 1.25/1.42 tff(6264,plain,
% 1.25/1.42 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6263, 238, 5813, 4225, 5392])).
% 1.25/1.42 tff(6265,plain,
% 1.25/1.42 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6264, 6257])).
% 1.25/1.42 tff(6266,plain,
% 1.25/1.42 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[5222, 6254, 5820])).
% 1.25/1.42 tff(6267,plain,
% 1.25/1.42 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[5643, 5823, 5392, 4225])).
% 1.25/1.42 tff(6268,plain,
% 1.25/1.42 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[5236, 51, 6267])).
% 1.25/1.42 tff(6269,plain,
% 1.25/1.42 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6268, 6266])).
% 1.25/1.42 tff(6270,plain,
% 1.25/1.42 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[410])).
% 1.25/1.42 tff(6271,plain,
% 1.25/1.42 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[410])).
% 1.25/1.42 tff(6272,plain,
% 1.25/1.42 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.25/1.42 inference(symmetry,[status(thm)],[6271])).
% 1.25/1.42 tff(6273,plain,
% 1.25/1.42 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6272])).
% 1.25/1.42 tff(6274,plain,
% 1.25/1.42 (~(s(elem!1) = s(s(z)))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[1291, 6273])).
% 1.25/1.42 tff(6275,plain,
% 1.25/1.42 (~b(s(s(s(elem!1))), s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[3895, 226, 546, 23])).
% 1.25/1.42 tff(6276,plain,
% 1.25/1.42 (~b(s(elem!1), s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[5664, 6275, 410])).
% 1.25/1.42 tff(6277,plain,
% 1.25/1.42 (r(s(elem!1), s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[473, 6276, 1])).
% 1.25/1.42 tff(6278,plain,
% 1.25/1.42 (~r(s(elem!1), s(s(z)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[483, 6277, 169])).
% 1.25/1.42 tff(6279,plain,
% 1.25/1.42 (b(s(elem!1), s(s(z)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[488, 6278, 6274])).
% 1.25/1.42 tff(6280,plain,
% 1.25/1.42 (b(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6279, 6270])).
% 1.25/1.42 tff(6281,plain,
% 1.25/1.42 (~b(s(z), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[3192, 226, 546, 23])).
% 1.25/1.42 tff(6282,plain,
% 1.25/1.42 (r(s(z), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[56, 6281])).
% 1.25/1.42 tff(6283,plain,
% 1.25/1.42 (~r(s(s(z)), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[200, 6282, 169])).
% 1.25/1.42 tff(6284,plain,
% 1.25/1.42 (b(s(s(z)), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[135, 6283, 22])).
% 1.25/1.42 tff(6285,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(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(z)))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6286,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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(z)))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6287,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6286, 6285])).
% 1.25/1.42 tff(6288,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6287, 238, 6284, 226, 23, 6280])).
% 1.25/1.42 tff(6289,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6290,plain,
% 1.25/1.42 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6289, 6254, 5823, 80, 5790, 4225])).
% 1.25/1.42 tff(6291,plain,
% 1.25/1.42 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[223, 6290, 5758])).
% 1.25/1.42 tff(6292,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6293,plain,
% 1.25/1.42 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6294,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6293])).
% 1.25/1.42 tff(6295,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6294, 6292])).
% 1.25/1.42 tff(6296,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6297,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6296, 6295])).
% 1.25/1.42 tff(6298,plain,
% 1.25/1.42 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6297, 124, 6291, 6269])).
% 1.25/1.42 tff(6299,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[2974, 51, 6298, 6265, 6255])).
% 1.25/1.42 tff(6300,plain,(b(z, s(z)) | b(s(s(z)), s(z)) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6301,plain,
% 1.25/1.42 (b(z, s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6300, 63, 64])).
% 1.25/1.42 tff(6302,plain,
% 1.25/1.42 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[534, 2574, 159])).
% 1.25/1.42 tff(6303,plain,
% 1.25/1.42 (b(s(s(z)), s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[2225, 160, 169, 1233])).
% 1.25/1.42 tff(6304,plain,
% 1.25/1.42 (s(elem!1) = s(s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6233, 1400, 546, 1, 169, 150, 160])).
% 1.25/1.42 tff(6305,plain,
% 1.25/1.42 (s(s(elem!1)) = s(s(s(z)))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6304])).
% 1.25/1.42 tff(6306,plain,
% 1.25/1.42 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6305])).
% 1.25/1.42 tff(6307,plain,
% 1.25/1.42 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6306])).
% 1.25/1.42 tff(6308,plain,
% 1.25/1.42 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6307, 1008])).
% 1.25/1.42 tff(6309,plain,
% 1.25/1.42 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.25/1.42 inference(symmetry,[status(thm)],[6308])).
% 1.25/1.42 tff(6310,plain,
% 1.25/1.42 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6309])).
% 1.25/1.42 tff(6311,plain,
% 1.25/1.42 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[2782, 6310])).
% 1.25/1.42 tff(6312,plain,
% 1.25/1.42 (elem!1 = s(z)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[379, 6304])).
% 1.25/1.42 tff(6313,plain,
% 1.25/1.42 (~b(s(z), elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[1802, 6312])).
% 1.25/1.42 tff(6314,plain,
% 1.25/1.42 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[2851, 6313, 546, 209, 306, 22, 160, 1400, 169])).
% 1.25/1.42 tff(6315,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6314, 6311])).
% 1.25/1.42 tff(6316,plain,(b(elem!1, s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6317,plain,
% 1.25/1.42 (b(elem!1, s(z))),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6316, 160, 306, 546, 169, 1, 150])).
% 1.25/1.42 tff(6318,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6319,plain,
% 1.25/1.42 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6320,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6319])).
% 1.25/1.42 tff(6321,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6320, 6318])).
% 1.25/1.42 tff(6322,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6323,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6322, 6321])).
% 1.25/1.42 tff(6324,plain,
% 1.25/1.42 (~b(z, elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6323, 238, 6317, 546, 1457])).
% 1.25/1.42 tff(6325,plain,
% 1.25/1.42 ((z = elem!1) | r(z, elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[3134, 51, 6324])).
% 1.25/1.42 tff(6326,plain,
% 1.25/1.42 (r(z, elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6325, 6102])).
% 1.25/1.42 tff(6327,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.25/1.42 tff(6328,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6329,plain,
% 1.25/1.42 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6330,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6329])).
% 1.25/1.42 tff(6331,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6330, 6328])).
% 1.25/1.42 tff(6332,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6333,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 1.25/1.42 tff(6334,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6333, 238, 228, 288, 227, 2180])).
% 1.25/1.42 tff(6335,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6336,plain,
% 1.25/1.42 (~b(s(s(elem!1)), elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6335, 2180, 227, 288])).
% 1.25/1.42 tff(6337,plain,
% 1.25/1.42 (r(s(s(elem!1)), elem!1)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[255, 6336, 248])).
% 1.25/1.42 tff(6338,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.25/1.42 tff(6339,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6340,plain,
% 1.25/1.42 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 1.25/1.42 inference(rewrite,[status(thm)],[])).
% 1.25/1.42 tff(6341,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))))),
% 1.25/1.42 inference(monotonicity,[status(thm)],[6340])).
% 1.25/1.42 tff(6342,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1)))),
% 1.25/1.42 inference(transitivity,[status(thm)],[6341, 6339])).
% 1.25/1.42 tff(6343,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.25/1.42 inference(quant_inst,[status(thm)],[])).
% 1.25/1.42 tff(6344,plain,
% 1.25/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))),
% 1.25/1.42 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 1.25/1.42 tff(6345,plain,
% 1.25/1.42 ($false),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6344, 124, 301, 6338, 6327])).
% 1.25/1.42 tff(6346,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.42 tff(6347,plain,
% 1.25/1.42 (~r(s(s(elem!1)), z)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[6346, 6337, 6327])).
% 1.25/1.42 tff(6348,plain,
% 1.25/1.42 (b(s(s(elem!1)), z)),
% 1.25/1.42 inference(unit_resolution,[status(thm)],[4905, 6347])).
% 1.25/1.42 tff(6349,plain,
% 1.25/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6350,plain,
% 1.25/1.43 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6351,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6350])).
% 1.25/1.43 tff(6352,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.25/1.43 inference(transitivity,[status(thm)],[6351, 6349])).
% 1.25/1.43 tff(6353,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6354,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6353, 6352])).
% 1.25/1.43 tff(6355,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6354, 238, 288, 227, 6348, 2180])).
% 1.25/1.43 tff(6356,plain,((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6357,plain,
% 1.25/1.43 (~b(s(s(z)), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6356, 6326, 6303, 6302, 167])).
% 1.25/1.43 tff(6358,plain,
% 1.25/1.43 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1260, 51, 1257])).
% 1.25/1.43 tff(6359,plain,
% 1.25/1.43 (s(s(z)) = s(elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6358, 6357])).
% 1.25/1.43 tff(6360,plain,
% 1.25/1.43 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6359])).
% 1.25/1.43 tff(6361,plain,
% 1.25/1.43 (s(z) = elem!1),
% 1.25/1.43 inference(transitivity,[status(thm)],[69, 6360, 154])).
% 1.25/1.43 tff(6362,plain,
% 1.25/1.43 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6361])).
% 1.25/1.43 tff(6363,plain,
% 1.25/1.43 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 1.25/1.43 inference(symmetry,[status(thm)],[6362])).
% 1.25/1.43 tff(6364,plain,
% 1.25/1.43 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6363])).
% 1.25/1.43 tff(6365,plain,
% 1.25/1.43 (~b(elem!1, s(z))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[839, 6364])).
% 1.25/1.43 tff(6366,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6317, 6365])).
% 1.25/1.43 tff(6367,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6368,plain,
% 1.25/1.43 (~r(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6367, 5414, 1457, 4225, 169, 1, 150])).
% 1.25/1.43 tff(6369,plain,
% 1.25/1.43 (b(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[56, 6368])).
% 1.25/1.43 tff(6370,plain,
% 1.25/1.43 (~b(z, s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[4886, 5414, 272, 6369, 1457])).
% 1.25/1.43 tff(6371,plain,
% 1.25/1.43 (r(z, s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2071, 6370])).
% 1.25/1.43 tff(6372,plain,
% 1.25/1.43 (b(s(z), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[5589, 1081, 1808, 1400])).
% 1.25/1.43 tff(6373,plain,
% 1.25/1.43 (~(elem!1 = s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1802, 6372])).
% 1.25/1.43 tff(6374,plain,
% 1.25/1.43 (r(elem!1, s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[363, 6373, 1400])).
% 1.25/1.43 tff(6375,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1457, 4118])).
% 1.25/1.43 tff(6376,plain,((~(s(elem!1) = s(z))) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6377,plain,
% 1.25/1.43 (~(s(elem!1) = s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6376, 1457, 1400])).
% 1.25/1.43 tff(6378,plain,
% 1.25/1.43 (r(s(elem!1), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[473, 6377, 1808])).
% 1.25/1.43 tff(6379,plain,
% 1.25/1.43 (~r(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2634, 124, 6374, 6378])).
% 1.25/1.43 tff(6380,plain,
% 1.25/1.43 (b(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[629, 387, 6379])).
% 1.25/1.43 tff(6381,plain,
% 1.25/1.43 (~r(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2626, 124, 6374, 6378])).
% 1.25/1.43 tff(6382,plain,
% 1.25/1.43 (b(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[408, 394, 6381])).
% 1.25/1.43 tff(6383,plain,
% 1.25/1.43 (~(s(s(z)) = s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[21, 6377])).
% 1.25/1.43 tff(6384,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6385,plain,
% 1.25/1.43 (((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6386,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6385])).
% 1.25/1.43 tff(6387,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.25/1.43 inference(transitivity,[status(thm)],[6386, 6384])).
% 1.25/1.43 tff(6388,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6389,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6388, 6387])).
% 1.25/1.43 tff(6390,plain,
% 1.25/1.43 (~b(z, s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6389, 238, 1817, 427, 1457])).
% 1.25/1.43 tff(6391,plain,
% 1.25/1.43 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1511, 51, 6390])).
% 1.25/1.43 tff(6392,plain,
% 1.25/1.43 (r(z, s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6391, 1450])).
% 1.25/1.43 tff(6393,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6394,plain,
% 1.25/1.43 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6395,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6394])).
% 1.25/1.43 tff(6396,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.43 inference(transitivity,[status(thm)],[6395, 6393])).
% 1.25/1.43 tff(6397,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6398,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 1.25/1.43 tff(6399,plain,
% 1.25/1.43 (~b(z, s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6398, 238, 427, 23, 1457])).
% 1.25/1.43 tff(6400,plain,
% 1.25/1.43 (r(z, s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2071, 6399])).
% 1.25/1.43 tff(6401,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6402,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6403,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6402, 6401])).
% 1.25/1.43 tff(6404,plain,
% 1.25/1.43 (~b(s(s(z)), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6403, 238, 1817, 427, 23])).
% 1.25/1.43 tff(6405,plain,
% 1.25/1.43 (r(s(s(z)), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[135, 6404, 114])).
% 1.25/1.43 tff(6406,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6407,plain,
% 1.25/1.43 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6408,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6407])).
% 1.25/1.43 tff(6409,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.25/1.43 inference(transitivity,[status(thm)],[6408, 6406])).
% 1.25/1.43 tff(6410,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6411,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6410, 6409])).
% 1.25/1.43 tff(6412,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6411, 124, 6405, 6400, 6392])).
% 1.25/1.43 tff(6413,plain,((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6414,plain,
% 1.25/1.43 (~b(s(s(elem!1)), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6413, 114, 427, 1457, 1817])).
% 1.25/1.43 tff(6415,plain,
% 1.25/1.43 (r(s(s(elem!1)), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[110, 51, 6414, 106])).
% 1.25/1.43 tff(6416,plain,
% 1.25/1.43 (~r(s(s(elem!1)), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[263, 6415, 1370])).
% 1.25/1.43 tff(6417,plain,
% 1.25/1.43 (b(s(s(elem!1)), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[255, 6416, 167])).
% 1.25/1.43 tff(6418,plain,
% 1.25/1.43 (~b(s(elem!1), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2644, 6417, 1816, 1370, 387])).
% 1.25/1.43 tff(6419,plain,
% 1.25/1.43 (r(s(elem!1), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[534, 6418, 159])).
% 1.25/1.43 tff(6420,plain,
% 1.25/1.43 (~r(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2626, 124, 1370, 1816])).
% 1.25/1.43 tff(6421,plain,
% 1.25/1.43 (b(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[408, 6420, 394])).
% 1.25/1.43 tff(6422,plain,
% 1.25/1.43 (~r(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2634, 124, 1370, 1816])).
% 1.25/1.43 tff(6423,plain,
% 1.25/1.43 (b(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[629, 6422, 387])).
% 1.25/1.43 tff(6424,plain,
% 1.25/1.43 (~b(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[3209, 6417, 546, 1817, 6423, 150, 1370, 6421, 114])).
% 1.25/1.43 tff(6425,plain,
% 1.25/1.43 (r(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[56, 6424])).
% 1.25/1.43 tff(6426,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[526, 6425, 6419, 1816])).
% 1.25/1.43 tff(6427,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6428,plain,
% 1.25/1.43 (~b(s(z), s(s(s(elem!1))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6427, 1817, 6383, 150, 6374, 6372, 1457, 1808])).
% 1.25/1.43 tff(6429,plain,
% 1.25/1.43 (r(s(z), s(s(s(elem!1))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[101, 6428])).
% 1.25/1.43 tff(6430,plain,
% 1.25/1.43 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[3142, 6429, 6382, 6378, 6374, 6380, 1817])).
% 1.25/1.43 tff(6431,plain,
% 1.25/1.43 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1814, 6430, 1081])).
% 1.25/1.43 tff(6432,plain,
% 1.25/1.43 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6431])).
% 1.25/1.43 tff(6433,plain,
% 1.25/1.43 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.25/1.43 inference(transitivity,[status(thm)],[723, 6432, 88])).
% 1.25/1.43 tff(6434,plain,
% 1.25/1.43 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6433])).
% 1.25/1.43 tff(6435,plain,
% 1.25/1.43 (s(s(s(z))) = s(elem!1)),
% 1.25/1.43 inference(transitivity,[status(thm)],[716, 6434, 17])).
% 1.25/1.43 tff(6436,plain,
% 1.25/1.43 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6435])).
% 1.25/1.43 tff(6437,plain,
% 1.25/1.43 (s(s(z)) = elem!1),
% 1.25/1.43 inference(transitivity,[status(thm)],[144, 6436, 154])).
% 1.25/1.43 tff(6438,plain,
% 1.25/1.43 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6437])).
% 1.25/1.43 tff(6439,plain,
% 1.25/1.43 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.25/1.43 inference(symmetry,[status(thm)],[6438])).
% 1.25/1.43 tff(6440,plain,
% 1.25/1.43 ((~b(elem!1, s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6439])).
% 1.25/1.43 tff(6441,plain,
% 1.25/1.43 (~b(s(s(z)), s(z))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[1400, 6440])).
% 1.25/1.43 tff(6442,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1817, 6441])).
% 1.25/1.43 tff(6443,plain,((~b(s(s(z)), s(z))) | b(elem!1, s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6444,plain,
% 1.25/1.43 (~b(s(s(z)), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6443, 150, 1081, 1400, 1457, 1808])).
% 1.25/1.43 tff(6445,plain,
% 1.25/1.43 (r(s(s(z)), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[79, 6444])).
% 1.25/1.43 tff(6446,plain,
% 1.25/1.43 (~r(s(s(z)), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[3252, 124, 6445, 6374])).
% 1.25/1.43 tff(6447,plain,
% 1.25/1.43 (~(s(elem!1) = s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[379, 6373])).
% 1.25/1.43 tff(6448,plain,
% 1.25/1.43 (~(s(s(z)) = s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1249, 6447])).
% 1.25/1.43 tff(6449,plain,
% 1.25/1.43 (~r(s(s(z)), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1256, 124, 6445, 6378])).
% 1.25/1.43 tff(6450,plain,
% 1.25/1.43 (b(s(s(z)), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1260, 51, 6449, 6448])).
% 1.25/1.43 tff(6451,plain,
% 1.25/1.43 (~b(s(s(z)), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1267, 238, 6380, 6382, 6450])).
% 1.25/1.43 tff(6452,plain,
% 1.25/1.43 (s(s(z)) = elem!1),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1275, 6451, 6446])).
% 1.25/1.43 tff(6453,plain,
% 1.25/1.43 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1385, 6452])).
% 1.25/1.43 tff(6454,plain,
% 1.25/1.43 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6453])).
% 1.25/1.43 tff(6455,plain,
% 1.25/1.43 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.25/1.43 inference(transitivity,[status(thm)],[723, 6454, 88])).
% 1.25/1.43 tff(6456,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6455])).
% 1.25/1.43 tff(6457,plain,
% 1.25/1.43 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[4990, 169, 1544, 2619, 306])).
% 1.25/1.43 tff(6458,plain,
% 1.25/1.43 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1814, 6457, 1081])).
% 1.25/1.43 tff(6459,plain,
% 1.25/1.43 (~(s(s(z)) = elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1385, 6457])).
% 1.25/1.43 tff(6460,plain,
% 1.25/1.43 (~b(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[3270, 6459, 330, 306, 114, 150, 6458, 1400])).
% 1.25/1.43 tff(6461,plain,
% 1.25/1.43 (r(s(z), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[56, 6460])).
% 1.25/1.43 tff(6462,plain,
% 1.25/1.43 (b(s(s(z)), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2225, 6461, 169, 2155])).
% 1.25/1.43 tff(6463,plain,
% 1.25/1.43 (~r(s(elem!1), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[526, 6461, 306])).
% 1.25/1.43 tff(6464,plain,
% 1.25/1.43 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[534, 6463, 159])).
% 1.25/1.43 tff(6465,plain,
% 1.25/1.43 (~b(s(s(elem!1)), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2644, 6464, 306, 2619, 387])).
% 1.25/1.43 tff(6466,plain,
% 1.25/1.43 (~(elem!1 = s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[4979, 6465, 2154])).
% 1.25/1.43 tff(6467,plain,
% 1.25/1.43 (b(s(elem!1), s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[488, 278, 1233])).
% 1.25/1.43 tff(6468,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6469,plain,
% 1.25/1.43 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6470,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6469])).
% 1.25/1.43 tff(6471,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.25/1.43 inference(transitivity,[status(thm)],[6470, 6468])).
% 1.25/1.43 tff(6472,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6473,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6472, 6471])).
% 1.25/1.43 tff(6474,plain,
% 1.25/1.43 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6473, 238, 227, 6467, 1587])).
% 1.25/1.43 tff(6475,assumption,(~r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.25/1.43 tff(6476,plain,
% 1.25/1.43 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1960, 51, 6475])).
% 1.25/1.43 tff(6477,plain,
% 1.25/1.43 (s(elem!1) = s(s(s(s(z))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6476, 6474])).
% 1.25/1.43 tff(6478,plain,
% 1.25/1.43 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6477])).
% 1.25/1.43 tff(6479,plain,
% 1.25/1.43 (elem!1 = s(s(s(z)))),
% 1.25/1.43 inference(transitivity,[status(thm)],[155, 6478, 715])).
% 1.25/1.43 tff(6480,plain,
% 1.25/1.43 (b(elem!1, s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6479])).
% 1.25/1.43 tff(6481,plain,
% 1.25/1.43 (r(elem!1, s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[363, 4576, 1400])).
% 1.25/1.43 tff(6482,plain,
% 1.25/1.43 (~r(elem!1, s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2461, 124, 169, 6481])).
% 1.25/1.43 tff(6483,plain,
% 1.25/1.43 (b(elem!1, s(s(z)))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[763, 6482, 541])).
% 1.25/1.43 tff(6484,plain,
% 1.25/1.43 (b(s(s(s(z))), s(s(z)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6483, 6480])).
% 1.25/1.43 tff(6485,plain,
% 1.25/1.43 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.25/1.43 inference(symmetry,[status(thm)],[6478])).
% 1.25/1.43 tff(6486,plain,
% 1.25/1.43 (s(s(s(z))) = elem!1),
% 1.25/1.43 inference(transitivity,[status(thm)],[716, 6485, 154])).
% 1.25/1.43 tff(6487,plain,
% 1.25/1.43 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6486])).
% 1.25/1.43 tff(6488,plain,
% 1.25/1.43 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.25/1.43 inference(symmetry,[status(thm)],[6487])).
% 1.25/1.43 tff(6489,plain,
% 1.25/1.43 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6477])).
% 1.25/1.43 tff(6490,plain,
% 1.25/1.43 (~r(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2634, 124, 6481, 306])).
% 1.25/1.43 tff(6491,plain,
% 1.25/1.43 (b(elem!1, s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[629, 6490, 391])).
% 1.25/1.43 tff(6492,plain,
% 1.25/1.43 (b(elem!1, s(s(s(s(z)))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6491, 6489])).
% 1.25/1.43 tff(6493,plain,
% 1.25/1.43 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6492, 6488])).
% 1.25/1.43 tff(6494,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6486])).
% 1.25/1.43 tff(6495,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.43 inference(symmetry,[status(thm)],[6494])).
% 1.25/1.43 tff(6496,plain,
% 1.25/1.43 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.25/1.43 inference(monotonicity,[status(thm)],[6477])).
% 1.25/1.43 tff(6497,plain,
% 1.25/1.43 (~r(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[2626, 124, 6481, 306])).
% 1.25/1.43 tff(6498,plain,
% 1.25/1.43 (b(s(elem!1), elem!1)),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[408, 6497, 2620])).
% 1.25/1.43 tff(6499,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), elem!1)),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6498, 6496])).
% 1.25/1.43 tff(6500,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6499, 6495])).
% 1.25/1.43 tff(6501,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[5183, 238, 6500, 1501, 6493, 6484])).
% 1.25/1.43 tff(6502,plain,((s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(z))) | r(s(elem!1), s(s(s(s(z))))) | (~r(s(elem!1), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6503,plain,
% 1.25/1.43 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6502, 6466, 3258, 387, 2115, 306, 169, 2154, 6462, 1400])).
% 1.25/1.43 tff(6504,plain,
% 1.25/1.43 (r(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1603, 6503, 1599])).
% 1.25/1.43 tff(6505,plain,
% 1.25/1.43 ($false),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1611, 124, 169, 1544, 6504])).
% 1.25/1.43 tff(6506,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | b(elem!1, s(z)) | (elem!1 = s(z)) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.43 tff(6507,plain,
% 1.25/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6506, 6445, 6378, 1400, 6373, 6383, 150, 1081])).
% 1.25/1.43 tff(6508,plain,
% 1.25/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[1623, 6507, 1619])).
% 1.25/1.43 tff(6509,plain,
% 1.25/1.43 (b(s(s(elem!1)), s(z))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6508, 6456])).
% 1.25/1.43 tff(6510,plain,
% 1.25/1.43 (~(s(z) = s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[425, 6377])).
% 1.25/1.43 tff(6511,plain,
% 1.25/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.25/1.43 inference(rewrite,[status(thm)],[])).
% 1.25/1.43 tff(6512,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.25/1.43 inference(quant_inst,[status(thm)],[])).
% 1.25/1.43 tff(6513,plain,
% 1.25/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.25/1.43 inference(modus_ponens,[status(thm)],[6512, 6511])).
% 1.25/1.43 tff(6514,plain,
% 1.25/1.43 (~b(s(z), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[6513, 238, 6380, 6382, 6372])).
% 1.25/1.43 tff(6515,plain,
% 1.25/1.43 (r(s(z), s(elem!1))),
% 1.25/1.43 inference(unit_resolution,[status(thm)],[439, 6514, 6510])).
% 1.25/1.44 tff(6516,plain,
% 1.25/1.44 (~r(elem!1, s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2461, 124, 6445, 6374])).
% 1.25/1.44 tff(6517,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6518,plain,
% 1.25/1.44 (((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6519,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6518])).
% 1.25/1.44 tff(6520,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6519, 6517])).
% 1.25/1.44 tff(6521,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(z)))))),
% 1.25/1.44 inference(quant_inst,[status(thm)],[])).
% 1.25/1.44 tff(6522,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(elem!1, s(s(z))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6521, 6520])).
% 1.25/1.44 tff(6523,plain,
% 1.25/1.44 (~b(elem!1, s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6522, 238, 6380, 6382, 6450])).
% 1.25/1.44 tff(6524,plain,
% 1.25/1.44 (elem!1 = s(s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[763, 6523, 6516])).
% 1.25/1.44 tff(6525,plain,
% 1.25/1.44 (~r(s(elem!1), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[483, 6445, 6378])).
% 1.25/1.44 tff(6526,plain,
% 1.25/1.44 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6455])).
% 1.25/1.44 tff(6527,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6528,plain,
% 1.25/1.44 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6529,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6528])).
% 1.25/1.44 tff(6530,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6529, 6527])).
% 1.25/1.44 tff(6531,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.25/1.44 inference(quant_inst,[status(thm)],[])).
% 1.25/1.44 tff(6532,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6531, 6530])).
% 1.25/1.44 tff(6533,plain,
% 1.25/1.44 (~b(z, s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6532, 238, 6372, 1457, 6508])).
% 1.25/1.44 tff(6534,plain,
% 1.25/1.44 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1487, 51, 6533])).
% 1.25/1.44 tff(6535,plain,
% 1.25/1.44 (r(z, s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6534, 1454])).
% 1.25/1.44 tff(6536,plain,
% 1.25/1.44 (r(z, s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6535, 6526])).
% 1.25/1.44 tff(6537,plain,
% 1.25/1.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[5931, 546, 169, 2222, 1784, 1228, 365])).
% 1.25/1.44 tff(6538,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[223, 6537, 545])).
% 1.25/1.44 tff(6539,plain,
% 1.25/1.44 (~b(s(s(s(elem!1))), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[5572, 6538, 5901, 2026, 507, 631])).
% 1.25/1.44 tff(6540,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[647, 6539, 5896])).
% 1.25/1.44 tff(6541,plain,
% 1.25/1.44 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[5508, 6540, 5901])).
% 1.25/1.44 tff(6542,plain,
% 1.25/1.44 (~r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1725, 6541, 169])).
% 1.25/1.44 tff(6543,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1781, 6542])).
% 1.25/1.44 tff(6544,plain,
% 1.25/1.44 (~b(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2798, 6543, 1784, 1457])).
% 1.25/1.44 tff(6545,plain,
% 1.25/1.44 (r(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[893, 6544, 3140])).
% 1.25/1.44 tff(6546,plain,
% 1.25/1.44 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[4153, 6543, 1784, 546])).
% 1.25/1.44 tff(6547,plain,
% 1.25/1.44 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1904, 6546])).
% 1.25/1.44 tff(6548,plain,
% 1.25/1.44 (~b(s(z), s(s(s(s(s(z))))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3641, 6543, 1457, 1784])).
% 1.25/1.44 tff(6549,plain,
% 1.25/1.44 (r(s(z), s(s(s(s(s(z))))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1709, 6548])).
% 1.25/1.44 tff(6550,plain,
% 1.25/1.44 ($false),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1660, 6549, 6547, 6545])).
% 1.25/1.44 tff(6551,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(elem!1), s(s(z))) | (~(s(s(z)) = elem!1)) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.44 tff(6552,plain,
% 1.25/1.44 (~b(s(z), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6551, 6508, 1457, 6445, 6536, 6382, 6380, 209, 6525, 6452, 6524])).
% 1.25/1.44 tff(6553,plain,
% 1.25/1.44 (r(s(z), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[101, 6552])).
% 1.25/1.44 tff(6554,plain,
% 1.25/1.44 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[450, 6553, 6515])).
% 1.25/1.44 tff(6555,plain,
% 1.25/1.44 (b(s(s(s(elem!1))), s(elem!1))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[459, 6554, 421])).
% 1.25/1.44 tff(6556,plain,
% 1.25/1.44 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6452])).
% 1.25/1.44 tff(6557,plain,
% 1.25/1.44 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6556, 511])).
% 1.25/1.44 tff(6558,plain,
% 1.25/1.44 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.25/1.44 inference(transitivity,[status(thm)],[6557, 641])).
% 1.25/1.44 tff(6559,plain,
% 1.25/1.44 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6558])).
% 1.25/1.44 tff(6560,plain,
% 1.25/1.44 (~(s(s(s(elem!1))) = elem!1)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[1291, 6559])).
% 1.25/1.44 tff(6561,plain,
% 1.25/1.44 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6557])).
% 1.25/1.44 tff(6562,plain,
% 1.25/1.44 (~(elem!1 = s(s(s(elem!1))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[1291, 6561])).
% 1.25/1.44 tff(6563,plain,
% 1.25/1.44 (~r(elem!1, s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1378, 6553, 6374])).
% 1.25/1.44 tff(6564,plain,
% 1.25/1.44 (b(elem!1, s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1319, 6563, 6562])).
% 1.25/1.44 tff(6565,plain,
% 1.25/1.44 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2717, 6564, 6380, 6555])).
% 1.25/1.44 tff(6566,plain,
% 1.25/1.44 (r(s(elem!1), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[539, 6565, 415])).
% 1.25/1.44 tff(6567,plain,
% 1.25/1.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1203, 6566, 6560, 150, 6380, 6555])).
% 1.25/1.44 tff(6568,plain,
% 1.25/1.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[223, 6567, 209])).
% 1.25/1.44 tff(6569,plain,
% 1.25/1.44 (b(s(s(z)), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6452])).
% 1.25/1.44 tff(6570,plain,
% 1.25/1.44 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6455])).
% 1.25/1.44 tff(6571,plain,
% 1.25/1.44 (~b(s(s(s(elem!1))), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[786, 6555, 6382, 6380])).
% 1.25/1.44 tff(6572,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[647, 6571, 6560])).
% 1.25/1.44 tff(6573,plain,
% 1.25/1.44 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[5508, 6572, 6453])).
% 1.25/1.44 tff(6574,plain,
% 1.25/1.44 (~r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1725, 6573, 6445])).
% 1.25/1.44 tff(6575,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1781, 6574])).
% 1.25/1.44 tff(6576,plain,
% 1.25/1.44 (~b(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2798, 6575, 6508, 1457])).
% 1.25/1.44 tff(6577,plain,
% 1.25/1.44 (r(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[893, 6576, 3140])).
% 1.25/1.44 tff(6578,plain,
% 1.25/1.44 (r(s(z), s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6577, 6570])).
% 1.25/1.44 tff(6579,plain,
% 1.25/1.44 (b(s(s(z)), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2225, 6578, 6445, 6525])).
% 1.25/1.44 tff(6580,plain,
% 1.25/1.44 (b(elem!1, s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6579, 6569])).
% 1.25/1.44 tff(6581,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6582,plain,
% 1.25/1.44 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6583,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6582])).
% 1.25/1.44 tff(6584,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6583, 6581])).
% 1.25/1.44 tff(6585,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.25/1.44 inference(quant_inst,[status(thm)],[])).
% 1.25/1.44 tff(6586,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6585, 6584])).
% 1.25/1.44 tff(6587,plain,
% 1.25/1.44 ($false),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6586, 238, 6580, 6564, 6568, 6509])).
% 1.25/1.44 tff(6588,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | b(elem!1, s(z)) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.44 tff(6589,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6588, 1400, 1457, 150, 1808])).
% 1.25/1.44 tff(6590,plain,
% 1.25/1.44 (s(elem!1) = s(s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1249, 1246])).
% 1.25/1.44 tff(6591,plain,
% 1.25/1.44 (elem!1 = s(z)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[379, 6590])).
% 1.25/1.44 tff(6592,plain,
% 1.25/1.44 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6591])).
% 1.25/1.44 tff(6593,plain,
% 1.25/1.44 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 1.25/1.44 inference(symmetry,[status(thm)],[6592])).
% 1.25/1.44 tff(6594,plain,
% 1.25/1.44 (r(s(elem!1), elem!1)),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[306, 6593])).
% 1.25/1.44 tff(6595,plain,
% 1.25/1.44 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6591])).
% 1.25/1.44 tff(6596,plain,
% 1.25/1.44 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6595])).
% 1.25/1.44 tff(6597,plain,
% 1.25/1.44 ((~r(s(z), s(s(elem!1)))) <=> (~r(elem!1, s(s(elem!1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6596])).
% 1.25/1.44 tff(6598,plain,
% 1.25/1.44 (~r(elem!1, s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[24, 6597])).
% 1.25/1.44 tff(6599,plain,
% 1.25/1.44 (~r(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3396, 6590, 63])).
% 1.25/1.44 tff(6600,plain,
% 1.25/1.44 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[893, 3140])).
% 1.25/1.44 tff(6601,plain,
% 1.25/1.44 (b(s(z), s(s(s(s(z)))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6600, 6599])).
% 1.25/1.44 tff(6602,plain,
% 1.25/1.44 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6591])).
% 1.25/1.44 tff(6603,plain,
% 1.25/1.44 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6602])).
% 1.25/1.44 tff(6604,plain,
% 1.25/1.44 (b(elem!1, s(s(s(elem!1))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[546, 6603])).
% 1.25/1.44 tff(6605,plain,
% 1.25/1.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[615, 250, 150, 602, 6604])).
% 1.25/1.44 tff(6606,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[223, 6605, 209])).
% 1.25/1.44 tff(6607,plain,
% 1.25/1.44 (b(s(s(elem!1)), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[255, 250, 167])).
% 1.25/1.44 tff(6608,plain,
% 1.25/1.44 (b(s(s(s(z))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1428, 6607, 6591])).
% 1.25/1.44 tff(6609,plain,
% 1.25/1.44 (~b(z, s(s(s(z))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3418, 6608, 1457, 2765])).
% 1.25/1.44 tff(6610,plain,
% 1.25/1.44 (~b(z, s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3526, 6609, 6590])).
% 1.25/1.44 tff(6611,plain,
% 1.25/1.44 (r(z, s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2071, 6610])).
% 1.25/1.44 tff(6612,plain,
% 1.25/1.44 (~r(z, s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[5525, 6611, 6606])).
% 1.25/1.44 tff(6613,plain,
% 1.25/1.44 (b(z, s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3795, 51, 6612, 3785])).
% 1.25/1.44 tff(6614,plain,
% 1.25/1.44 (s(s(s(z))) = s(s(elem!1))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[1246])).
% 1.25/1.44 tff(6615,plain,
% 1.25/1.44 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6614])).
% 1.25/1.44 tff(6616,plain,
% 1.25/1.44 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6615])).
% 1.25/1.44 tff(6617,plain,
% 1.25/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3439, 6606, 169, 167, 2765, 6591])).
% 1.25/1.44 tff(6618,plain,
% 1.25/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1624, 6617])).
% 1.25/1.44 tff(6619,plain,
% 1.25/1.44 (b(s(s(s(elem!1))), s(z))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6618, 6616])).
% 1.25/1.44 tff(6620,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6621,plain,
% 1.25/1.44 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.44 inference(rewrite,[status(thm)],[])).
% 1.25/1.44 tff(6622,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6621])).
% 1.25/1.44 tff(6623,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6622, 6620])).
% 1.25/1.44 tff(6624,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.44 inference(quant_inst,[status(thm)],[])).
% 1.25/1.44 tff(6625,plain,
% 1.25/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6624, 6623])).
% 1.25/1.44 tff(6626,plain,
% 1.25/1.44 ($false),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6625, 238, 6619, 546, 1457, 6613])).
% 1.25/1.44 tff(6627,plain,(r(s(s(elem!1)), elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~(s(s(z)) = s(elem!1))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.44 tff(6628,plain,
% 1.25/1.44 (r(s(s(elem!1)), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[6627, 1246, 1457, 4225, 169, 6601, 150, 6598])).
% 1.25/1.44 tff(6629,plain,
% 1.25/1.44 (~r(s(s(elem!1)), s(elem!1))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[403, 6628, 6594])).
% 1.25/1.44 tff(6630,plain,
% 1.25/1.44 (b(s(s(elem!1)), s(elem!1))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[323, 6629, 272])).
% 1.25/1.44 tff(6631,plain,
% 1.25/1.44 (b(elem!1, s(s(s(elem!1))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[4225, 6603])).
% 1.25/1.44 tff(6632,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6615])).
% 1.25/1.44 tff(6633,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6632])).
% 1.25/1.44 tff(6634,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[1040, 6633])).
% 1.25/1.44 tff(6635,plain,
% 1.25/1.44 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6615])).
% 1.25/1.44 tff(6636,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6635])).
% 1.25/1.44 tff(6637,plain,
% 1.25/1.44 (r(s(elem!1), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[534, 528, 159])).
% 1.25/1.44 tff(6638,plain,
% 1.25/1.44 (~r(s(s(elem!1)), elem!1)),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[700, 6637, 395])).
% 1.25/1.44 tff(6639,plain,
% 1.25/1.44 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[615, 6638, 150, 602, 543])).
% 1.25/1.44 tff(6640,plain,
% 1.25/1.44 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[223, 6639, 209])).
% 1.25/1.44 tff(6641,plain,
% 1.25/1.44 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6640, 6636])).
% 1.25/1.44 tff(6642,plain,
% 1.25/1.44 (b(s(s(z)), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[1246])).
% 1.25/1.44 tff(6643,plain,
% 1.25/1.44 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6642])).
% 1.25/1.44 tff(6644,plain,
% 1.25/1.44 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6643])).
% 1.25/1.44 tff(6645,plain,
% 1.25/1.44 (~b(s(s(z)), s(s(elem!1)))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[528, 6644])).
% 1.25/1.44 tff(6646,plain,
% 1.25/1.44 (r(s(s(z)), s(s(elem!1)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[135, 6645, 114])).
% 1.25/1.44 tff(6647,plain,
% 1.25/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[3439, 6640, 169, 167, 2765, 6591])).
% 1.25/1.44 tff(6648,plain,
% 1.25/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1624, 6647])).
% 1.25/1.44 tff(6649,plain,
% 1.25/1.44 (~b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[2798, 6648, 1457, 2765])).
% 1.25/1.44 tff(6650,plain,
% 1.25/1.44 (r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1781, 6649])).
% 1.25/1.44 tff(6651,plain,
% 1.25/1.44 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1725, 6650, 169])).
% 1.25/1.44 tff(6652,plain,
% 1.25/1.44 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1738, 6651])).
% 1.25/1.44 tff(6653,plain,
% 1.25/1.44 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[1246])).
% 1.25/1.44 tff(6654,plain,
% 1.25/1.44 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6653])).
% 1.25/1.44 tff(6655,plain,
% 1.25/1.44 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.25/1.44 inference(monotonicity,[status(thm)],[6615])).
% 1.25/1.44 tff(6656,plain,
% 1.25/1.44 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.25/1.44 inference(symmetry,[status(thm)],[6655])).
% 1.25/1.44 tff(6657,plain,
% 1.25/1.44 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.44 inference(transitivity,[status(thm)],[6656, 6654])).
% 1.25/1.44 tff(6658,plain,
% 1.25/1.44 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1169, 6640, 6637])).
% 1.25/1.44 tff(6659,plain,
% 1.25/1.44 (b(s(elem!1), s(s(s(elem!1))))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[539, 6658, 415])).
% 1.25/1.44 tff(6660,plain,
% 1.25/1.44 (b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.44 inference(modus_ponens,[status(thm)],[6659, 6657])).
% 1.25/1.44 tff(6661,plain,
% 1.25/1.44 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[4437, 6660, 1786, 6652])).
% 1.25/1.44 tff(6662,plain,
% 1.25/1.44 (r(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.44 inference(unit_resolution,[status(thm)],[1564, 6661])).
% 1.25/1.44 tff(6663,assumption,(r(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.25/1.44 tff(6664,plain,
% 1.25/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6665,plain,
% 1.25/1.45 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6666,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6665])).
% 1.25/1.45 tff(6667,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6666, 6664])).
% 1.25/1.45 tff(6668,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6669,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6668, 6667])).
% 1.25/1.45 tff(6670,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6669, 124, 169, 192, 1546, 6663])).
% 1.25/1.45 tff(6671,plain,((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6672,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6671, 6662, 6646, 169, 6641])).
% 1.25/1.45 tff(6673,plain,(b(s(elem!1), s(s(elem!1))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(s(z)) = s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6674,plain,
% 1.25/1.45 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6673, 6634, 114, 169, 1246, 1457, 6601, 150, 6598, 6631, 6594])).
% 1.25/1.45 tff(6675,plain,
% 1.25/1.45 (s(s(elem!1)) = s(s(s(z)))),
% 1.25/1.45 inference(symmetry,[status(thm)],[6614])).
% 1.25/1.45 tff(6676,plain,
% 1.25/1.45 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6675])).
% 1.25/1.45 tff(6677,plain,
% 1.25/1.45 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6676, 2347])).
% 1.25/1.45 tff(6678,plain,
% 1.25/1.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.25/1.45 inference(symmetry,[status(thm)],[6677])).
% 1.25/1.45 tff(6679,plain,
% 1.25/1.45 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6678])).
% 1.25/1.45 tff(6680,plain,
% 1.25/1.45 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[1092, 6679])).
% 1.25/1.45 tff(6681,plain,
% 1.25/1.45 (s(elem!1) = s(s(z))),
% 1.25/1.45 inference(symmetry,[status(thm)],[1246])).
% 1.25/1.45 tff(6682,plain,
% 1.25/1.45 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6681])).
% 1.25/1.45 tff(6683,plain,
% 1.25/1.45 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.25/1.45 inference(symmetry,[status(thm)],[6682])).
% 1.25/1.45 tff(6684,plain,
% 1.25/1.45 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6683])).
% 1.25/1.45 tff(6685,plain,
% 1.25/1.45 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[1729, 6684])).
% 1.25/1.45 tff(6686,plain,
% 1.25/1.45 (~(elem!1 = s(s(s(elem!1))))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1364, 6591])).
% 1.25/1.45 tff(6687,plain,
% 1.25/1.45 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6591])).
% 1.25/1.45 tff(6688,plain,
% 1.25/1.45 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.25/1.45 inference(symmetry,[status(thm)],[6687])).
% 1.25/1.45 tff(6689,plain,
% 1.25/1.45 (b(elem!1, s(s(elem!1)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[57, 6688])).
% 1.25/1.45 tff(6690,plain,
% 1.25/1.45 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3317, 6628, 6594, 415, 6689, 6686, 159])).
% 1.25/1.45 tff(6691,plain,
% 1.25/1.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[223, 6690, 209])).
% 1.25/1.45 tff(6692,plain,
% 1.25/1.45 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3439, 6691, 169, 167, 6601, 6591])).
% 1.25/1.45 tff(6693,plain,
% 1.25/1.45 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1624, 6692])).
% 1.25/1.45 tff(6694,plain,
% 1.25/1.45 (~b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2798, 6693, 1457, 6601])).
% 1.25/1.45 tff(6695,plain,
% 1.25/1.45 (r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1781, 6694])).
% 1.25/1.45 tff(6696,plain,
% 1.25/1.45 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6591])).
% 1.25/1.45 tff(6697,plain,
% 1.25/1.45 (r(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6628, 6696])).
% 1.25/1.45 tff(6698,plain,
% 1.25/1.45 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[5262, 124, 6697, 6695])).
% 1.25/1.45 tff(6699,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6700,plain,
% 1.25/1.45 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6701,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6700])).
% 1.25/1.45 tff(6702,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6701, 6699])).
% 1.25/1.45 tff(6703,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6704,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6703, 6702])).
% 1.25/1.45 tff(6705,plain,
% 1.25/1.45 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6704, 124, 306, 6695])).
% 1.25/1.45 tff(6706,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2695, 6705, 6698, 6685, 6680, 6674, 6630])).
% 1.25/1.45 tff(6707,plain,((~(s(s(z)) = s(elem!1))) | (~r(s(elem!1), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | r(s(z), s(s(elem!1))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6708,plain,
% 1.25/1.45 (~(s(s(z)) = s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6707, 6589, 1457, 169, 150, 114, 306, 24, 63])).
% 1.25/1.45 tff(6709,plain,
% 1.25/1.45 (b(s(s(z)), s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6358, 6708])).
% 1.25/1.45 tff(6710,plain,
% 1.25/1.45 ((~(s(s(z)) = s(elem!1))) <=> (~(s(elem!1) = s(s(z))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[1245])).
% 1.25/1.45 tff(6711,plain,
% 1.25/1.45 (~(s(elem!1) = s(s(z)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6708, 6710])).
% 1.25/1.45 tff(6712,plain,
% 1.25/1.45 (b(s(elem!1), s(s(z)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[488, 6711, 1233])).
% 1.25/1.45 tff(6713,plain,
% 1.25/1.45 (~(elem!1 = s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[280, 6711])).
% 1.25/1.45 tff(6714,plain,
% 1.25/1.45 (r(elem!1, s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[363, 6713, 1400])).
% 1.25/1.45 tff(6715,plain,
% 1.25/1.45 (~r(elem!1, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[5000, 6714, 306])).
% 1.25/1.45 tff(6716,plain,
% 1.25/1.45 (b(elem!1, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[629, 6715, 387])).
% 1.25/1.45 tff(6717,plain,
% 1.25/1.45 (~b(elem!1, s(s(z)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4760, 238, 6716, 6712, 6709])).
% 1.25/1.45 tff(6718,plain,
% 1.25/1.45 (~r(elem!1, s(s(z)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2461, 124, 169, 6714])).
% 1.25/1.45 tff(6719,plain,
% 1.25/1.45 (elem!1 = s(s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[763, 6718, 6717])).
% 1.25/1.45 tff(6720,plain,
% 1.25/1.45 (~b(s(s(z)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4393, 238, 6716, 6712, 6709])).
% 1.25/1.45 tff(6721,plain,
% 1.25/1.45 (~r(s(s(z)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3252, 124, 169, 6714])).
% 1.25/1.45 tff(6722,plain,
% 1.25/1.45 (s(s(z)) = elem!1),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1275, 6721, 6720])).
% 1.25/1.45 tff(6723,plain,
% 1.25/1.45 (~r(s(elem!1), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2626, 124, 6714, 306])).
% 1.25/1.45 tff(6724,plain,
% 1.25/1.45 (b(s(elem!1), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[408, 6723, 394])).
% 1.25/1.45 tff(6725,plain,
% 1.25/1.45 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1385, 6722])).
% 1.25/1.45 tff(6726,plain,
% 1.25/1.45 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4990, 6725, 169, 306, 6714])).
% 1.25/1.45 tff(6727,plain,
% 1.25/1.45 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1624, 6726])).
% 1.25/1.45 tff(6728,plain,
% 1.25/1.45 (~r(z, s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6551, 6727, 4225, 169, 6716, 1457, 1233, 209, 6724, 6722, 6719])).
% 1.25/1.45 tff(6729,plain,
% 1.25/1.45 (b(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4855, 6727, 6722])).
% 1.25/1.45 tff(6730,plain,
% 1.25/1.45 (~b(z, s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4875, 6729, 57, 1457])).
% 1.25/1.45 tff(6731,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2071, 6730, 6728])).
% 1.25/1.45 tff(6732,plain,(b(elem!1, s(z)) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (elem!1 = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | r(s(z), s(s(elem!1))) | r(s(z), s(s(s(elem!1)))) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6733,plain,
% 1.25/1.45 (b(elem!1, s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6732, 5414, 169, 1457, 150, 22, 6368, 63, 1808])).
% 1.25/1.45 tff(6734,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6735,plain,
% 1.25/1.45 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6736,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z)))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6735])).
% 1.25/1.45 tff(6737,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6736, 6734])).
% 1.25/1.45 tff(6738,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6739,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(z)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6738, 6737])).
% 1.25/1.45 tff(6740,plain,
% 1.25/1.45 (~b(z, elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6739, 238, 6369, 6733, 1457])).
% 1.25/1.45 tff(6741,plain,
% 1.25/1.45 ((z = elem!1) | r(z, elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3134, 51, 6740])).
% 1.25/1.45 tff(6742,plain,
% 1.25/1.45 (r(z, elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6741, 6102])).
% 1.25/1.45 tff(6743,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6744,plain,
% 1.25/1.45 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6745,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6744])).
% 1.25/1.45 tff(6746,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6745, 6743])).
% 1.25/1.45 tff(6747,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6748,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6747, 6746])).
% 1.25/1.45 tff(6749,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6748, 124, 301, 2026, 6327])).
% 1.25/1.45 tff(6750,plain,((~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6751,plain,
% 1.25/1.45 (~r(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6750, 6371, 6742])).
% 1.25/1.45 tff(6752,plain,
% 1.25/1.45 (b(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[255, 6751, 167])).
% 1.25/1.45 tff(6753,plain,
% 1.25/1.45 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3152, 6752, 4225, 6369])).
% 1.25/1.45 tff(6754,plain,
% 1.25/1.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[223, 6753, 209])).
% 1.25/1.45 tff(6755,plain,
% 1.25/1.45 (~r(s(s(s(elem!1))), z)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3520, 6754, 6371])).
% 1.25/1.45 tff(6756,plain,
% 1.25/1.45 (b(s(s(s(elem!1))), z)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6058, 51, 821, 6755])).
% 1.25/1.45 tff(6757,plain,
% 1.25/1.45 (~r(z, s(s(s(elem!1))))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[5525, 6754, 6371])).
% 1.25/1.45 tff(6758,plain,
% 1.25/1.45 (b(z, s(s(s(elem!1))))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3795, 51, 6757, 3785])).
% 1.25/1.45 tff(6759,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6760,plain,
% 1.25/1.45 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6761,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6760])).
% 1.25/1.45 tff(6762,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6761, 6759])).
% 1.25/1.45 tff(6763,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6764,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6763, 6762])).
% 1.25/1.45 tff(6765,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6764, 238, 4225, 1457, 6758, 6756])).
% 1.25/1.45 tff(6766,plain,(b(s(elem!1), s(z)) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | r(s(z), s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6767,plain,
% 1.25/1.45 (b(s(elem!1), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6766, 150, 80, 1457, 63, 1])).
% 1.25/1.45 tff(6768,plain,
% 1.25/1.45 (~b(s(elem!1), z)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6164, 238, 6767, 4225, 1457])).
% 1.25/1.45 tff(6769,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.25/1.45 tff(6770,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 1.25/1.45 tff(6771,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[1884, 51, 39, 6770, 6769])).
% 1.25/1.45 tff(6772,plain,(b(s(elem!1), z) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6773,plain,
% 1.25/1.45 (r(s(elem!1), z)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6772, 6768])).
% 1.25/1.45 tff(6774,plain,
% 1.25/1.45 (~(s(elem!1) = s(s(z)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[5817, 6767, 64])).
% 1.25/1.45 tff(6775,plain,
% 1.25/1.45 (~b(z, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6043, 238, 1152, 546, 1457])).
% 1.25/1.45 tff(6776,plain,
% 1.25/1.45 ((z = s(elem!1)) | r(z, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3115, 51, 6775])).
% 1.25/1.45 tff(6777,plain,
% 1.25/1.45 (r(z, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6776, 3105])).
% 1.25/1.45 tff(6778,plain,
% 1.25/1.45 (~r(s(z), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6233, 1400, 546, 1, 169, 150, 278])).
% 1.25/1.45 tff(6779,plain,
% 1.25/1.45 (b(s(z), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[56, 6778])).
% 1.25/1.45 tff(6780,plain,
% 1.25/1.45 (r(elem!1, s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[363, 1400, 4576])).
% 1.25/1.45 tff(6781,plain,
% 1.25/1.45 (~b(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3192, 226, 546, 1137])).
% 1.25/1.45 tff(6782,plain,
% 1.25/1.45 (r(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[112, 6781])).
% 1.25/1.45 tff(6783,plain,
% 1.25/1.45 (~b(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[3152, 226, 546, 1137])).
% 1.25/1.45 tff(6784,plain,
% 1.25/1.45 (r(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[255, 6783, 248])).
% 1.25/1.45 tff(6785,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[263, 6784, 6782, 1370])).
% 1.25/1.45 tff(6786,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (s(s(elem!1)) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6787,plain,
% 1.25/1.45 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6786, 6780, 167, 546, 6779])).
% 1.25/1.45 tff(6788,plain,
% 1.25/1.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[223, 6787, 209])).
% 1.25/1.45 tff(6789,plain,
% 1.25/1.45 (~r(s(elem!1), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[5635, 6788, 546, 1152, 415])).
% 1.25/1.45 tff(6790,plain,
% 1.25/1.45 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[534, 6789, 159])).
% 1.25/1.45 tff(6791,plain,
% 1.25/1.45 (~b(s(s(elem!1)), s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4533, 6790, 1152, 6779])).
% 1.25/1.45 tff(6792,plain,
% 1.25/1.45 (r(s(s(elem!1)), s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[323, 6791, 272])).
% 1.25/1.45 tff(6793,plain,
% 1.25/1.45 (~r(z, s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4930, 124, 6792, 6777])).
% 1.25/1.45 tff(6794,plain,
% 1.25/1.45 (b(z, s(s(elem!1)))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[2071, 6793])).
% 1.25/1.45 tff(6795,plain,
% 1.25/1.45 (~b(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[4875, 6794, 6779, 1457])).
% 1.25/1.45 tff(6796,plain,
% 1.25/1.45 (r(s(s(elem!1)), s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[112, 6795])).
% 1.25/1.45 tff(6797,plain,
% 1.25/1.45 (~r(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[263, 6796, 6780])).
% 1.25/1.45 tff(6798,plain,
% 1.25/1.45 (b(s(s(elem!1)), elem!1)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[255, 6797, 167])).
% 1.25/1.45 tff(6799,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6800,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6801,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6800, 6799])).
% 1.25/1.45 tff(6802,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6801, 238, 6798, 6779, 6794, 1457])).
% 1.25/1.45 tff(6803,plain,(b(elem!1, s(z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6804,plain,
% 1.25/1.45 (b(elem!1, s(z))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6803, 6767, 1457, 4225, 1, 80, 150, 6774])).
% 1.25/1.45 tff(6805,plain,
% 1.25/1.45 (~b(elem!1, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6240, 238, 6804, 6767, 4225])).
% 1.25/1.45 tff(6806,plain,
% 1.25/1.45 (r(elem!1, s(elem!1))),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[629, 6805, 387])).
% 1.25/1.45 tff(6807,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.25/1.45 tff(6808,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6809,plain,
% 1.25/1.45 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6810,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z))))),
% 1.25/1.45 inference(monotonicity,[status(thm)],[6809])).
% 1.25/1.45 tff(6811,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 1.25/1.45 inference(transitivity,[status(thm)],[6810, 6808])).
% 1.25/1.45 tff(6812,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 1.25/1.45 inference(quant_inst,[status(thm)],[])).
% 1.25/1.45 tff(6813,plain,
% 1.25/1.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)) | (~r(elem!1, z))),
% 1.25/1.45 inference(modus_ponens,[status(thm)],[6812, 6811])).
% 1.25/1.45 tff(6814,plain,
% 1.25/1.45 ($false),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6813, 124, 590, 5067, 6807])).
% 1.25/1.45 tff(6815,plain,((~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.45 tff(6816,plain,
% 1.25/1.45 (~r(elem!1, z)),
% 1.25/1.45 inference(unit_resolution,[status(thm)],[6815, 6806, 6773])).
% 1.25/1.45 tff(6817,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6818,plain,
% 1.25/1.45 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.45 inference(rewrite,[status(thm)],[])).
% 1.25/1.45 tff(6819,plain,
% 1.25/1.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6818])).
% 1.25/1.46 tff(6820,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6819, 6817])).
% 1.25/1.46 tff(6821,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6822,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6821, 6820])).
% 1.25/1.46 tff(6823,plain,
% 1.25/1.46 (~b(elem!1, z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6822, 238, 6804, 4225, 1457])).
% 1.25/1.46 tff(6824,plain,
% 1.25/1.46 ($false),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[4843, 51, 6823, 4831, 6816])).
% 1.25/1.46 tff(6825,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(z)), s(z)) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.46 tff(6826,plain,
% 1.25/1.46 (elem!1 = s(s(elem!1))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6825, 63, 1, 64, 1457])).
% 1.25/1.46 tff(6827,plain,
% 1.25/1.46 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6826])).
% 1.25/1.46 tff(6828,plain,
% 1.25/1.46 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 1.25/1.46 inference(symmetry,[status(thm)],[6827])).
% 1.25/1.46 tff(6829,plain,
% 1.25/1.46 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6828])).
% 1.25/1.46 tff(6830,plain,
% 1.25/1.46 (~r(s(s(z)), s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[130, 124, 169, 162])).
% 1.25/1.46 tff(6831,plain,
% 1.25/1.46 (b(s(s(z)), s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[135, 6830, 114])).
% 1.25/1.46 tff(6832,plain,
% 1.25/1.46 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[5222, 2597, 114])).
% 1.25/1.46 tff(6833,plain,
% 1.25/1.46 (~r(s(s(elem!1)), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[2523, 124, 169, 162])).
% 1.25/1.46 tff(6834,plain,
% 1.25/1.46 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[5230, 51, 6833])).
% 1.25/1.46 tff(6835,plain,
% 1.25/1.46 (b(s(s(elem!1)), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6834, 5226])).
% 1.25/1.46 tff(6836,plain,
% 1.25/1.46 (~r(s(s(s(s(z)))), s(z))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[5246, 6835, 169, 162, 6832, 6831])).
% 1.25/1.46 tff(6837,plain,
% 1.25/1.46 (b(s(s(s(s(z)))), s(z))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1624, 6836])).
% 1.25/1.46 tff(6838,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6839,plain,
% 1.25/1.46 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6840,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6839])).
% 1.25/1.46 tff(6841,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6840, 6838])).
% 1.25/1.46 tff(6842,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6843,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6842, 6841])).
% 1.25/1.46 tff(6844,plain,
% 1.25/1.46 (~b(s(s(s(s(z)))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6843, 238, 546, 1457, 6837])).
% 1.25/1.46 tff(6845,plain,
% 1.25/1.46 (r(s(s(s(s(z)))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1499, 51, 726, 6844])).
% 1.25/1.46 tff(6846,plain,
% 1.25/1.46 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[2991, 226, 546, 1784])).
% 1.25/1.46 tff(6847,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6848,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6849,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6848, 6847])).
% 1.25/1.46 tff(6850,plain,
% 1.25/1.46 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6849, 238, 227, 226, 5238])).
% 1.25/1.46 tff(6851,plain,
% 1.25/1.46 (r(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[3233, 6850])).
% 1.25/1.46 tff(6852,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6853,plain,
% 1.25/1.46 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6854,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6853])).
% 1.25/1.46 tff(6855,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6854, 6852])).
% 1.25/1.46 tff(6856,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6857,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6856, 6855])).
% 1.25/1.46 tff(6858,plain,
% 1.25/1.46 (~r(z, s(s(s(elem!1))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6857, 124, 3002, 1575])).
% 1.25/1.46 tff(6859,plain,
% 1.25/1.46 (b(z, s(s(s(elem!1))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[3795, 51, 6858, 3785])).
% 1.25/1.46 tff(6860,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6861,plain,
% 1.25/1.46 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6862,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6861])).
% 1.25/1.46 tff(6863,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6862, 6860])).
% 1.25/1.46 tff(6864,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6865,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 1.25/1.46 tff(6866,plain,
% 1.25/1.46 (~r(s(s(s(elem!1))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6865, 124, 3002, 1575])).
% 1.25/1.46 tff(6867,plain,
% 1.25/1.46 (b(s(s(s(elem!1))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6058, 51, 821, 6866])).
% 1.25/1.46 tff(6868,plain,
% 1.25/1.46 ($false),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6764, 238, 546, 1457, 6867, 6859])).
% 1.25/1.46 tff(6869,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.46 tff(6870,plain,
% 1.25/1.46 (~r(z, s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6869, 6851, 1457, 546])).
% 1.25/1.46 tff(6871,plain,
% 1.25/1.46 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1511, 51, 6870])).
% 1.25/1.46 tff(6872,plain,
% 1.25/1.46 (b(z, s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6871, 1450])).
% 1.25/1.46 tff(6873,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6874,plain,
% 1.25/1.46 (((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6875,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6874])).
% 1.25/1.46 tff(6876,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6875, 6873])).
% 1.25/1.46 tff(6877,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6878,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 1.25/1.46 tff(6879,plain,
% 1.25/1.46 (~b(s(s(elem!1)), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6878, 238, 227, 6872, 5238])).
% 1.25/1.46 tff(6880,plain,
% 1.25/1.46 (r(s(s(elem!1)), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[4030, 51, 92, 6879])).
% 1.25/1.46 tff(6881,plain,
% 1.25/1.46 (~b(s(s(s(s(z)))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6843, 238, 546, 1457, 1784])).
% 1.25/1.46 tff(6882,plain,
% 1.25/1.46 (r(s(s(s(s(z)))), z)),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1499, 51, 726, 6881])).
% 1.25/1.46 tff(6883,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6884,plain,
% 1.25/1.46 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6885,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 1.25/1.46 inference(monotonicity,[status(thm)],[6884])).
% 1.25/1.46 tff(6886,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.46 inference(transitivity,[status(thm)],[6885, 6883])).
% 1.25/1.46 tff(6887,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6888,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6887, 6886])).
% 1.25/1.46 tff(6889,plain,
% 1.25/1.46 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6888, 124, 6882, 6880])).
% 1.25/1.46 tff(6890,plain,
% 1.25/1.46 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[5236, 51, 5233, 6889])).
% 1.25/1.46 tff(6891,plain,
% 1.25/1.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.25/1.46 inference(rewrite,[status(thm)],[])).
% 1.25/1.46 tff(6892,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.25/1.46 inference(quant_inst,[status(thm)],[])).
% 1.25/1.46 tff(6893,plain,
% 1.25/1.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.25/1.46 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 1.25/1.46 tff(6894,plain,
% 1.25/1.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6893, 238, 227, 5238, 6890])).
% 1.25/1.46 tff(6895,plain,
% 1.25/1.46 (r(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1564, 6894])).
% 1.25/1.46 tff(6896,plain,
% 1.25/1.46 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[3010, 6895, 6851])).
% 1.25/1.46 tff(6897,plain,
% 1.25/1.46 ($false),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[2974, 51, 6896, 6846, 3797])).
% 1.25/1.46 tff(6898,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.46 tff(6899,plain,
% 1.25/1.46 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6898, 6837, 6831, 6835, 6832, 1457, 546, 2963])).
% 1.25/1.46 tff(6900,plain,
% 1.25/1.46 (~b(s(z), s(s(s(s(z)))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[2798, 1783, 1457, 1784])).
% 1.25/1.46 tff(6901,plain,
% 1.25/1.46 (r(s(z), s(s(s(s(z)))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[6600, 6900])).
% 1.25/1.46 tff(6902,plain,
% 1.25/1.46 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[4153, 1783, 546, 1784])).
% 1.25/1.46 tff(6903,plain,
% 1.25/1.46 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[1904, 6902])).
% 1.25/1.46 tff(6904,plain,
% 1.25/1.46 (~b(s(z), s(s(s(s(s(z))))))),
% 1.25/1.46 inference(unit_resolution,[status(thm)],[3641, 1783, 1457, 1784])).
% 1.25/1.46 tff(6905,plain,
% 1.25/1.46 (r(s(z), s(s(s(s(s(z))))))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[1709, 6904])).
% 1.25/1.47 tff(6906,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[1660, 6905, 6903, 6901])).
% 1.25/1.47 tff(6907,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6908,plain,
% 1.25/1.47 (~b(s(s(s(s(s(z))))), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6907, 6837, 1457, 546])).
% 1.25/1.47 tff(6909,plain,
% 1.25/1.47 (r(s(s(s(s(s(z))))), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[1781, 6908])).
% 1.25/1.47 tff(6910,plain,
% 1.25/1.47 (~(s(elem!1) = elem!1)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[5283, 6909, 6835, 2073, 6831, 162, 169])).
% 1.25/1.47 tff(6911,plain,
% 1.25/1.47 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[5315, 6910, 2073])).
% 1.25/1.47 tff(6912,plain,
% 1.25/1.47 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[223, 6911, 6899])).
% 1.25/1.47 tff(6913,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6914,plain,
% 1.25/1.47 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6915,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6914])).
% 1.25/1.47 tff(6916,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6915, 6913])).
% 1.25/1.47 tff(6917,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6918,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6917, 6916])).
% 1.25/1.47 tff(6919,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6918, 124, 210, 162, 2964])).
% 1.25/1.47 tff(6920,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6921,plain,
% 1.25/1.47 (~r(s(s(s(elem!1))), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6920, 6912, 162])).
% 1.25/1.47 tff(6922,plain,
% 1.25/1.47 (b(s(s(s(elem!1))), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[576, 51, 94, 6921])).
% 1.25/1.47 tff(6923,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.25/1.47 tff(6924,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.25/1.47 tff(6925,assumption,(b(s(z), z)), introduced(assumption)).
% 1.25/1.47 tff(6926,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6927,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6928,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 1.25/1.47 tff(6929,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6928, 238, 564, 1457, 6923, 6925])).
% 1.25/1.47 tff(6930,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6931,plain,
% 1.25/1.47 (~b(s(z), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6930, 6923, 1457, 564])).
% 1.25/1.47 tff(6932,plain,
% 1.25/1.47 (r(s(z), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[5701, 6931])).
% 1.25/1.47 tff(6933,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6934,plain,
% 1.25/1.47 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6935,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6934])).
% 1.25/1.47 tff(6936,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6935, 6933])).
% 1.25/1.47 tff(6937,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6938,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6937, 6936])).
% 1.25/1.47 tff(6939,plain,
% 1.25/1.47 (~r(s(z), s(s(s(s(z)))))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6938, 124, 6932, 6924])).
% 1.25/1.47 tff(6940,plain,
% 1.25/1.47 (b(s(z), s(s(s(s(z)))))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6600, 6939])).
% 1.25/1.47 tff(6941,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6942,plain,
% 1.25/1.47 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6943,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6942])).
% 1.25/1.47 tff(6944,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6943, 6941])).
% 1.25/1.47 tff(6945,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6946,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6945, 6944])).
% 1.25/1.47 tff(6947,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6946, 238, 6940, 564, 1457, 6923])).
% 1.25/1.47 tff(6948,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6949,plain,
% 1.25/1.47 (~b(s(s(s(elem!1))), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6948, 6922, 1457, 6845])).
% 1.25/1.47 tff(6950,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.25/1.47 tff(6951,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6058, 51, 821, 4264, 6950])).
% 1.25/1.47 tff(6952,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6953,plain,
% 1.25/1.47 (r(s(s(s(elem!1))), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6952, 6949])).
% 1.25/1.47 tff(6954,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6955,plain,
% 1.25/1.47 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6956,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6955])).
% 1.25/1.47 tff(6957,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6956, 6954])).
% 1.25/1.47 tff(6958,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6959,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6958, 6957])).
% 1.25/1.47 tff(6960,plain,
% 1.25/1.47 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6959, 124, 6953, 6845])).
% 1.25/1.47 tff(6961,plain,
% 1.25/1.47 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[2974, 51, 6960, 2963])).
% 1.25/1.47 tff(6962,plain,
% 1.25/1.47 ($false),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[3994, 238, 6922, 546, 6837, 6961])).
% 1.25/1.47 tff(6963,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.47 tff(6964,plain,
% 1.25/1.47 (~r(s(s(elem!1)), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6963, 4225, 1457, 6826, 80, 22])).
% 1.25/1.47 tff(6965,plain,
% 1.25/1.47 (b(s(s(elem!1)), s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[112, 6964])).
% 1.25/1.47 tff(6966,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6967,plain,
% 1.25/1.47 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6968,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6967])).
% 1.25/1.47 tff(6969,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6968, 6966])).
% 1.25/1.47 tff(6970,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6971,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6970, 6969])).
% 1.25/1.47 tff(6972,plain,
% 1.25/1.47 (~b(s(s(elem!1)), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6971, 238, 4225, 6965, 1457])).
% 1.25/1.47 tff(6973,plain,
% 1.25/1.47 (r(s(s(elem!1)), z)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[4905, 6972])).
% 1.25/1.47 tff(6974,plain,
% 1.25/1.47 ((elem!1 = s(z)) <=> (s(s(elem!1)) = s(z))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6826])).
% 1.25/1.47 tff(6975,plain,
% 1.25/1.47 ((elem!1 = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6974, 2369])).
% 1.25/1.47 tff(6976,plain,
% 1.25/1.47 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 1.25/1.47 inference(symmetry,[status(thm)],[6975])).
% 1.25/1.47 tff(6977,plain,
% 1.25/1.47 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6976])).
% 1.25/1.47 tff(6978,plain,
% 1.25/1.47 (~(elem!1 = s(z))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[41, 6977])).
% 1.25/1.47 tff(6979,plain,
% 1.25/1.47 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6826])).
% 1.25/1.47 tff(6980,plain,
% 1.25/1.47 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.25/1.47 inference(symmetry,[status(thm)],[6979])).
% 1.25/1.47 tff(6981,plain,
% 1.25/1.47 ((~r(s(s(elem!1)), s(z))) <=> (~r(elem!1, s(z)))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6980])).
% 1.25/1.47 tff(6982,plain,
% 1.25/1.47 (~r(elem!1, s(z))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6964, 6981])).
% 1.25/1.47 tff(6983,plain,
% 1.25/1.47 (b(elem!1, s(z))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[363, 6982, 6978])).
% 1.25/1.47 tff(6984,plain,
% 1.25/1.47 (s(s(elem!1)) = elem!1),
% 1.25/1.47 inference(symmetry,[status(thm)],[6826])).
% 1.25/1.47 tff(6985,plain,
% 1.25/1.47 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6984])).
% 1.25/1.47 tff(6986,plain,
% 1.25/1.47 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6985, 767])).
% 1.25/1.47 tff(6987,plain,
% 1.25/1.47 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.25/1.47 inference(transitivity,[status(thm)],[6986, 789])).
% 1.25/1.47 tff(6988,plain,
% 1.25/1.47 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6987])).
% 1.25/1.47 tff(6989,plain,
% 1.25/1.47 (s(elem!1) = s(s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[2097, 6826])).
% 1.25/1.47 tff(6990,plain,
% 1.25/1.47 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[5222, 6989, 22])).
% 1.25/1.47 tff(6991,plain,
% 1.25/1.47 (~(s(s(s(s(z)))) = elem!1)),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6990, 6988])).
% 1.25/1.47 tff(6992,plain,
% 1.25/1.47 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6826])).
% 1.25/1.47 tff(6993,plain,
% 1.25/1.47 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.25/1.47 inference(symmetry,[status(thm)],[6992])).
% 1.25/1.47 tff(6994,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6995,plain,
% 1.25/1.47 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(6996,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[6995])).
% 1.25/1.47 tff(6997,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.25/1.47 inference(transitivity,[status(thm)],[6996, 6994])).
% 1.25/1.47 tff(6998,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(6999,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[6998, 6997])).
% 1.25/1.47 tff(7000,plain,
% 1.25/1.47 (~b(z, s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[6999, 238, 4225, 6965, 1457])).
% 1.25/1.47 tff(7001,plain,
% 1.25/1.47 (r(z, s(s(elem!1)))),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[2071, 7000])).
% 1.25/1.47 tff(7002,plain,
% 1.25/1.47 (r(z, elem!1)),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[7001, 6993])).
% 1.25/1.47 tff(7003,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(7004,plain,
% 1.25/1.47 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(7005,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.25/1.47 inference(monotonicity,[status(thm)],[7004])).
% 1.25/1.47 tff(7006,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.25/1.47 inference(transitivity,[status(thm)],[7005, 7003])).
% 1.25/1.47 tff(7007,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.25/1.47 inference(quant_inst,[status(thm)],[])).
% 1.25/1.47 tff(7008,plain,
% 1.25/1.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.25/1.47 inference(modus_ponens,[status(thm)],[7007, 7006])).
% 1.25/1.47 tff(7009,plain,
% 1.25/1.47 (~b(s(s(s(s(z)))), elem!1)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[7008, 238, 370, 546, 1784])).
% 1.25/1.47 tff(7010,plain,
% 1.25/1.47 (r(s(s(s(s(z)))), elem!1)),
% 1.25/1.47 inference(unit_resolution,[status(thm)],[2131, 7009, 2950])).
% 1.25/1.47 tff(7011,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(7012,plain,
% 1.25/1.47 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)))),
% 1.25/1.47 inference(rewrite,[status(thm)],[])).
% 1.25/1.47 tff(7013,plain,
% 1.25/1.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7012])).
% 1.25/1.48 tff(7014,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7013, 7011])).
% 1.25/1.48 tff(7015,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.25/1.48 inference(quant_inst,[status(thm)],[])).
% 1.25/1.48 tff(7016,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 1.25/1.48 tff(7017,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7016, 124, 7010, 6327, 6882])).
% 1.25/1.48 tff(7018,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7019,plain,
% 1.25/1.48 (~b(s(s(s(s(z)))), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7018, 7002, 6991, 4225, 1457, 6983])).
% 1.25/1.48 tff(7020,plain,
% 1.25/1.48 (r(s(s(s(s(z)))), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1624, 7019])).
% 1.25/1.48 tff(7021,plain,
% 1.25/1.48 (~r(s(s(s(z))), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[5185, 7020, 80])).
% 1.25/1.48 tff(7022,plain,
% 1.25/1.48 (b(s(s(s(z))), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[5118, 7021])).
% 1.25/1.48 tff(7023,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7024,plain,
% 1.25/1.48 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7025,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7024])).
% 1.25/1.48 tff(7026,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7025, 7023])).
% 1.25/1.48 tff(7027,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 1.25/1.48 inference(quant_inst,[status(thm)],[])).
% 1.25/1.48 tff(7028,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7027, 7026])).
% 1.25/1.48 tff(7029,plain,
% 1.25/1.48 (~b(s(s(s(z))), z)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7028, 238, 4225, 1457, 7022])).
% 1.25/1.48 tff(7030,plain,
% 1.25/1.48 (r(s(s(s(z))), z)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1524, 7029])).
% 1.25/1.48 tff(7031,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7032,plain,
% 1.25/1.48 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7033,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7032])).
% 1.25/1.48 tff(7034,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7033, 7031])).
% 1.25/1.48 tff(7035,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.25/1.48 inference(quant_inst,[status(thm)],[])).
% 1.25/1.48 tff(7036,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7035, 7034])).
% 1.25/1.48 tff(7037,plain,
% 1.25/1.48 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7036, 124, 7030, 6973])).
% 1.25/1.48 tff(7038,plain,
% 1.25/1.48 (~r(s(s(s(z))), elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7037, 6829])).
% 1.25/1.48 tff(7039,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.25/1.48 tff(7040,plain,
% 1.25/1.48 (s(s(s(z))) = s(s(elem!1))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7039, 2073])).
% 1.25/1.48 tff(7041,plain,
% 1.25/1.48 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7040])).
% 1.25/1.48 tff(7042,plain,
% 1.25/1.48 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7041])).
% 1.25/1.48 tff(7043,plain,
% 1.25/1.48 (s(s(s(elem!1))) = s(elem!1)),
% 1.25/1.48 inference(symmetry,[status(thm)],[2597])).
% 1.25/1.48 tff(7044,plain,
% 1.25/1.48 (s(s(s(elem!1))) = s(s(z))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7043, 18, 7042, 138])).
% 1.25/1.48 tff(7045,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1291, 7044])).
% 1.25/1.48 tff(7046,plain,((~(s(s(s(z))) = elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7047,plain,
% 1.25/1.48 (~(s(s(s(z))) = elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7046, 6826])).
% 1.25/1.48 tff(7048,plain,
% 1.25/1.48 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[6984])).
% 1.25/1.48 tff(7049,plain,
% 1.25/1.48 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7048])).
% 1.25/1.48 tff(7050,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7051,plain,
% 1.25/1.48 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7052,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7051])).
% 1.25/1.48 tff(7053,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7052, 7050])).
% 1.25/1.48 tff(7054,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.25/1.48 inference(quant_inst,[status(thm)],[])).
% 1.25/1.48 tff(7055,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7054, 7053])).
% 1.25/1.48 tff(7056,plain,
% 1.25/1.48 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7055, 238, 4225, 6965, 7022])).
% 1.25/1.48 tff(7057,plain,
% 1.25/1.48 (~b(s(s(s(z))), elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7056, 7049])).
% 1.25/1.48 tff(7058,plain,
% 1.25/1.48 (r(s(s(s(z))), elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[5094, 7057, 7047])).
% 1.25/1.48 tff(7059,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7058, 7038])).
% 1.25/1.48 tff(7060,plain,(r(s(z), s(s(s(elem!1)))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7061,plain,
% 1.25/1.48 (s(elem!1) = s(z)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7060, 6301, 64, 63])).
% 1.25/1.48 tff(7062,plain,
% 1.25/1.48 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7061])).
% 1.25/1.48 tff(7063,plain,
% 1.25/1.48 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7062])).
% 1.25/1.48 tff(7064,plain,
% 1.25/1.48 (z = elem!1),
% 1.25/1.48 inference(transitivity,[status(thm)],[769, 7063, 154])).
% 1.25/1.48 tff(7065,plain,
% 1.25/1.48 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7064])).
% 1.25/1.48 tff(7066,plain,
% 1.25/1.48 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.25/1.48 inference(symmetry,[status(thm)],[7065])).
% 1.25/1.48 tff(7067,plain,
% 1.25/1.48 (elem!1 = z),
% 1.25/1.48 inference(transitivity,[status(thm)],[155, 7062, 26])).
% 1.25/1.48 tff(7068,plain,
% 1.25/1.48 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = z)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7067])).
% 1.25/1.48 tff(7069,plain,
% 1.25/1.48 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.25/1.48 inference(symmetry,[status(thm)],[7068])).
% 1.25/1.48 tff(7070,plain,
% 1.25/1.48 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7069])).
% 1.25/1.48 tff(7071,plain,
% 1.25/1.48 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[1006, 7070])).
% 1.25/1.48 tff(7072,plain,
% 1.25/1.48 (s(s(z)) = s(s(elem!1))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[357, 7061])).
% 1.25/1.48 tff(7073,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7072])).
% 1.25/1.48 tff(7074,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7073, 3730])).
% 1.25/1.48 tff(7075,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(transitivity,[status(thm)],[7074, 4108])).
% 1.25/1.48 tff(7076,plain,
% 1.25/1.48 ((~(s(s(z)) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7075])).
% 1.25/1.48 tff(7077,plain,
% 1.25/1.48 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[4960, 7072])).
% 1.25/1.48 tff(7078,plain,
% 1.25/1.48 (~(s(s(z)) = elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1385, 7077])).
% 1.25/1.48 tff(7079,plain,
% 1.25/1.48 (~(s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7078, 7076])).
% 1.25/1.48 tff(7080,plain,
% 1.25/1.48 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7067])).
% 1.25/1.48 tff(7081,plain,
% 1.25/1.48 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.25/1.48 inference(symmetry,[status(thm)],[7080])).
% 1.25/1.48 tff(7082,plain,
% 1.25/1.48 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7081])).
% 1.25/1.48 tff(7083,plain,
% 1.25/1.48 (s(s(elem!1)) = s(s(z))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7072])).
% 1.25/1.48 tff(7084,plain,
% 1.25/1.48 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7083])).
% 1.25/1.48 tff(7085,plain,
% 1.25/1.48 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7084])).
% 1.25/1.48 tff(7086,plain,
% 1.25/1.48 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7072])).
% 1.25/1.48 tff(7087,plain,
% 1.25/1.48 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7086])).
% 1.25/1.48 tff(7088,plain,
% 1.25/1.48 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7087])).
% 1.25/1.48 tff(7089,plain,
% 1.25/1.48 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7072])).
% 1.25/1.48 tff(7090,plain,
% 1.25/1.48 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7089])).
% 1.25/1.48 tff(7091,plain,
% 1.25/1.48 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[1291, 7090])).
% 1.25/1.48 tff(7092,plain,
% 1.25/1.48 (~b(s(s(elem!1)), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[5399, 7072, 64])).
% 1.25/1.48 tff(7093,plain,
% 1.25/1.48 (r(s(s(elem!1)), s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[112, 7092])).
% 1.25/1.48 tff(7094,plain,
% 1.25/1.48 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[807])).
% 1.25/1.48 tff(7095,plain,
% 1.25/1.48 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[807])).
% 1.25/1.48 tff(7096,plain,
% 1.25/1.48 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7095])).
% 1.25/1.48 tff(7097,plain,
% 1.25/1.48 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7096])).
% 1.25/1.48 tff(7098,plain,
% 1.25/1.48 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[806])).
% 1.25/1.48 tff(7099,plain,
% 1.25/1.48 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7098])).
% 1.25/1.48 tff(7100,plain,
% 1.25/1.48 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7099])).
% 1.25/1.48 tff(7101,plain,
% 1.25/1.48 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[5165, 7100])).
% 1.25/1.48 tff(7102,plain,
% 1.25/1.48 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7101, 7097])).
% 1.25/1.48 tff(7103,plain,
% 1.25/1.48 (b(elem!1, s(z))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[6376, 353, 1457])).
% 1.25/1.48 tff(7104,plain,
% 1.25/1.48 (r(s(s(elem!1)), s(elem!1))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[162, 4089])).
% 1.25/1.48 tff(7105,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(monotonicity,[status(thm)],[804])).
% 1.25/1.48 tff(7106,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7105, 3730])).
% 1.25/1.48 tff(7107,plain,
% 1.25/1.48 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(transitivity,[status(thm)],[7106, 4108])).
% 1.25/1.48 tff(7108,plain,
% 1.25/1.48 ((~(s(s(z)) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7107])).
% 1.25/1.48 tff(7109,plain,
% 1.25/1.48 (~(s(s(z)) = elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1385, 5782])).
% 1.25/1.48 tff(7110,plain,
% 1.25/1.48 (~(s(s(elem!1)) = elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7109, 7108])).
% 1.25/1.48 tff(7111,plain,
% 1.25/1.48 (b(elem!1, s(elem!1))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[370, 4093])).
% 1.25/1.48 tff(7112,plain,
% 1.25/1.48 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[353])).
% 1.25/1.48 tff(7113,plain,
% 1.25/1.48 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7112])).
% 1.25/1.48 tff(7114,plain,
% 1.25/1.48 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7113])).
% 1.25/1.48 tff(7115,plain,
% 1.25/1.48 (~(s(elem!1) = s(s(elem!1)))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[41, 7114])).
% 1.25/1.48 tff(7116,plain,
% 1.25/1.48 (~r(s(elem!1), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[3876, 24, 353])).
% 1.25/1.48 tff(7117,plain,
% 1.25/1.48 (b(s(elem!1), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[534, 7116, 7115])).
% 1.25/1.48 tff(7118,plain,
% 1.25/1.48 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7106])).
% 1.25/1.48 tff(7119,plain,
% 1.25/1.48 (~(elem!1 = s(s(elem!1)))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7109, 7118])).
% 1.25/1.48 tff(7120,plain,
% 1.25/1.48 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.25/1.48 inference(transitivity,[status(thm)],[4082, 641])).
% 1.25/1.48 tff(7121,plain,
% 1.25/1.48 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7120])).
% 1.25/1.48 tff(7122,plain,
% 1.25/1.48 (~(s(s(s(elem!1))) = elem!1)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[821, 7121])).
% 1.25/1.48 tff(7123,plain,
% 1.25/1.48 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(z) = s(s(s(elem!1))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[353])).
% 1.25/1.48 tff(7124,plain,
% 1.25/1.48 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7123, 4237])).
% 1.25/1.48 tff(7125,plain,
% 1.25/1.48 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7124])).
% 1.25/1.48 tff(7126,plain,
% 1.25/1.48 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7125, 5535])).
% 1.25/1.48 tff(7127,plain,
% 1.25/1.48 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7126])).
% 1.25/1.48 tff(7128,plain,
% 1.25/1.48 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[94, 7127])).
% 1.25/1.48 tff(7129,plain,
% 1.25/1.48 (b(s(s(s(elem!1))), s(elem!1))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[459, 2709, 7128])).
% 1.25/1.48 tff(7130,plain,
% 1.25/1.48 (~b(elem!1, s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[1193, 7129, 631, 7110, 210, 288, 7122])).
% 1.25/1.48 tff(7131,plain,
% 1.25/1.48 (r(elem!1, s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[606, 7130, 7119])).
% 1.25/1.48 tff(7132,plain,
% 1.25/1.48 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[815])).
% 1.25/1.48 tff(7133,plain,
% 1.25/1.48 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 1.25/1.48 inference(symmetry,[status(thm)],[7132])).
% 1.25/1.48 tff(7134,plain,
% 1.25/1.48 (r(z, s(s(elem!1)))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[591, 7133])).
% 1.25/1.48 tff(7135,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[2066, 7134])).
% 1.25/1.48 tff(7136,plain,(r(z, s(s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7137,plain,
% 1.25/1.48 (r(z, s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7136, 7131, 353])).
% 1.25/1.48 tff(7138,plain,
% 1.25/1.48 (~b(s(s(s(elem!1))), elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[639, 7129, 631, 288])).
% 1.25/1.48 tff(7139,plain,
% 1.25/1.48 (r(s(s(s(elem!1))), elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[647, 7138, 7122])).
% 1.25/1.48 tff(7140,plain,
% 1.25/1.48 (r(s(s(s(elem!1))), z)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[4266, 7139, 353])).
% 1.25/1.48 tff(7141,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[3520, 7140, 7137, 210])).
% 1.25/1.48 tff(7142,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7143,plain,
% 1.25/1.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7142, 7117, 7111, 353, 307])).
% 1.25/1.48 tff(7144,plain,
% 1.25/1.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[223, 7143, 4087])).
% 1.25/1.48 tff(7145,plain,
% 1.25/1.48 (~b(s(s(elem!1)), elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[3152, 7144, 546, 57])).
% 1.25/1.48 tff(7146,plain,
% 1.25/1.48 (r(s(s(elem!1)), elem!1)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[255, 7145, 7110])).
% 1.25/1.48 tff(7147,plain,
% 1.25/1.48 (r(s(s(elem!1)), z)),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[301, 4103])).
% 1.25/1.48 tff(7148,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[4902, 7147])).
% 1.25/1.48 tff(7149,plain,(r(s(s(elem!1)), z) | (~r(s(s(elem!1)), elem!1)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.48 tff(7150,plain,
% 1.25/1.48 (r(s(s(elem!1)), z)),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7149, 7146, 353])).
% 1.25/1.48 tff(7151,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7152,plain,
% 1.25/1.48 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.25/1.48 inference(rewrite,[status(thm)],[])).
% 1.25/1.48 tff(7153,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.25/1.48 inference(monotonicity,[status(thm)],[7152])).
% 1.25/1.48 tff(7154,plain,
% 1.25/1.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.25/1.48 inference(transitivity,[status(thm)],[7153, 7151])).
% 1.25/1.48 tff(7155,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.25/1.48 inference(quant_inst,[status(thm)],[])).
% 1.25/1.48 tff(7156,plain,
% 1.25/1.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.25/1.48 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 1.25/1.48 tff(7157,plain,
% 1.25/1.48 ($false),
% 1.25/1.48 inference(unit_resolution,[status(thm)],[7156, 238, 1137, 226, 546, 744])).
% 1.25/1.48 tff(7158,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.49 tff(7159,plain,
% 1.25/1.49 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7158, 57, 7144, 546])).
% 1.25/1.49 tff(7160,plain,
% 1.25/1.49 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[2549, 51, 7159, 4185])).
% 1.25/1.49 tff(7161,plain,
% 1.25/1.49 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762])).
% 1.25/1.49 tff(7162,plain,
% 1.25/1.49 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7161])).
% 1.25/1.49 tff(7163,plain,
% 1.25/1.49 (~b(elem!1, s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[554, 7144, 546, 370])).
% 1.25/1.49 tff(7164,plain,
% 1.25/1.49 (~b(z, s(s(s(elem!1))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.25/1.49 tff(7165,plain,
% 1.25/1.49 (r(z, s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[3795, 51, 3785, 7164])).
% 1.25/1.49 tff(7166,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7167,plain,
% 1.25/1.49 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7168,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7167])).
% 1.25/1.49 tff(7169,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7168, 7166])).
% 1.25/1.49 tff(7170,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7171,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7170, 7169])).
% 1.25/1.49 tff(7172,plain,
% 1.25/1.49 ($false),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7171, 124, 7165, 7160, 7150])).
% 1.25/1.49 tff(7173,plain,(r(s(z), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(z))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.49 tff(7174,plain,
% 1.25/1.49 (r(s(z), s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7173, 546, 353, 7103, 7104])).
% 1.25/1.49 tff(7175,plain,
% 1.25/1.49 (~b(elem!1, s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[578, 7174, 546, 7103, 4087])).
% 1.25/1.49 tff(7176,plain,
% 1.25/1.49 (r(elem!1, s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1319, 7175, 4084])).
% 1.25/1.49 tff(7177,plain,
% 1.25/1.49 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762, 807])).
% 1.25/1.49 tff(7178,plain,
% 1.25/1.49 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7177])).
% 1.25/1.49 tff(7179,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 1.25/1.49 tff(7180,plain,
% 1.25/1.49 (s(s(s(s(z)))) = z),
% 1.25/1.49 inference(symmetry,[status(thm)],[7179])).
% 1.25/1.49 tff(7181,plain,
% 1.25/1.49 ($false),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[726, 7180])).
% 1.25/1.49 tff(7182,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.49 tff(7183,plain,
% 1.25/1.49 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762])).
% 1.25/1.49 tff(7184,plain,
% 1.25/1.49 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = z)),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762])).
% 1.25/1.49 tff(7185,plain,
% 1.25/1.49 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.25/1.49 inference(symmetry,[status(thm)],[7184])).
% 1.25/1.49 tff(7186,plain,
% 1.25/1.49 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7185])).
% 1.25/1.49 tff(7187,plain,
% 1.25/1.49 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[1006, 7186])).
% 1.25/1.49 tff(7188,plain,
% 1.25/1.49 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.25/1.49 inference(monotonicity,[status(thm)],[815])).
% 1.25/1.49 tff(7189,plain,
% 1.25/1.49 ((~b(s(s(s(s(s(z))))), z)) <=> (~b(s(s(s(s(s(z))))), elem!1))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7188])).
% 1.25/1.49 tff(7190,plain,
% 1.25/1.49 (~b(z, s(s(s(elem!1))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7175, 7162])).
% 1.25/1.49 tff(7191,plain,
% 1.25/1.49 (r(z, s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[3795, 51, 3785, 7190])).
% 1.25/1.49 tff(7192,plain,
% 1.25/1.49 (~r(z, s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[5525, 210, 7191])).
% 1.25/1.49 tff(7193,plain,
% 1.25/1.49 (b(z, s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[2071, 7192])).
% 1.25/1.49 tff(7194,plain,
% 1.25/1.49 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1397, 210, 7104])).
% 1.25/1.49 tff(7195,plain,
% 1.25/1.49 (b(s(s(s(elem!1))), s(elem!1))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[459, 7194, 7128])).
% 1.25/1.49 tff(7196,plain,
% 1.25/1.49 (b(elem!1, s(elem!1))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7103, 4093])).
% 1.25/1.49 tff(7197,plain,
% 1.25/1.49 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.25/1.49 inference(symmetry,[status(thm)],[4073])).
% 1.25/1.49 tff(7198,plain,
% 1.25/1.49 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762])).
% 1.25/1.49 tff(7199,plain,
% 1.25/1.49 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.25/1.49 inference(transitivity,[status(thm)],[7198, 2036])).
% 1.25/1.49 tff(7200,plain,
% 1.25/1.49 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7199])).
% 1.25/1.49 tff(7201,plain,
% 1.25/1.49 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 1.25/1.49 inference(transitivity,[status(thm)],[7200, 7197, 2902])).
% 1.25/1.49 tff(7202,plain,
% 1.25/1.49 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7201])).
% 1.25/1.49 tff(7203,plain,
% 1.25/1.49 (~(s(elem!1) = elem!1)),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[72, 7202])).
% 1.25/1.49 tff(7204,plain,
% 1.25/1.49 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.25/1.49 inference(monotonicity,[status(thm)],[353])).
% 1.25/1.49 tff(7205,plain,
% 1.25/1.49 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.25/1.49 inference(symmetry,[status(thm)],[7204])).
% 1.25/1.49 tff(7206,plain,
% 1.25/1.49 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.25/1.49 inference(monotonicity,[status(thm)],[3762])).
% 1.25/1.49 tff(7207,plain,
% 1.25/1.49 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.25/1.49 inference(symmetry,[status(thm)],[7206])).
% 1.25/1.49 tff(7208,plain,
% 1.25/1.49 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.25/1.49 inference(transitivity,[status(thm)],[7207, 7205])).
% 1.25/1.49 tff(7209,plain,
% 1.25/1.49 ((~r(s(z), z)) <=> (~r(s(elem!1), elem!1))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7208])).
% 1.25/1.49 tff(7210,plain,
% 1.25/1.49 (~r(s(s(s(elem!1))), s(z))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[6920, 210, 162])).
% 1.25/1.49 tff(7211,plain,
% 1.25/1.49 (b(s(s(s(elem!1))), s(z))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[576, 51, 94, 7210])).
% 1.25/1.49 tff(7212,plain,
% 1.25/1.49 (b(s(z), s(s(s(z))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[546, 5762])).
% 1.25/1.49 tff(7213,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.25/1.49 inference(symmetry,[status(thm)],[4068])).
% 1.25/1.49 tff(7214,plain,
% 1.25/1.49 ((~r(s(s(s(elem!1))), s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7213])).
% 1.25/1.49 tff(7215,plain,
% 1.25/1.49 (~r(s(s(s(z))), s(z))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7210, 7214])).
% 1.25/1.49 tff(7216,plain,
% 1.25/1.49 (b(s(s(s(z))), s(z))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[5118, 7215])).
% 1.25/1.49 tff(7217,plain,
% 1.25/1.49 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[804])).
% 1.25/1.49 tff(7218,plain,
% 1.25/1.49 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7217])).
% 1.25/1.49 tff(7219,plain,
% 1.25/1.49 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[805])).
% 1.25/1.49 tff(7220,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7219])).
% 1.25/1.49 tff(7221,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7220, 7218])).
% 1.25/1.49 tff(7222,plain,
% 1.25/1.49 (r(s(s(s(z))), s(s(z)))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[210, 7221])).
% 1.25/1.49 tff(7223,plain,
% 1.25/1.49 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[804])).
% 1.25/1.49 tff(7224,plain,
% 1.25/1.49 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7223])).
% 1.25/1.49 tff(7225,plain,
% 1.25/1.49 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(z)), s(s(s(s(z))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7224])).
% 1.25/1.49 tff(7226,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7227,plain,
% 1.25/1.49 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7228,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7227])).
% 1.25/1.49 tff(7229,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7228, 7226])).
% 1.25/1.49 tff(7230,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7231,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7230, 7229])).
% 1.25/1.49 tff(7232,plain,
% 1.25/1.49 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7231, 124, 162, 1544])).
% 1.25/1.49 tff(7233,plain,
% 1.25/1.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7232, 7225])).
% 1.25/1.49 tff(7234,plain,
% 1.25/1.49 (b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1604, 7233])).
% 1.25/1.49 tff(7235,plain,
% 1.25/1.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1533, 7234, 1457, 7222, 7216, 7212])).
% 1.25/1.49 tff(7236,plain,
% 1.25/1.49 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[5176, 7235])).
% 1.25/1.49 tff(7237,plain,
% 1.25/1.49 (~b(s(z), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[4178, 7236, 546, 7211, 804])).
% 1.25/1.49 tff(7238,plain,
% 1.25/1.49 (r(s(z), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[6600, 7237])).
% 1.25/1.49 tff(7239,plain,
% 1.25/1.49 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[4043])).
% 1.25/1.49 tff(7240,plain,
% 1.25/1.49 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7239])).
% 1.25/1.49 tff(7241,plain,
% 1.25/1.49 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7234, 7240])).
% 1.25/1.49 tff(7242,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[804])).
% 1.25/1.49 tff(7243,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7242])).
% 1.25/1.49 tff(7244,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(z)))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[210, 7243])).
% 1.25/1.49 tff(7245,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[1075])).
% 1.25/1.49 tff(7246,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(symmetry,[status(thm)],[7245])).
% 1.25/1.49 tff(7247,plain,
% 1.25/1.49 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7246])).
% 1.25/1.49 tff(7248,assumption,(~b(s(s(s(s(z)))), s(s(elem!1)))), introduced(assumption)).
% 1.25/1.49 tff(7249,plain,
% 1.25/1.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7248, 3916])).
% 1.25/1.49 tff(7250,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), s(s(z)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1564, 7249])).
% 1.25/1.49 tff(7251,plain,
% 1.25/1.49 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[3010, 7250, 3002])).
% 1.25/1.49 tff(7252,plain,
% 1.25/1.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7251, 7247])).
% 1.25/1.49 tff(7253,plain,
% 1.25/1.49 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[4960, 13])).
% 1.25/1.49 tff(7254,plain,
% 1.25/1.49 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[2893, 7253])).
% 1.25/1.49 tff(7255,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[5236, 51, 7254, 7248])).
% 1.25/1.49 tff(7256,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7257,plain,
% 1.25/1.49 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7258,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7257])).
% 1.25/1.49 tff(7259,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7258, 7256])).
% 1.25/1.49 tff(7260,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7261,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7260, 7259])).
% 1.25/1.49 tff(7262,plain,
% 1.25/1.49 (~r(s(z), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7261, 124, 160, 7255])).
% 1.25/1.49 tff(7263,plain,
% 1.25/1.49 (b(s(z), s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[6600, 7262])).
% 1.25/1.49 tff(7264,plain,
% 1.25/1.49 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[4178, 7263, 546, 564, 13])).
% 1.25/1.49 tff(7265,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[5176, 7264])).
% 1.25/1.49 tff(7266,plain,
% 1.25/1.49 ($false),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7265, 7252])).
% 1.25/1.49 tff(7267,plain,(b(s(s(s(s(z)))), s(s(elem!1))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.49 tff(7268,plain,
% 1.25/1.49 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7267, 7211, 546, 804, 7174, 7244])).
% 1.25/1.49 tff(7269,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7270,plain,
% 1.25/1.49 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7271,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7270])).
% 1.25/1.49 tff(7272,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7271, 7269])).
% 1.25/1.49 tff(7273,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(z)))))))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7274,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7273, 7272])).
% 1.25/1.49 tff(7275,plain,
% 1.25/1.49 (~b(z, s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7274, 238, 7193, 7268, 7241])).
% 1.25/1.49 tff(7276,plain,
% 1.25/1.49 (r(z, s(s(s(s(z)))))),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1487, 51, 7275, 7182])).
% 1.25/1.49 tff(7277,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7278,plain,
% 1.25/1.49 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7279,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7278])).
% 1.25/1.49 tff(7280,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7279, 7277])).
% 1.25/1.49 tff(7281,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7282,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7281, 7280])).
% 1.25/1.49 tff(7283,plain,
% 1.25/1.49 ($false),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7282, 124, 1650, 5517, 4278, 3476])).
% 1.25/1.49 tff(7284,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.49 tff(7285,plain,
% 1.25/1.49 (~r(s(z), z)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7284, 7276, 7191, 7238])).
% 1.25/1.49 tff(7286,plain,
% 1.25/1.49 (~r(s(elem!1), elem!1)),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7285, 7209])).
% 1.25/1.49 tff(7287,plain,
% 1.25/1.49 (b(s(elem!1), elem!1)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[408, 7286, 7203])).
% 1.25/1.49 tff(7288,plain,
% 1.25/1.49 (~b(s(s(s(elem!1))), elem!1)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[786, 7287, 7196, 7195])).
% 1.25/1.49 tff(7289,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), elem!1)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[647, 7288, 7122])).
% 1.25/1.49 tff(7290,plain,
% 1.25/1.49 (~r(s(s(elem!1)), elem!1)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1182, 7289, 210])).
% 1.25/1.49 tff(7291,plain,
% 1.25/1.49 (~r(s(s(elem!1)), z)),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7290, 4104])).
% 1.25/1.49 tff(7292,plain,
% 1.25/1.49 (b(s(s(elem!1)), z)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[4030, 51, 92, 7291])).
% 1.25/1.49 tff(7293,plain,
% 1.25/1.49 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.25/1.49 inference(symmetry,[status(thm)],[4186])).
% 1.25/1.49 tff(7294,plain,
% 1.25/1.49 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(z)), s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7293])).
% 1.25/1.49 tff(7295,plain,
% 1.25/1.49 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[805])).
% 1.25/1.49 tff(7296,plain,
% 1.25/1.49 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7236, 7295])).
% 1.25/1.49 tff(7297,plain,
% 1.25/1.49 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[805])).
% 1.25/1.49 tff(7298,plain,
% 1.25/1.49 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[806])).
% 1.25/1.49 tff(7299,plain,
% 1.25/1.49 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7298])).
% 1.25/1.49 tff(7300,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7301,plain,
% 1.25/1.49 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(rewrite,[status(thm)],[])).
% 1.25/1.49 tff(7302,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.25/1.49 inference(monotonicity,[status(thm)],[7301])).
% 1.25/1.49 tff(7303,plain,
% 1.25/1.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.25/1.49 inference(transitivity,[status(thm)],[7302, 7300])).
% 1.25/1.49 tff(7304,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.25/1.49 inference(quant_inst,[status(thm)],[])).
% 1.25/1.49 tff(7305,plain,
% 1.25/1.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.25/1.49 inference(modus_ponens,[status(thm)],[7304, 7303])).
% 1.25/1.49 tff(7306,plain,
% 1.25/1.49 (~b(s(s(s(s(z)))), z)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[7305, 238, 7193, 7268, 7241])).
% 1.25/1.49 tff(7307,plain,
% 1.25/1.49 (r(s(s(s(s(z)))), z)),
% 1.25/1.49 inference(unit_resolution,[status(thm)],[1499, 51, 726, 7306])).
% 1.25/1.49 tff(7308,plain,
% 1.25/1.49 (~b(s(s(s(elem!1))), z)),
% 1.25/1.50 inference(unit_resolution,[status(thm)],[6948, 7307, 1457, 7211])).
% 1.25/1.50 tff(7309,plain,
% 1.25/1.50 (r(s(s(s(elem!1))), z)),
% 1.25/1.50 inference(unit_resolution,[status(thm)],[6952, 7308])).
% 1.25/1.50 tff(7310,plain,
% 1.25/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.25/1.50 inference(rewrite,[status(thm)],[])).
% 1.25/1.50 tff(7311,plain,
% 1.25/1.50 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.25/1.50 inference(rewrite,[status(thm)],[])).
% 1.25/1.50 tff(7312,plain,
% 1.25/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7311])).
% 1.35/1.50 tff(7313,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[7312, 7310])).
% 1.35/1.50 tff(7314,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7315,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7314, 7313])).
% 1.35/1.50 tff(7316,plain,
% 1.35/1.50 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7315, 124, 1544, 7309, 7307])).
% 1.35/1.50 tff(7317,plain,
% 1.35/1.50 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7316, 7299])).
% 1.35/1.50 tff(7318,plain,
% 1.35/1.50 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[5167, 7317])).
% 1.35/1.50 tff(7319,plain,
% 1.35/1.50 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7318, 7297])).
% 1.35/1.50 tff(7320,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7321,plain,
% 1.35/1.50 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7322,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7321])).
% 1.35/1.50 tff(7323,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[7322, 7320])).
% 1.35/1.50 tff(7324,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7325,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7324, 7323])).
% 1.35/1.50 tff(7326,plain,
% 1.35/1.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7325, 238, 7319, 7296, 7241])).
% 1.35/1.50 tff(7327,plain,
% 1.35/1.50 (~b(s(s(z)), s(s(s(z))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7326, 7294])).
% 1.35/1.50 tff(7328,plain,
% 1.35/1.50 (r(s(s(z)), s(s(s(z))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[4334, 7327])).
% 1.35/1.50 tff(7329,plain,
% 1.35/1.50 (~r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1725, 1717, 169])).
% 1.35/1.50 tff(7330,plain,
% 1.35/1.50 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1781, 7329])).
% 1.35/1.50 tff(7331,plain,
% 1.35/1.50 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[4329, 1717, 4321])).
% 1.35/1.50 tff(7332,plain,
% 1.35/1.50 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1101, 7331])).
% 1.35/1.50 tff(7333,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[5745, 7332, 7330, 1455, 1456])).
% 1.35/1.50 tff(7334,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7335,plain,
% 1.35/1.50 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7334, 7328, 7216, 7212, 169])).
% 1.35/1.50 tff(7336,plain,
% 1.35/1.50 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1738, 7335])).
% 1.35/1.50 tff(7337,plain,
% 1.35/1.50 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[4318, 7336, 804])).
% 1.35/1.50 tff(7338,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.35/1.50 tff(7339,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7340,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7341,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7340, 7339])).
% 1.35/1.50 tff(7342,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7341, 238, 2078, 4047, 4122, 7338])).
% 1.35/1.50 tff(7343,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7344,plain,
% 1.35/1.50 (~b(s(s(s(s(s(z))))), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7343, 7337, 7292, 7193])).
% 1.35/1.50 tff(7345,plain,
% 1.35/1.50 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7344, 7189])).
% 1.35/1.50 tff(7346,plain,
% 1.35/1.50 (r(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1064, 7345, 7187])).
% 1.35/1.50 tff(7347,plain,
% 1.35/1.50 (r(s(s(s(s(s(z))))), z)),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7346, 7183])).
% 1.35/1.50 tff(7348,plain,
% 1.35/1.50 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[4437, 7336, 1565, 7234])).
% 1.35/1.50 tff(7349,plain,
% 1.35/1.50 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1904, 7348])).
% 1.35/1.50 tff(7350,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.35/1.50 tff(7351,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7352,plain,
% 1.35/1.50 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7353,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7352])).
% 1.35/1.50 tff(7354,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.50 inference(transitivity,[status(thm)],[7353, 7351])).
% 1.35/1.50 tff(7355,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7356,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7355, 7354])).
% 1.35/1.50 tff(7357,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7356, 124, 1652, 1544, 7350, 6924])).
% 1.35/1.50 tff(7358,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7359,plain,
% 1.35/1.50 (~r(s(s(s(s(s(z))))), z)),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7358, 7349, 1544, 7307])).
% 1.35/1.50 tff(7360,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7359, 7347])).
% 1.35/1.50 tff(7361,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7362,plain,
% 1.35/1.50 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7361, 210, 169, 353, 1457, 546, 162])).
% 1.35/1.50 tff(7363,plain,
% 1.35/1.50 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1624, 7362])).
% 1.35/1.50 tff(7364,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7365,plain,
% 1.35/1.50 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7366,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7365])).
% 1.35/1.50 tff(7367,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[7366, 7364])).
% 1.35/1.50 tff(7368,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7369,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 1.35/1.50 tff(7370,plain,
% 1.35/1.50 (~b(z, s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7369, 238, 546, 1457, 7363])).
% 1.35/1.50 tff(7371,plain,
% 1.35/1.50 (r(z, s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1487, 51, 7370, 7182])).
% 1.35/1.50 tff(7372,plain,
% 1.35/1.50 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7371, 7178])).
% 1.35/1.50 tff(7373,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7374,plain,
% 1.35/1.50 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.35/1.50 inference(rewrite,[status(thm)],[])).
% 1.35/1.50 tff(7375,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7374])).
% 1.35/1.50 tff(7376,plain,
% 1.35/1.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.35/1.50 inference(transitivity,[status(thm)],[7375, 7373])).
% 1.35/1.50 tff(7377,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.35/1.50 inference(quant_inst,[status(thm)],[])).
% 1.35/1.50 tff(7378,plain,
% 1.35/1.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7377, 7376])).
% 1.35/1.50 tff(7379,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7378, 124, 1666, 1321, 940])).
% 1.35/1.50 tff(7380,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7381,plain,
% 1.35/1.50 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7380, 7372, 7176])).
% 1.35/1.50 tff(7382,plain,
% 1.35/1.50 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[921, 7381, 7102])).
% 1.35/1.50 tff(7383,plain,
% 1.35/1.50 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7382, 7094])).
% 1.35/1.50 tff(7384,plain,
% 1.35/1.50 ($false),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[3994, 238, 7211, 546, 7363, 7383])).
% 1.35/1.50 tff(7385,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~(s(elem!1) = s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.50 tff(7386,plain,
% 1.35/1.50 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7385, 4225, 7061, 6301, 80, 7093])).
% 1.35/1.50 tff(7387,plain,
% 1.35/1.50 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[223, 7386, 7091])).
% 1.35/1.50 tff(7388,plain,
% 1.35/1.50 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7067])).
% 1.35/1.50 tff(7389,plain,
% 1.35/1.50 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.35/1.50 inference(transitivity,[status(thm)],[7388, 3716])).
% 1.35/1.50 tff(7390,plain,
% 1.35/1.50 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.35/1.50 inference(symmetry,[status(thm)],[7389])).
% 1.35/1.50 tff(7391,plain,
% 1.35/1.50 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7390])).
% 1.35/1.50 tff(7392,plain,
% 1.35/1.50 (~(elem!1 = s(s(s(elem!1))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[821, 7391])).
% 1.35/1.50 tff(7393,plain,
% 1.35/1.50 (b(elem!1, s(z))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[6376, 7061, 6301])).
% 1.35/1.50 tff(7394,plain,
% 1.35/1.50 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.35/1.50 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.50 tff(7395,plain,
% 1.35/1.50 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.35/1.50 inference(symmetry,[status(thm)],[7394])).
% 1.35/1.50 tff(7396,plain,
% 1.35/1.50 (r(s(s(elem!1)), s(elem!1))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7093, 7395])).
% 1.35/1.50 tff(7397,plain,
% 1.35/1.50 (r(s(z), s(s(elem!1)))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7173, 4225, 7061, 7393, 7396])).
% 1.35/1.50 tff(7398,plain,
% 1.35/1.50 (~b(elem!1, s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[578, 7397, 4225, 7393, 7091])).
% 1.35/1.50 tff(7399,plain,
% 1.35/1.50 (r(elem!1, s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1319, 7398, 7392])).
% 1.35/1.50 tff(7400,plain,
% 1.35/1.50 (~b(z, s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7369, 238, 546, 1457, 1784])).
% 1.35/1.50 tff(7401,plain,
% 1.35/1.50 (r(z, s(s(s(s(z)))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[1487, 51, 7400, 7182])).
% 1.35/1.50 tff(7402,plain,
% 1.35/1.50 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7401, 7178])).
% 1.35/1.50 tff(7403,plain,
% 1.35/1.50 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[7380, 7402, 1321])).
% 1.35/1.50 tff(7404,plain,
% 1.35/1.50 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(unit_resolution,[status(thm)],[921, 7403, 7102])).
% 1.35/1.50 tff(7405,plain,
% 1.35/1.50 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.50 inference(modus_ponens,[status(thm)],[7404, 7094])).
% 1.35/1.51 tff(7406,plain,
% 1.35/1.51 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2991, 1784, 546, 226])).
% 1.35/1.51 tff(7407,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7406, 7405])).
% 1.35/1.51 tff(7408,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(7409,plain,
% 1.35/1.51 (~b(s(s(s(s(z)))), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7408, 7399, 7061, 4225, 6301, 7387])).
% 1.35/1.51 tff(7410,plain,
% 1.35/1.51 (r(s(s(s(s(z)))), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1624, 7409])).
% 1.35/1.51 tff(7411,plain,
% 1.35/1.51 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7231, 124, 7093, 7410])).
% 1.35/1.51 tff(7412,plain,
% 1.35/1.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7411, 7088])).
% 1.35/1.51 tff(7413,plain,
% 1.35/1.51 (b(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1604, 7412])).
% 1.35/1.51 tff(7414,plain,
% 1.35/1.51 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7413, 7085])).
% 1.35/1.51 tff(7415,plain,
% 1.35/1.51 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7072])).
% 1.35/1.51 tff(7416,plain,
% 1.35/1.51 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.35/1.51 inference(symmetry,[status(thm)],[7415])).
% 1.35/1.51 tff(7417,plain,
% 1.35/1.51 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7416])).
% 1.35/1.51 tff(7418,plain,
% 1.35/1.51 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.35/1.51 inference(symmetry,[status(thm)],[7417])).
% 1.35/1.51 tff(7419,plain,
% 1.35/1.51 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7418])).
% 1.35/1.51 tff(7420,plain,
% 1.35/1.51 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[5165, 7419])).
% 1.35/1.51 tff(7421,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2958, 124, 7093, 7410])).
% 1.35/1.51 tff(7422,plain,
% 1.35/1.51 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2893, 7077])).
% 1.35/1.51 tff(7423,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[5236, 51, 7422, 7421])).
% 1.35/1.51 tff(7424,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7425,plain,
% 1.35/1.51 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7426,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7425])).
% 1.35/1.51 tff(7427,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7426, 7424])).
% 1.35/1.51 tff(7428,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7429,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7428, 7427])).
% 1.35/1.51 tff(7430,plain,
% 1.35/1.51 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7429, 238, 7387, 7423, 7414])).
% 1.35/1.51 tff(7431,plain,
% 1.35/1.51 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[2974, 51, 7430, 7420])).
% 1.35/1.51 tff(7432,plain,
% 1.35/1.51 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7067])).
% 1.35/1.51 tff(7433,plain,
% 1.35/1.51 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7432])).
% 1.35/1.51 tff(7434,plain,
% 1.35/1.51 (~b(z, s(s(s(elem!1))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7398, 7433])).
% 1.35/1.51 tff(7435,plain,
% 1.35/1.51 (r(z, s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3795, 51, 3785, 7434])).
% 1.35/1.51 tff(7436,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7437,plain,
% 1.35/1.51 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7438,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7437])).
% 1.35/1.51 tff(7439,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7438, 7436])).
% 1.35/1.51 tff(7440,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7441,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7440, 7439])).
% 1.35/1.51 tff(7442,plain,
% 1.35/1.51 (~r(z, s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7441, 124, 7435, 7431])).
% 1.35/1.51 tff(7443,plain,
% 1.35/1.51 (b(z, s(s(s(s(z)))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1487, 51, 7442, 7182])).
% 1.35/1.51 tff(7444,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7445,plain,
% 1.35/1.51 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7446,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7445])).
% 1.35/1.51 tff(7447,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7446, 7444])).
% 1.35/1.51 tff(7448,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7449,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7448, 7447])).
% 1.35/1.51 tff(7450,plain,
% 1.35/1.51 (~r(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7449, 124, 7435, 7431])).
% 1.35/1.51 tff(7451,plain,
% 1.35/1.51 (b(s(s(s(s(z)))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1499, 51, 726, 7450])).
% 1.35/1.51 tff(7452,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7453,plain,
% 1.35/1.51 (((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7454,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7453])).
% 1.35/1.51 tff(7455,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7454, 7452])).
% 1.35/1.51 tff(7456,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7457,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7456, 7455])).
% 1.35/1.51 tff(7458,plain,
% 1.35/1.51 (~b(s(s(elem!1)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7457, 238, 7451, 7443, 7414])).
% 1.35/1.51 tff(7459,plain,
% 1.35/1.51 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7458, 7082])).
% 1.35/1.51 tff(7460,plain,
% 1.35/1.51 (r(s(s(elem!1)), elem!1)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[255, 7459, 7079])).
% 1.35/1.51 tff(7461,plain,
% 1.35/1.51 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.35/1.51 inference(transitivity,[status(thm)],[7390, 641])).
% 1.35/1.51 tff(7462,plain,
% 1.35/1.51 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7461])).
% 1.35/1.51 tff(7463,plain,
% 1.35/1.51 (~(s(s(s(elem!1))) = elem!1)),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[821, 7462])).
% 1.35/1.51 tff(7464,plain,
% 1.35/1.51 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.51 tff(7465,plain,
% 1.35/1.51 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.35/1.51 inference(symmetry,[status(thm)],[7464])).
% 1.35/1.51 tff(7466,plain,
% 1.35/1.51 (b(elem!1, s(elem!1))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7393, 7465])).
% 1.35/1.51 tff(7467,plain,
% 1.35/1.51 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.51 tff(7468,plain,
% 1.35/1.51 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.35/1.51 inference(symmetry,[status(thm)],[7467])).
% 1.35/1.51 tff(7469,plain,
% 1.35/1.51 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7468])).
% 1.35/1.51 tff(7470,plain,
% 1.35/1.51 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[41, 7469])).
% 1.35/1.51 tff(7471,plain,
% 1.35/1.51 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.51 tff(7472,plain,
% 1.35/1.51 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.51 inference(symmetry,[status(thm)],[7471])).
% 1.35/1.51 tff(7473,plain,
% 1.35/1.51 (~r(s(s(s(z))), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[5185, 7410, 80])).
% 1.35/1.51 tff(7474,plain,
% 1.35/1.51 (b(s(s(s(z))), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[5118, 7473])).
% 1.35/1.51 tff(7475,plain,
% 1.35/1.51 (b(s(s(s(elem!1))), s(z))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3886, 7474, 7072])).
% 1.35/1.51 tff(7476,plain,
% 1.35/1.51 (b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7475, 7472])).
% 1.35/1.51 tff(7477,plain,
% 1.35/1.51 (~b(s(s(s(elem!1))), elem!1)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1222, 7476, 7079, 7387, 7470, 7466])).
% 1.35/1.51 tff(7478,plain,
% 1.35/1.51 (r(s(s(s(elem!1))), elem!1)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[647, 7477, 7463])).
% 1.35/1.51 tff(7479,plain,
% 1.35/1.51 (r(s(s(s(elem!1))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[4266, 7478, 7061])).
% 1.35/1.51 tff(7480,plain,
% 1.35/1.51 (r(s(s(elem!1)), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[4905, 7458])).
% 1.35/1.51 tff(7481,plain,
% 1.35/1.51 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[3850, 804])).
% 1.35/1.51 tff(7482,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7483,plain,
% 1.35/1.51 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7484,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7483])).
% 1.35/1.51 tff(7485,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7484, 7482])).
% 1.35/1.51 tff(7486,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7487,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7486, 7485])).
% 1.35/1.51 tff(7488,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7487, 124, 301, 5272, 4353])).
% 1.35/1.51 tff(7489,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(7490,plain,
% 1.35/1.51 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7489, 5272, 301])).
% 1.35/1.51 tff(7491,plain,
% 1.35/1.51 (r(s(s(s(s(s(z))))), z)),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[5272, 7183])).
% 1.35/1.51 tff(7492,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.35/1.51 tff(7493,plain,
% 1.35/1.51 ($false),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7492, 7491])).
% 1.35/1.51 tff(7494,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), z) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.51 tff(7495,plain,
% 1.35/1.51 (r(s(s(s(s(s(z))))), z)),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7494, 5272, 353])).
% 1.35/1.51 tff(7496,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7497,plain,
% 1.35/1.51 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), 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(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7498,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7497])).
% 1.35/1.51 tff(7499,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7498, 7496])).
% 1.35/1.51 tff(7500,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7501,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7500, 7499])).
% 1.35/1.51 tff(7502,plain,
% 1.35/1.51 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7501, 124, 162, 7495, 6338])).
% 1.35/1.51 tff(7503,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7504,plain,
% 1.35/1.51 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.51 inference(rewrite,[status(thm)],[])).
% 1.35/1.51 tff(7505,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[7504])).
% 1.35/1.51 tff(7506,plain,
% 1.35/1.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.35/1.51 inference(transitivity,[status(thm)],[7505, 7503])).
% 1.35/1.51 tff(7507,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(7508,plain,
% 1.35/1.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 1.35/1.51 tff(7509,plain,
% 1.35/1.51 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[7508, 124, 3512, 7495])).
% 1.35/1.51 tff(7510,plain,
% 1.35/1.51 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[1814, 7509, 5782])).
% 1.35/1.51 tff(7511,plain,
% 1.35/1.51 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.35/1.51 inference(commutativity,[status(thm)],[])).
% 1.35/1.52 tff(7512,plain,
% 1.35/1.52 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.35/1.52 inference(symmetry,[status(thm)],[7511])).
% 1.35/1.52 tff(7513,plain,
% 1.35/1.52 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(z)))))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7512])).
% 1.35/1.52 tff(7514,plain,
% 1.35/1.52 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[2417, 7513])).
% 1.35/1.52 tff(7515,assumption,(~r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.35/1.52 tff(7516,plain,
% 1.35/1.52 (((~![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)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7517,plain,
% 1.35/1.52 ((~![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)))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7518,plain,
% 1.35/1.52 ((~![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))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7517, 7516])).
% 1.35/1.52 tff(7519,plain,
% 1.35/1.52 ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7518, 51, 7515])).
% 1.35/1.52 tff(7520,plain,
% 1.35/1.52 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7519, 7514])).
% 1.35/1.52 tff(7521,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7522,plain,
% 1.35/1.52 (((~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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7523,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7522])).
% 1.35/1.52 tff(7524,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[7523, 7521])).
% 1.35/1.52 tff(7525,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7526,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7525, 7524])).
% 1.35/1.52 tff(7527,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7526, 238, 226, 1040, 7520, 2687])).
% 1.35/1.52 tff(7528,plain,(r(s(s(elem!1)), s(s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7529,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7528, 7510, 7502, 7490, 226, 7481])).
% 1.35/1.52 tff(7530,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~(s(elem!1) = s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7531,plain,
% 1.35/1.52 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7530, 7387, 7093, 7480, 7479, 7061, 7460])).
% 1.35/1.52 tff(7532,plain,
% 1.35/1.52 (b(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1064, 7531, 7071])).
% 1.35/1.52 tff(7533,plain,
% 1.35/1.52 (b(s(s(s(s(s(z))))), z)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7532, 7066])).
% 1.35/1.52 tff(7534,plain,
% 1.35/1.52 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7067])).
% 1.35/1.52 tff(7535,plain,
% 1.35/1.52 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.52 tff(7536,plain,
% 1.35/1.52 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.35/1.52 inference(transitivity,[status(thm)],[7535, 7534])).
% 1.35/1.52 tff(7537,plain,
% 1.35/1.52 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7061])).
% 1.35/1.52 tff(7538,plain,
% 1.35/1.52 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.35/1.52 inference(symmetry,[status(thm)],[7537])).
% 1.35/1.52 tff(7539,plain,
% 1.35/1.52 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7067])).
% 1.35/1.52 tff(7540,plain,
% 1.35/1.52 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.35/1.52 inference(transitivity,[status(thm)],[7539, 2036])).
% 1.35/1.52 tff(7541,plain,
% 1.35/1.52 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.35/1.52 inference(symmetry,[status(thm)],[7540])).
% 1.35/1.52 tff(7542,plain,
% 1.35/1.52 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 1.35/1.52 inference(transitivity,[status(thm)],[7541, 7538, 2902])).
% 1.35/1.52 tff(7543,plain,
% 1.35/1.52 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7542])).
% 1.35/1.52 tff(7544,plain,
% 1.35/1.52 (~(s(elem!1) = elem!1)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[72, 7543])).
% 1.35/1.52 tff(7545,plain,
% 1.35/1.52 (~r(s(elem!1), elem!1)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[403, 7460, 7396])).
% 1.35/1.52 tff(7546,plain,
% 1.35/1.52 (b(s(elem!1), elem!1)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[408, 7545, 7544])).
% 1.35/1.52 tff(7547,plain,
% 1.35/1.52 (b(s(z), z)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7546, 7536])).
% 1.35/1.52 tff(7548,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7549,plain,
% 1.35/1.52 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7550,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7549])).
% 1.35/1.52 tff(7551,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[7550, 7548])).
% 1.35/1.52 tff(7552,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7553,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7552, 7551])).
% 1.35/1.52 tff(7554,plain,
% 1.35/1.52 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7553, 238, 6301, 7451, 7547])).
% 1.35/1.52 tff(7555,plain,
% 1.35/1.52 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[6600, 7554])).
% 1.35/1.52 tff(7556,plain,
% 1.35/1.52 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.35/1.52 inference(symmetry,[status(thm)],[7188])).
% 1.35/1.52 tff(7557,plain,
% 1.35/1.52 (b(s(s(s(s(s(z))))), z)),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[5293, 7556])).
% 1.35/1.52 tff(7558,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.35/1.52 tff(7559,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7560,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7561,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7560, 7559])).
% 1.35/1.52 tff(7562,plain,
% 1.35/1.52 (~b(s(s(s(s(s(z))))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7561, 238, 1786, 1457, 7558])).
% 1.35/1.52 tff(7563,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7562, 7557])).
% 1.35/1.52 tff(7564,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7565,plain,
% 1.35/1.52 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7564, 7532, 7061, 6301, 7451])).
% 1.35/1.52 tff(7566,plain,
% 1.35/1.52 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1904, 7565])).
% 1.35/1.52 tff(7567,plain,
% 1.35/1.52 (~r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1660, 7566, 7555])).
% 1.35/1.52 tff(7568,plain,
% 1.35/1.52 (b(s(z), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1709, 7567])).
% 1.35/1.52 tff(7569,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7570,plain,
% 1.35/1.52 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7571,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7570])).
% 1.35/1.52 tff(7572,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.35/1.52 inference(transitivity,[status(thm)],[7571, 7569])).
% 1.35/1.52 tff(7573,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7574,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7573, 7572])).
% 1.35/1.52 tff(7575,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7574, 238, 1457, 1785, 6925, 7338])).
% 1.35/1.52 tff(7576,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7577,plain,
% 1.35/1.52 (~b(s(s(s(s(s(z))))), z)),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7576, 7568, 6301, 7547])).
% 1.35/1.52 tff(7578,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7577, 7533])).
% 1.35/1.52 tff(7579,plain,(r(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7580,plain,
% 1.35/1.52 (r(s(z), s(s(s(elem!1))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7579, 64])).
% 1.35/1.52 tff(7581,plain,
% 1.35/1.52 (~b(s(s(z)), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2841, 2288, 169, 1545])).
% 1.35/1.52 tff(7582,plain,
% 1.35/1.52 (r(s(s(z)), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[4334, 7581])).
% 1.35/1.52 tff(7583,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[5127, 124, 169, 2288, 7582])).
% 1.35/1.52 tff(7584,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7585,plain,
% 1.35/1.52 (~r(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7584, 1545, 80])).
% 1.35/1.52 tff(7586,plain,
% 1.35/1.52 (b(s(s(s(z))), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[5118, 7585])).
% 1.35/1.52 tff(7587,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7588,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7589,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7588, 7587])).
% 1.35/1.52 tff(7590,plain,
% 1.35/1.52 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7589, 238, 1137, 1784, 1456])).
% 1.35/1.52 tff(7591,plain,
% 1.35/1.52 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[5176, 7590])).
% 1.35/1.52 tff(7592,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~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))))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7593,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7594,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~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)))))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 1.35/1.52 tff(7595,plain,
% 1.35/1.52 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7594, 238, 1137, 1783, 1456])).
% 1.35/1.52 tff(7596,plain,
% 1.35/1.52 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1101, 7595])).
% 1.35/1.52 tff(7597,plain,
% 1.35/1.52 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[3504, 7596, 7591])).
% 1.35/1.52 tff(7598,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7599,plain,
% 1.35/1.52 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~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))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7600,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~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)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7599])).
% 1.35/1.52 tff(7601,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~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))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[7600, 7598])).
% 1.35/1.52 tff(7602,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7603,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7602, 7601])).
% 1.35/1.52 tff(7604,plain,
% 1.35/1.52 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7603, 238, 1137, 1784, 1783])).
% 1.35/1.52 tff(7605,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1051, 51, 7604, 7597, 2782])).
% 1.35/1.52 tff(7606,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7607,plain,
% 1.35/1.52 (~b(s(z), s(s(elem!1)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7606, 5411, 7586, 5409])).
% 1.35/1.52 tff(7608,plain,
% 1.35/1.52 (r(s(z), s(s(elem!1)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[56, 7607])).
% 1.35/1.52 tff(7609,plain,
% 1.35/1.52 (~r(s(s(elem!1)), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[1351, 160, 114, 161, 150, 64])).
% 1.35/1.52 tff(7610,plain,
% 1.35/1.52 (b(s(s(elem!1)), s(z))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[112, 7609])).
% 1.35/1.52 tff(7611,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7612,plain,
% 1.35/1.52 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(7613,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7612])).
% 1.35/1.52 tff(7614,plain,
% 1.35/1.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[7613, 7611])).
% 1.35/1.52 tff(7615,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(7616,plain,
% 1.35/1.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[7615, 7614])).
% 1.35/1.52 tff(7617,plain,
% 1.35/1.52 ($false),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7616, 238, 202, 224, 191, 7610])).
% 1.35/1.52 tff(7618,plain,((~r(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.52 tff(7619,plain,
% 1.35/1.52 (elem!1 = s(s(elem!1))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[7618, 7608, 64, 7580, 114])).
% 1.35/1.52 tff(7620,plain,
% 1.35/1.52 (s(elem!1) = s(s(s(elem!1)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[2097, 7619])).
% 1.35/1.52 tff(7621,plain,
% 1.35/1.52 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[7620])).
% 1.35/1.52 tff(7622,plain,
% 1.35/1.53 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7621])).
% 1.35/1.53 tff(7623,plain,
% 1.35/1.53 (r(s(z), s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7580, 7622])).
% 1.35/1.53 tff(7624,plain,
% 1.35/1.53 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[6009, 7623, 7608])).
% 1.35/1.53 tff(7625,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7626,plain,
% 1.35/1.53 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7627,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7626])).
% 1.35/1.53 tff(7628,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[7627, 7625])).
% 1.35/1.53 tff(7629,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(7630,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7629, 7628])).
% 1.35/1.53 tff(7631,plain,
% 1.35/1.53 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7630, 238, 1785, 1784, 1456])).
% 1.35/1.53 tff(7632,plain,
% 1.35/1.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5176, 7631])).
% 1.35/1.53 tff(7633,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7634,plain,
% 1.35/1.53 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7635,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7634])).
% 1.35/1.53 tff(7636,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[7635, 7633])).
% 1.35/1.53 tff(7637,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(7638,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7637, 7636])).
% 1.35/1.53 tff(7639,plain,
% 1.35/1.53 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7638, 238, 1785, 1783, 1456])).
% 1.35/1.53 tff(7640,plain,
% 1.35/1.53 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1101, 7639])).
% 1.35/1.53 tff(7641,plain,
% 1.35/1.53 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3504, 7640, 7632])).
% 1.35/1.53 tff(7642,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1051, 51, 3638, 7641, 2782])).
% 1.35/1.53 tff(7643,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7644,plain,
% 1.35/1.53 (~b(s(z), s(s(s(s(s(z))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7643, 5411, 7586, 5409])).
% 1.35/1.53 tff(7645,plain,
% 1.35/1.53 (r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1709, 7644])).
% 1.35/1.53 tff(7646,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[200, 7608, 80])).
% 1.35/1.53 tff(7647,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[135, 7646, 114])).
% 1.35/1.53 tff(7648,plain,
% 1.35/1.53 (~r(s(s(elem!1)), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5041, 7647, 80, 1545])).
% 1.35/1.53 tff(7649,plain,
% 1.35/1.53 (b(s(s(elem!1)), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[112, 7648])).
% 1.35/1.53 tff(7650,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[58])).
% 1.35/1.53 tff(7651,plain,
% 1.35/1.53 (~b(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5363, 58, 81])).
% 1.35/1.53 tff(7652,plain,
% 1.35/1.53 (r(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[56, 7651])).
% 1.35/1.53 tff(7653,plain,
% 1.35/1.53 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2016, 7652, 1651])).
% 1.35/1.53 tff(7654,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7650])).
% 1.35/1.53 tff(7655,plain,
% 1.35/1.53 (s(elem!1) = s(s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[208, 58])).
% 1.35/1.53 tff(7656,plain,
% 1.35/1.53 (elem!1 = s(s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[158, 7655])).
% 1.35/1.53 tff(7657,plain,
% 1.35/1.53 (s(elem!1) = s(s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2097, 7656])).
% 1.35/1.53 tff(7658,plain,
% 1.35/1.53 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2106, 7657])).
% 1.35/1.53 tff(7659,plain,
% 1.35/1.53 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2420, 51, 2666])).
% 1.35/1.53 tff(7660,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7659, 7658])).
% 1.35/1.53 tff(7661,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7660, 7654])).
% 1.35/1.53 tff(7662,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1081, 7661])).
% 1.35/1.53 tff(7663,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7664,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7663, 7653, 58])).
% 1.35/1.53 tff(7665,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7664, 7650])).
% 1.35/1.53 tff(7666,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[200, 7652, 169])).
% 1.35/1.53 tff(7667,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[135, 7666, 114])).
% 1.35/1.53 tff(7668,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7669,plain,
% 1.35/1.53 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7670,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7669])).
% 1.35/1.53 tff(7671,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[7670, 7668])).
% 1.35/1.53 tff(7672,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(7673,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 1.35/1.53 tff(7674,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7673, 238, 7667, 23, 7665, 3445])).
% 1.35/1.53 tff(7675,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7676,plain,
% 1.35/1.53 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7675, 7649, 114, 7645, 80, 81])).
% 1.35/1.53 tff(7677,plain,
% 1.35/1.53 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5343, 7676])).
% 1.35/1.53 tff(7678,plain,
% 1.35/1.53 (~(elem!1 = s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[386, 7677])).
% 1.35/1.53 tff(7679,plain,
% 1.35/1.53 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7620])).
% 1.35/1.53 tff(7680,plain,
% 1.35/1.53 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7679])).
% 1.35/1.53 tff(7681,plain,
% 1.35/1.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[218, 7608, 7580])).
% 1.35/1.53 tff(7682,plain,
% 1.35/1.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[223, 7676, 7681])).
% 1.35/1.53 tff(7683,plain,
% 1.35/1.53 (b(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7682, 7680])).
% 1.35/1.53 tff(7684,plain,
% 1.35/1.53 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7619])).
% 1.35/1.53 tff(7685,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.35/1.53 inference(symmetry,[status(thm)],[7684])).
% 1.35/1.53 tff(7686,plain,
% 1.35/1.53 (b(s(s(z)), elem!1)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7647, 7685])).
% 1.35/1.53 tff(7687,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7620])).
% 1.35/1.53 tff(7688,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7687])).
% 1.35/1.53 tff(7689,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[177, 7580, 80])).
% 1.35/1.53 tff(7690,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[190, 7689])).
% 1.35/1.53 tff(7691,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7690, 7688])).
% 1.35/1.53 tff(7692,plain,
% 1.35/1.53 (~b(elem!1, s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5355, 7691, 7686, 7683])).
% 1.35/1.53 tff(7693,plain,
% 1.35/1.53 (r(elem!1, s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[629, 7692, 7678])).
% 1.35/1.53 tff(7694,plain,
% 1.35/1.53 (r(s(s(elem!1)), s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[590, 5325])).
% 1.35/1.53 tff(7695,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[318, 7694])).
% 1.35/1.53 tff(7696,plain,((~r(elem!1, s(elem!1))) | r(s(s(elem!1)), s(elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7697,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7696, 7693, 7624, 7619])).
% 1.35/1.53 tff(7698,plain,((~r(z, s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7699,plain,
% 1.35/1.53 (~r(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7698, 81, 22, 64])).
% 1.35/1.53 tff(7700,plain,
% 1.35/1.53 (b(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1542, 7699])).
% 1.35/1.53 tff(7701,plain,
% 1.35/1.53 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5378])).
% 1.35/1.53 tff(7702,plain,
% 1.35/1.53 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7701])).
% 1.35/1.53 tff(7703,plain,
% 1.35/1.53 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7702])).
% 1.35/1.53 tff(7704,plain,
% 1.35/1.53 (~(s(elem!1) = s(s(z)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[1291, 7703])).
% 1.35/1.53 tff(7705,plain,
% 1.35/1.53 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5377])).
% 1.35/1.53 tff(7706,plain,
% 1.35/1.53 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7705])).
% 1.35/1.53 tff(7707,plain,
% 1.35/1.53 (r(elem!1, s(z))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[113, 7706])).
% 1.35/1.53 tff(7708,plain,
% 1.35/1.53 (s(elem!1) = s(s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5022, 1137, 169, 1, 82, 1370, 278])).
% 1.35/1.53 tff(7709,plain,
% 1.35/1.53 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5363, 1137, 81])).
% 1.35/1.53 tff(7710,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5343, 7709, 7708])).
% 1.35/1.53 tff(7711,plain,((~b(s(z), s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(elem!1) = s(z)) | b(s(s(elem!1)), s(z)) | (~r(elem!1, s(z))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7712,plain,
% 1.35/1.53 (~b(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7711, 82, 80, 1, 81, 7707, 7704])).
% 1.35/1.53 tff(7713,plain,
% 1.35/1.53 (r(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[56, 7712])).
% 1.35/1.53 tff(7714,plain,
% 1.35/1.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[218, 7713, 7580])).
% 1.35/1.53 tff(7715,plain,
% 1.35/1.53 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5377])).
% 1.35/1.53 tff(7716,plain,
% 1.35/1.53 (r(s(s(elem!1)), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7715])).
% 1.35/1.53 tff(7717,plain,
% 1.35/1.53 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5378])).
% 1.35/1.53 tff(7718,plain,
% 1.35/1.53 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7717])).
% 1.35/1.53 tff(7719,plain,
% 1.35/1.53 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5377])).
% 1.35/1.53 tff(7720,plain,
% 1.35/1.53 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(elem!1))),
% 1.35/1.53 inference(transitivity,[status(thm)],[7719, 7718, 7716])).
% 1.35/1.53 tff(7721,plain,
% 1.35/1.53 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7720])).
% 1.35/1.53 tff(7722,plain,
% 1.35/1.53 (~r(elem!1, s(s(s(elem!1))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1378, 7707, 7580])).
% 1.35/1.53 tff(7723,plain,
% 1.35/1.53 (~r(elem!1, s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7722, 7721])).
% 1.35/1.53 tff(7724,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5378])).
% 1.35/1.53 tff(7725,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7724])).
% 1.35/1.53 tff(7726,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7690, 7725])).
% 1.35/1.53 tff(7727,plain,
% 1.35/1.53 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[5377])).
% 1.35/1.53 tff(7728,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.35/1.53 inference(symmetry,[status(thm)],[7727])).
% 1.35/1.53 tff(7729,plain,
% 1.35/1.53 (b(s(s(z)), elem!1)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[5380, 7728])).
% 1.35/1.53 tff(7730,plain,
% 1.35/1.53 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[410])).
% 1.35/1.53 tff(7731,plain,
% 1.35/1.53 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7730])).
% 1.35/1.53 tff(7732,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.35/1.53 tff(7733,plain,
% 1.35/1.53 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[223, 545, 7732])).
% 1.35/1.53 tff(7734,plain,
% 1.35/1.53 (b(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7733, 7731])).
% 1.35/1.53 tff(7735,plain,
% 1.35/1.53 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5343, 545])).
% 1.35/1.53 tff(7736,plain,
% 1.35/1.53 (~(elem!1 = s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[386, 7735])).
% 1.35/1.53 tff(7737,plain,
% 1.35/1.53 (b(elem!1, s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[629, 7736, 2936])).
% 1.35/1.53 tff(7738,plain,
% 1.35/1.53 (~b(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5355, 7737, 5347, 2180])).
% 1.35/1.53 tff(7739,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7738, 7734])).
% 1.35/1.53 tff(7740,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~(s(elem!1) = s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(elem!1))) | r(elem!1, s(elem!1)) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7741,plain,
% 1.35/1.53 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7740, 5378, 7729, 7726, 7723, 7714])).
% 1.35/1.53 tff(7742,plain,
% 1.35/1.53 (s(elem!1) = elem!1),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5315, 7741, 5377])).
% 1.35/1.53 tff(7743,plain,
% 1.35/1.53 (~r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5283, 7742, 113, 5377, 5380, 5386, 80])).
% 1.35/1.53 tff(7744,plain,
% 1.35/1.53 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1781, 7743])).
% 1.35/1.53 tff(7745,plain,
% 1.35/1.53 (~b(s(z), s(s(s(s(s(z))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[3641, 7744, 7700, 5388])).
% 1.35/1.53 tff(7746,plain,
% 1.35/1.53 (r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1709, 7745])).
% 1.35/1.53 tff(7747,plain,
% 1.35/1.53 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2798, 7744, 7700, 5388])).
% 1.35/1.53 tff(7748,plain,
% 1.35/1.53 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[6600, 7747])).
% 1.35/1.53 tff(7749,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1660, 7748, 7746, 5376])).
% 1.35/1.53 tff(7750,plain,(b(s(s(elem!1)), s(z)) | (s(elem!1) = s(z)) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7751,plain,
% 1.35/1.53 (b(s(s(elem!1)), s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7750, 81, 1, 64])).
% 1.35/1.53 tff(7752,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 1.35/1.53 tff(7753,plain,
% 1.35/1.53 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7752])).
% 1.35/1.53 tff(7754,plain,
% 1.35/1.53 (s(s(z)) = s(elem!1)),
% 1.35/1.53 inference(transitivity,[status(thm)],[144, 7753, 17])).
% 1.35/1.53 tff(7755,plain,
% 1.35/1.53 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7754])).
% 1.35/1.53 tff(7756,plain,
% 1.35/1.53 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7755])).
% 1.35/1.53 tff(7757,plain,
% 1.35/1.53 (elem!1 = s(z)),
% 1.35/1.53 inference(transitivity,[status(thm)],[155, 7756, 12])).
% 1.35/1.53 tff(7758,plain,
% 1.35/1.53 (s(z) = elem!1),
% 1.35/1.53 inference(transitivity,[status(thm)],[69, 7755, 154])).
% 1.35/1.53 tff(7759,plain,
% 1.35/1.53 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7758])).
% 1.35/1.53 tff(7760,plain,
% 1.35/1.53 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7759])).
% 1.35/1.53 tff(7761,plain,
% 1.35/1.53 (~(elem!1 = s(s(elem!1)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[41, 7760])).
% 1.35/1.53 tff(7762,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[4823, 7761, 7757, 64, 114, 7580, 81])).
% 1.35/1.53 tff(7763,plain,((~(s(s(s(z))) = s(s(elem!1)))) | b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7764,plain,
% 1.35/1.53 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7763, 81, 114, 64])).
% 1.35/1.53 tff(7765,plain,
% 1.35/1.53 (~r(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7698, 81, 114, 64])).
% 1.35/1.53 tff(7766,plain,
% 1.35/1.53 (b(z, s(z))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[1542, 7765])).
% 1.35/1.53 tff(7767,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7768,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(7769,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 1.35/1.53 tff(7770,plain,
% 1.35/1.53 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7769, 238, 1137, 23, 1456])).
% 1.35/1.53 tff(7771,plain,
% 1.35/1.53 (r(s(s(s(z))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[5739, 51, 5729, 7770])).
% 1.35/1.53 tff(7772,plain,
% 1.35/1.53 (~b(z, s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[4875, 1137, 1457, 23])).
% 1.35/1.53 tff(7773,plain,
% 1.35/1.53 (r(z, s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2071, 7772])).
% 1.35/1.53 tff(7774,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7775,plain,
% 1.35/1.53 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(7776,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7775])).
% 1.35/1.53 tff(7777,plain,
% 1.35/1.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.35/1.53 inference(transitivity,[status(thm)],[7776, 7774])).
% 1.35/1.53 tff(7778,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)))),
% 1.35/1.53 inference(quant_inst,[status(thm)],[])).
% 1.35/1.53 tff(7779,plain,
% 1.35/1.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7778, 7777])).
% 1.35/1.53 tff(7780,plain,
% 1.35/1.53 ($false),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7779, 124, 5103, 7773, 7771])).
% 1.35/1.53 tff(7781,plain,((~b(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.53 tff(7782,plain,
% 1.35/1.53 (~b(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7781, 23, 7766, 1456, 7764])).
% 1.35/1.53 tff(7783,plain,
% 1.35/1.53 (r(s(z), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[56, 7782])).
% 1.35/1.53 tff(7784,plain,
% 1.35/1.53 (elem!1 = s(s(elem!1))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[7618, 7783, 64, 7580, 114])).
% 1.35/1.53 tff(7785,plain,
% 1.35/1.53 (s(elem!1) = s(s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[2097, 7784])).
% 1.35/1.53 tff(7786,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7785])).
% 1.35/1.53 tff(7787,plain,
% 1.35/1.53 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7786])).
% 1.35/1.53 tff(7788,plain,
% 1.35/1.53 (b(s(s(z)), s(elem!1))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7690, 7787])).
% 1.35/1.53 tff(7789,plain,
% 1.35/1.53 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7784])).
% 1.35/1.53 tff(7790,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.35/1.53 inference(symmetry,[status(thm)],[7789])).
% 1.35/1.53 tff(7791,plain,
% 1.35/1.53 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[200, 7783, 80])).
% 1.35/1.53 tff(7792,plain,
% 1.35/1.53 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[135, 7791, 114])).
% 1.35/1.53 tff(7793,plain,
% 1.35/1.53 (b(s(s(z)), elem!1)),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7792, 7790])).
% 1.35/1.53 tff(7794,plain,
% 1.35/1.53 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7785])).
% 1.35/1.53 tff(7795,plain,
% 1.35/1.53 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(symmetry,[status(thm)],[7794])).
% 1.35/1.53 tff(7796,plain,
% 1.35/1.53 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 1.35/1.53 inference(monotonicity,[status(thm)],[7795])).
% 1.35/1.53 tff(7797,plain,
% 1.35/1.53 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.53 inference(unit_resolution,[status(thm)],[218, 7783, 7580])).
% 1.35/1.53 tff(7798,plain,
% 1.35/1.53 (~r(s(elem!1), s(s(elem!1)))),
% 1.35/1.53 inference(modus_ponens,[status(thm)],[7797, 7796])).
% 1.35/1.53 tff(7799,plain,
% 1.35/1.54 (~r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7675, 58, 114, 23, 169, 81])).
% 1.35/1.54 tff(7800,plain,
% 1.35/1.54 (b(s(z), s(s(s(s(s(z))))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1709, 7799])).
% 1.35/1.54 tff(7801,plain,
% 1.35/1.54 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[135, 2214, 114])).
% 1.35/1.54 tff(7802,plain,
% 1.35/1.54 (s(elem!1) = elem!1),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5315, 58, 2073])).
% 1.35/1.54 tff(7803,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(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))))), s(s(z)))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7804,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(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))))), s(s(z)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7805,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7804, 7803])).
% 1.35/1.54 tff(7806,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7805, 238, 227, 1906, 23, 4122])).
% 1.35/1.54 tff(7807,plain,((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7808,plain,
% 1.35/1.54 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7807, 1739, 227, 23])).
% 1.35/1.54 tff(7809,plain,
% 1.35/1.54 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5275, 2665, 389])).
% 1.35/1.54 tff(7810,plain,
% 1.35/1.54 (b(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1064, 7809, 5256])).
% 1.35/1.54 tff(7811,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5296, 7810, 7808, 2073])).
% 1.35/1.54 tff(7812,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(s(elem!1) = elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7813,plain,
% 1.35/1.54 (~r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7812, 7802, 7801, 23, 2073, 160, 169])).
% 1.35/1.54 tff(7814,plain,
% 1.35/1.54 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1781, 7813])).
% 1.35/1.54 tff(7815,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7816,plain,
% 1.35/1.54 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7817,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7816])).
% 1.35/1.54 tff(7818,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[7817, 7815])).
% 1.35/1.54 tff(7819,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7820,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7819, 7818])).
% 1.35/1.54 tff(7821,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7820, 238, 23, 1785, 1783, 4122])).
% 1.35/1.54 tff(7822,plain,((~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~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,[]))).
% 1.35/1.54 tff(7823,plain,
% 1.35/1.54 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7822, 7800, 23, 7814])).
% 1.35/1.54 tff(7824,plain,
% 1.35/1.54 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5296, 7823, 2073])).
% 1.35/1.54 tff(7825,plain,
% 1.35/1.54 (r(s(s(s(s(s(z))))), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1064, 7824, 5256])).
% 1.35/1.54 tff(7826,plain,
% 1.35/1.54 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5275, 7825, 7802])).
% 1.35/1.54 tff(7827,plain,
% 1.35/1.54 (~r(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2050, 7826, 7814, 2040, 7800])).
% 1.35/1.54 tff(7828,plain,
% 1.35/1.54 (b(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2071, 7827])).
% 1.35/1.54 tff(7829,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7830,plain,
% 1.35/1.54 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7831,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7830])).
% 1.35/1.54 tff(7832,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[7831, 7829])).
% 1.35/1.54 tff(7833,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7834,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7833, 7832])).
% 1.35/1.54 tff(7835,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7834, 238, 7828, 23, 6212, 7800])).
% 1.35/1.54 tff(7836,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | r(z, s(z)) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7837,plain,
% 1.35/1.54 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7836, 23, 7765, 7784, 7783, 80, 114, 81])).
% 1.35/1.54 tff(7838,plain,
% 1.35/1.54 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5343, 7837])).
% 1.35/1.54 tff(7839,plain,
% 1.35/1.54 (b(s(elem!1), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[534, 7838, 7798])).
% 1.35/1.54 tff(7840,plain,
% 1.35/1.54 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7785])).
% 1.35/1.54 tff(7841,plain,
% 1.35/1.54 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.35/1.54 inference(symmetry,[status(thm)],[7840])).
% 1.35/1.54 tff(7842,plain,
% 1.35/1.54 (r(s(z), s(elem!1))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7580, 7841])).
% 1.35/1.54 tff(7843,plain,
% 1.35/1.54 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[6009, 7842, 7783])).
% 1.35/1.54 tff(7844,plain,
% 1.35/1.54 (~r(elem!1, s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7696, 7843, 7784])).
% 1.35/1.54 tff(7845,plain,
% 1.35/1.54 (~(elem!1 = s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[386, 7838])).
% 1.35/1.54 tff(7846,plain,
% 1.35/1.54 (b(elem!1, s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[629, 7845, 7844])).
% 1.35/1.54 tff(7847,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5355, 7846, 7839, 7793, 7788])).
% 1.35/1.54 tff(7848,plain,((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7849,plain,
% 1.35/1.54 (~b(s(s(s(z))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7848, 7751, 81, 64, 22])).
% 1.35/1.54 tff(7850,plain,
% 1.35/1.54 (r(s(s(s(z))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5118, 7849])).
% 1.35/1.54 tff(7851,plain,
% 1.35/1.54 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5185, 7850, 80])).
% 1.35/1.54 tff(7852,plain,
% 1.35/1.54 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1624, 7851])).
% 1.35/1.54 tff(7853,plain,
% 1.35/1.54 (r(s(s(s(z))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5118, 1425])).
% 1.35/1.54 tff(7854,plain,
% 1.35/1.54 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5185, 7853, 80])).
% 1.35/1.54 tff(7855,plain,
% 1.35/1.54 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1624, 7854])).
% 1.35/1.54 tff(7856,plain,
% 1.35/1.54 (~r(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7618, 150, 64, 7580, 114])).
% 1.35/1.54 tff(7857,plain,
% 1.35/1.54 (b(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[56, 7856])).
% 1.35/1.54 tff(7858,plain,
% 1.35/1.54 (s(s(s(z))) = s(elem!1)),
% 1.35/1.54 inference(transitivity,[status(thm)],[716, 5217, 17])).
% 1.35/1.54 tff(7859,plain,
% 1.35/1.54 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7858])).
% 1.35/1.54 tff(7860,plain,
% 1.35/1.54 ((~b(s(s(s(z))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7859])).
% 1.35/1.54 tff(7861,plain,
% 1.35/1.54 (~b(s(elem!1), s(z))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[1425, 7860])).
% 1.35/1.54 tff(7862,plain,
% 1.35/1.54 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[2891])).
% 1.35/1.54 tff(7863,plain,
% 1.35/1.54 (b(s(s(s(elem!1))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.54 inference(symmetry,[status(thm)],[7862])).
% 1.35/1.54 tff(7864,plain,
% 1.35/1.54 ((~b(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7863])).
% 1.35/1.54 tff(7865,plain,
% 1.35/1.54 ((~![X: $i] : (~b(X, X))) | (~b(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7866,plain,
% 1.35/1.54 (~b(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7865, 837])).
% 1.35/1.54 tff(7867,plain,
% 1.35/1.54 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7866, 7864])).
% 1.35/1.54 tff(7868,plain,
% 1.35/1.54 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7858])).
% 1.35/1.54 tff(7869,plain,
% 1.35/1.54 (s(s(z)) = elem!1),
% 1.35/1.54 inference(transitivity,[status(thm)],[144, 7868, 154])).
% 1.35/1.54 tff(7870,plain,
% 1.35/1.54 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7869])).
% 1.35/1.54 tff(7871,plain,
% 1.35/1.54 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7870])).
% 1.35/1.54 tff(7872,plain,
% 1.35/1.54 (~b(elem!1, s(z))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[64, 7871])).
% 1.35/1.54 tff(7873,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[6588, 7872, 7867, 1457, 150, 7861])).
% 1.35/1.54 tff(7874,plain,((~(s(s(s(s(z)))) = s(s(elem!1)))) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | b(s(s(z)), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7875,plain,
% 1.35/1.54 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7874, 150, 1457, 64, 1425])).
% 1.35/1.54 tff(7876,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5200, 238, 7857, 1457, 7855])).
% 1.35/1.54 tff(7877,plain,
% 1.35/1.54 (r(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1499, 51, 726, 7876])).
% 1.35/1.54 tff(7878,plain,
% 1.35/1.54 (r(s(s(elem!1)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4905, 4903])).
% 1.35/1.54 tff(7879,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7880,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7881,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7880, 7879])).
% 1.35/1.54 tff(7882,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7881, 238, 1137, 23, 1784])).
% 1.35/1.54 tff(7883,plain,
% 1.35/1.54 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5236, 51, 5233, 7882])).
% 1.35/1.54 tff(7884,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[6888, 124, 7883, 7878, 6924])).
% 1.35/1.54 tff(7885,plain,(b(s(s(elem!1)), z) | (~r(s(s(s(s(z)))), z)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7886,plain,
% 1.35/1.54 (b(s(s(elem!1)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7885, 7877, 7875, 7857, 23, 7855])).
% 1.35/1.54 tff(7887,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7888,plain,
% 1.35/1.54 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.35/1.54 inference(rewrite,[status(thm)],[])).
% 1.35/1.54 tff(7889,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7888])).
% 1.35/1.54 tff(7890,plain,
% 1.35/1.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))))),
% 1.35/1.54 inference(transitivity,[status(thm)],[7889, 7887])).
% 1.35/1.54 tff(7891,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.35/1.54 inference(quant_inst,[status(thm)],[])).
% 1.35/1.54 tff(7892,plain,
% 1.35/1.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7891, 7890])).
% 1.35/1.54 tff(7893,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7892, 238, 7857, 7886, 23, 1457])).
% 1.35/1.54 tff(7894,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | b(s(s(z)), s(z)) | b(s(s(s(z))), s(z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7895,plain,
% 1.35/1.54 (elem!1 = s(s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7894, 7751, 7700, 64, 7849, 22])).
% 1.35/1.54 tff(7896,plain,
% 1.35/1.54 (b(s(s(z)), elem!1)),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7801, 5323])).
% 1.35/1.54 tff(7897,plain,
% 1.35/1.54 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[2597])).
% 1.35/1.54 tff(7898,plain,
% 1.35/1.54 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.35/1.54 inference(symmetry,[status(thm)],[7897])).
% 1.35/1.54 tff(7899,plain,
% 1.35/1.54 (r(s(z), s(elem!1))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[161, 7898])).
% 1.35/1.54 tff(7900,plain,
% 1.35/1.54 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[6009, 160, 7899])).
% 1.35/1.54 tff(7901,plain,
% 1.35/1.54 (~r(elem!1, s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7696, 7900, 2073])).
% 1.35/1.54 tff(7902,plain,
% 1.35/1.54 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[177, 161, 169])).
% 1.35/1.54 tff(7903,plain,
% 1.35/1.54 (b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[190, 7902])).
% 1.35/1.54 tff(7904,plain,
% 1.35/1.54 (b(s(s(z)), s(elem!1))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7903, 5320])).
% 1.35/1.54 tff(7905,plain,
% 1.35/1.54 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7836, 160, 2040, 23, 2073, 169, 114, 81])).
% 1.35/1.54 tff(7906,plain,
% 1.35/1.54 (~b(s(s(z)), elem!1)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7740, 7905, 2597, 7904, 7901, 219])).
% 1.35/1.54 tff(7907,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7906, 7896])).
% 1.35/1.54 tff(7908,plain,((~r(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | r(z, s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7909,plain,
% 1.35/1.54 (~r(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7908, 7895, 22, 7699, 7751, 80, 81, 7580])).
% 1.35/1.54 tff(7910,plain,
% 1.35/1.54 (b(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[56, 7909])).
% 1.35/1.54 tff(7911,plain,
% 1.35/1.54 (s(elem!1) = s(s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2097, 7895])).
% 1.35/1.54 tff(7912,plain,
% 1.35/1.54 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5222, 7911, 22])).
% 1.35/1.54 tff(7913,plain,
% 1.35/1.54 (~b(s(s(elem!1)), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7892, 238, 7910, 7751, 7700])).
% 1.35/1.54 tff(7914,plain,
% 1.35/1.54 (~r(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7885, 7913, 7912, 7910, 7751, 7852])).
% 1.35/1.54 tff(7915,plain,
% 1.35/1.54 (~b(s(s(s(s(z)))), z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5200, 238, 7910, 7700, 7852])).
% 1.35/1.54 tff(7916,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[1499, 51, 726, 7915, 7914])).
% 1.35/1.54 tff(7917,plain,(b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7918,plain,
% 1.35/1.54 (b(s(z), s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7917, 1, 64])).
% 1.35/1.54 tff(7919,plain,
% 1.35/1.54 (~r(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7618, 150, 64, 7580, 22])).
% 1.35/1.54 tff(7920,plain,
% 1.35/1.54 (b(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[56, 7919])).
% 1.35/1.54 tff(7921,plain,
% 1.35/1.54 (b(z, s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5756, 7920, 7918, 64])).
% 1.35/1.54 tff(7922,plain,
% 1.35/1.54 (~b(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4914, 7921, 1, 272, 7920])).
% 1.35/1.54 tff(7923,plain,
% 1.35/1.54 (r(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2071, 7922])).
% 1.35/1.54 tff(7924,plain,
% 1.35/1.54 (~b(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4914, 1457, 1, 275, 1137])).
% 1.35/1.54 tff(7925,plain,
% 1.35/1.54 (~r(z, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4932, 1457, 1137, 307, 1, 162])).
% 1.35/1.54 tff(7926,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[2071, 7925, 7924])).
% 1.35/1.54 tff(7927,plain,((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7928,plain,
% 1.35/1.54 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7927, 7921, 1, 113, 7920, 272])).
% 1.35/1.54 tff(7929,plain,
% 1.35/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[323, 7928, 272])).
% 1.35/1.54 tff(7930,plain,
% 1.35/1.54 (~b(s(elem!1), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4949, 7929, 7921, 7920, 159, 7923])).
% 1.35/1.54 tff(7931,plain,
% 1.35/1.54 (r(s(elem!1), s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[473, 7930, 1])).
% 1.35/1.54 tff(7932,plain,
% 1.35/1.54 (~r(elem!1, s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[6786, 226, 546, 167, 7857])).
% 1.35/1.54 tff(7933,plain,
% 1.35/1.54 (elem!1 = s(z)),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5028, 7932, 64, 7580, 114, 150, 226])).
% 1.35/1.54 tff(7934,plain,
% 1.35/1.54 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 1.35/1.54 inference(monotonicity,[status(thm)],[7933])).
% 1.35/1.54 tff(7935,plain,
% 1.35/1.54 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 1.35/1.54 inference(symmetry,[status(thm)],[7934])).
% 1.35/1.54 tff(7936,plain,
% 1.35/1.54 (b(elem!1, s(s(elem!1)))),
% 1.35/1.54 inference(modus_ponens,[status(thm)],[7857, 7935])).
% 1.35/1.54 tff(7937,plain,
% 1.35/1.54 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4806, 7932, 64, 7580, 114, 150])).
% 1.35/1.54 tff(7938,plain,
% 1.35/1.54 (b(elem!1, s(s(s(elem!1))))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4820, 7937, 7690])).
% 1.35/1.54 tff(7939,plain,
% 1.35/1.54 (~b(elem!1, s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3306, 7938, 289, 226])).
% 1.35/1.54 tff(7940,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7939, 7936])).
% 1.35/1.54 tff(7941,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7942,plain,
% 1.35/1.54 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7941, 7929, 64, 22, 150, 7918])).
% 1.35/1.54 tff(7943,plain,
% 1.35/1.54 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[223, 7942, 209])).
% 1.35/1.54 tff(7944,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.35/1.54 tff(7945,plain,
% 1.35/1.54 (s(s(z)) = s(z)),
% 1.35/1.54 inference(symmetry,[status(thm)],[7944])).
% 1.35/1.54 tff(7946,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[74, 7945])).
% 1.35/1.54 tff(7947,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7948,plain,
% 1.35/1.54 (~(elem!1 = s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4445, 192, 80, 7580, 692, 210, 167, 7920])).
% 1.35/1.54 tff(7949,plain,
% 1.35/1.54 (r(elem!1, s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4545, 192, 64, 7580, 150, 1, 7920, 210])).
% 1.35/1.54 tff(7950,plain,
% 1.35/1.54 (s(elem!1) = s(s(z))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[5022, 7949, 80, 1, 82, 159, 7920])).
% 1.35/1.54 tff(7951,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[379, 7950, 7948])).
% 1.35/1.54 tff(7952,plain,((~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(z)) | b(s(s(elem!1)), s(z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(z)), s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.54 tff(7953,plain,
% 1.35/1.54 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[7952, 7943, 82, 1, 64, 150])).
% 1.35/1.54 tff(7954,plain,
% 1.35/1.54 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[135, 7953, 22])).
% 1.35/1.54 tff(7955,plain,
% 1.35/1.54 (~b(s(z), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4553, 238, 7929, 7920, 7954])).
% 1.35/1.54 tff(7956,plain,
% 1.35/1.54 (r(s(z), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4557, 51, 7955, 7947])).
% 1.35/1.54 tff(7957,plain,
% 1.35/1.54 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4568, 7956, 7580])).
% 1.35/1.54 tff(7958,plain,
% 1.35/1.54 (b(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[3233, 7957])).
% 1.35/1.54 tff(7959,plain,
% 1.35/1.54 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[315, 306, 162])).
% 1.35/1.54 tff(7960,plain,
% 1.35/1.54 (b(s(s(elem!1)), s(elem!1))),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[323, 7959, 3294])).
% 1.35/1.54 tff(7961,plain,
% 1.35/1.54 ($false),
% 1.35/1.54 inference(unit_resolution,[status(thm)],[4521, 7960, 1234, 161, 1137, 418, 206, 210, 7903, 433, 1235])).
% 1.35/1.54 tff(7962,plain,((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(z) = s(elem!1)) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(elem!1) = s(s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(7963,plain,
% 1.35/1.55 (s(elem!1) = s(s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7962, 7958, 7580, 415, 159, 7920, 426, 7943, 7931, 113, 80])).
% 1.35/1.55 tff(7964,plain,
% 1.35/1.55 (elem!1 = s(z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[379, 7963])).
% 1.35/1.55 tff(7965,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[7964])).
% 1.35/1.55 tff(7966,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(symmetry,[status(thm)],[7965])).
% 1.35/1.55 tff(7967,plain,
% 1.35/1.55 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[7966])).
% 1.35/1.55 tff(7968,plain,
% 1.35/1.55 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3152, 226, 546, 7857])).
% 1.35/1.55 tff(7969,plain,
% 1.35/1.55 (b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1456, 1423])).
% 1.35/1.55 tff(7970,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[249, 7969])).
% 1.35/1.55 tff(7971,plain,((~b(s(s(s(z))), s(z))) | b(s(s(elem!1)), elem!1) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(7972,plain,
% 1.35/1.55 (~(elem!1 = s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7971, 7968, 1456])).
% 1.35/1.55 tff(7973,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5028, 7972, 7932, 64, 7580, 114, 150, 226])).
% 1.35/1.55 tff(7974,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(7975,plain,
% 1.35/1.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7974, 1456, 22, 150, 64, 7918])).
% 1.35/1.55 tff(7976,plain,
% 1.35/1.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[223, 7975, 209])).
% 1.35/1.55 tff(7977,plain,
% 1.35/1.55 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7952, 7976, 82, 1, 64, 150])).
% 1.35/1.55 tff(7978,plain,
% 1.35/1.55 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[135, 7977, 22])).
% 1.35/1.55 tff(7979,plain,
% 1.35/1.55 (~b(s(z), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4553, 238, 7929, 7920, 7978])).
% 1.35/1.55 tff(7980,plain,
% 1.35/1.55 (r(s(z), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4557, 51, 7979, 7947])).
% 1.35/1.55 tff(7981,plain,
% 1.35/1.55 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4568, 7980, 7580])).
% 1.35/1.55 tff(7982,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3233, 7981])).
% 1.35/1.55 tff(7983,plain,
% 1.35/1.55 (s(elem!1) = s(s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7962, 7982, 7580, 415, 159, 7920, 426, 7976, 7931, 113, 80])).
% 1.35/1.55 tff(7984,plain,
% 1.35/1.55 (elem!1 = s(z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[379, 7983])).
% 1.35/1.55 tff(7985,plain,
% 1.35/1.55 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[7984])).
% 1.35/1.55 tff(7986,plain,
% 1.35/1.55 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(symmetry,[status(thm)],[7985])).
% 1.35/1.55 tff(7987,plain,
% 1.35/1.55 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[7986])).
% 1.35/1.55 tff(7988,plain,
% 1.35/1.55 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[82, 7987])).
% 1.35/1.55 tff(7989,plain,
% 1.35/1.55 (b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7971, 7984, 1456])).
% 1.35/1.55 tff(7990,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7989, 7988])).
% 1.35/1.55 tff(7991,plain,((~b(s(s(s(z))), s(z))) | b(s(s(elem!1)), s(z)) | (s(elem!1) = s(z)) | b(s(s(z)), s(z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(7992,plain,
% 1.35/1.55 (~b(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7991, 150, 1, 64, 82])).
% 1.35/1.55 tff(7993,plain,
% 1.35/1.55 (r(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5118, 7992])).
% 1.35/1.55 tff(7994,plain,
% 1.35/1.55 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5185, 7993, 80])).
% 1.35/1.55 tff(7995,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1624, 7994])).
% 1.35/1.55 tff(7996,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5200, 238, 7920, 7921, 7995])).
% 1.35/1.55 tff(7997,plain,
% 1.35/1.55 (r(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1499, 51, 726, 7996])).
% 1.35/1.55 tff(7998,plain,
% 1.35/1.55 (~r(s(s(s(elem!1))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3520, 7943, 7923])).
% 1.35/1.55 tff(7999,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6952, 7998])).
% 1.35/1.55 tff(8000,plain,
% 1.35/1.55 (~b(s(s(s(elem!1))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6948, 7999, 7921, 7997])).
% 1.35/1.55 tff(8001,plain,
% 1.35/1.55 (~b(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8000, 7967])).
% 1.35/1.55 tff(8002,plain,
% 1.35/1.55 (~(elem!1 = s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1364, 7964])).
% 1.35/1.55 tff(8003,plain,
% 1.35/1.55 (~(s(s(s(elem!1))) = elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[516, 8002])).
% 1.35/1.55 tff(8004,plain,
% 1.35/1.55 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1428, 7964, 7992])).
% 1.35/1.55 tff(8005,plain,
% 1.35/1.55 (r(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[255, 8004, 167])).
% 1.35/1.55 tff(8006,plain,
% 1.35/1.55 (~r(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1182, 8005, 7943])).
% 1.35/1.55 tff(8007,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[647, 8006, 8003])).
% 1.35/1.55 tff(8008,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8007, 8001])).
% 1.35/1.55 tff(8009,plain,((elem!1 = s(s(elem!1))) | b(s(s(elem!1)), s(z)) | (s(elem!1) = s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8010,plain,
% 1.35/1.55 (elem!1 = s(s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8009, 82, 1, 64])).
% 1.35/1.55 tff(8011,plain,
% 1.35/1.55 (~b(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6963, 8010, 22, 7918, 80, 113])).
% 1.35/1.55 tff(8012,plain,
% 1.35/1.55 (~b(s(z), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5756, 8011, 7918, 64])).
% 1.35/1.55 tff(8013,plain,
% 1.35/1.55 (r(s(z), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[56, 8012])).
% 1.35/1.55 tff(8014,plain,
% 1.35/1.55 (r(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1542, 8011])).
% 1.35/1.55 tff(8015,plain,
% 1.35/1.55 (~b(s(s(z)), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5041, 8014, 80, 113])).
% 1.35/1.55 tff(8016,plain,
% 1.35/1.55 (r(s(s(z)), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[135, 8015, 22])).
% 1.35/1.55 tff(8017,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[200, 8016, 8013, 80])).
% 1.35/1.55 tff(8018,plain,(b(s(s(elem!1)), s(z)) | b(s(s(z)), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8019,plain,
% 1.35/1.55 (b(s(s(elem!1)), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8018, 1, 64])).
% 1.35/1.55 tff(8020,plain,
% 1.35/1.55 (b(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5756, 7857, 546, 64])).
% 1.35/1.55 tff(8021,plain,
% 1.35/1.55 (b(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7894, 8020, 23, 64, 150, 114])).
% 1.35/1.55 tff(8022,plain,
% 1.35/1.55 (s(s(s(z))) = s(s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7781, 8021, 23, 7857, 8020])).
% 1.35/1.55 tff(8023,plain,
% 1.35/1.55 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8022])).
% 1.35/1.55 tff(8024,plain,
% 1.35/1.55 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8023])).
% 1.35/1.55 tff(8025,plain,
% 1.35/1.55 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8024])).
% 1.35/1.55 tff(8026,plain,
% 1.35/1.55 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[8025, 1008])).
% 1.35/1.55 tff(8027,plain,
% 1.35/1.55 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8026])).
% 1.35/1.55 tff(8028,plain,
% 1.35/1.55 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8027])).
% 1.35/1.55 tff(8029,plain,
% 1.35/1.55 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[2782, 8028])).
% 1.35/1.55 tff(8030,plain,
% 1.35/1.55 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8022])).
% 1.35/1.55 tff(8031,plain,
% 1.35/1.55 (s(s(z)) = s(elem!1)),
% 1.35/1.55 inference(transitivity,[status(thm)],[144, 8030, 17])).
% 1.35/1.55 tff(8032,plain,
% 1.35/1.55 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8031])).
% 1.35/1.55 tff(8033,plain,
% 1.35/1.55 (s(z) = elem!1),
% 1.35/1.55 inference(transitivity,[status(thm)],[69, 8032, 154])).
% 1.35/1.55 tff(8034,plain,
% 1.35/1.55 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8033])).
% 1.35/1.55 tff(8035,plain,
% 1.35/1.55 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8034])).
% 1.35/1.55 tff(8036,plain,
% 1.35/1.55 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8035])).
% 1.35/1.55 tff(8037,plain,
% 1.35/1.55 (~r(elem!1, s(z))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[852, 8036])).
% 1.35/1.55 tff(8038,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4806, 8037, 8029, 64, 7580, 114, 150])).
% 1.35/1.55 tff(8039,plain,((elem!1 = s(s(elem!1))) | b(s(s(z)), s(z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8040,plain,
% 1.35/1.55 (elem!1 = s(s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8039, 22, 64, 8019, 7918])).
% 1.35/1.55 tff(8041,plain,
% 1.35/1.55 (s(elem!1) = s(s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[2097, 8040])).
% 1.35/1.55 tff(8042,plain,
% 1.35/1.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6289, 8041, 7918, 80, 1, 8019])).
% 1.35/1.55 tff(8043,plain,
% 1.35/1.55 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[2572, 2, 546])).
% 1.35/1.55 tff(8044,plain,
% 1.35/1.55 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[218, 544, 161])).
% 1.35/1.55 tff(8045,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[223, 8044, 8043, 5616])).
% 1.35/1.55 tff(8046,plain,(b(s(z), s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8047,plain,
% 1.35/1.55 (b(s(z), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8046, 8042, 7580, 7918])).
% 1.35/1.55 tff(8048,plain,
% 1.35/1.55 (b(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5756, 8047, 7918, 64])).
% 1.35/1.55 tff(8049,plain,
% 1.35/1.55 (s(s(elem!1)) = elem!1),
% 1.35/1.55 inference(symmetry,[status(thm)],[8040])).
% 1.35/1.55 tff(8050,plain,
% 1.35/1.55 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8049])).
% 1.35/1.55 tff(8051,plain,
% 1.35/1.55 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8050])).
% 1.35/1.55 tff(8052,plain,
% 1.35/1.55 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8051])).
% 1.35/1.55 tff(8053,plain,
% 1.35/1.55 (~(s(s(s(z))) = elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7046, 8040])).
% 1.35/1.55 tff(8054,plain,
% 1.35/1.55 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8053, 8052])).
% 1.35/1.55 tff(8055,plain,
% 1.35/1.55 (~b(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7781, 8047, 8019, 8054, 8048])).
% 1.35/1.55 tff(8056,plain,
% 1.35/1.55 (r(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5118, 8055])).
% 1.35/1.55 tff(8057,plain,
% 1.35/1.55 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5185, 8056, 80])).
% 1.35/1.55 tff(8058,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1624, 8057])).
% 1.35/1.55 tff(8059,plain,
% 1.35/1.55 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5222, 8041, 22])).
% 1.35/1.55 tff(8060,plain,
% 1.35/1.55 (~b(s(s(elem!1)), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7892, 238, 8047, 8019, 8048])).
% 1.35/1.55 tff(8061,plain,
% 1.35/1.55 (~r(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7885, 8060, 8019, 8059, 8047, 8058])).
% 1.35/1.55 tff(8062,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5200, 238, 8047, 8048, 8058])).
% 1.35/1.55 tff(8063,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1499, 51, 726, 8062, 8061])).
% 1.35/1.55 tff(8064,plain,((s(elem!1) = s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8065,plain,
% 1.35/1.55 (s(elem!1) = s(z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8064, 64])).
% 1.35/1.55 tff(8066,plain,
% 1.35/1.55 (s(s(z)) = s(s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[357, 8065])).
% 1.35/1.55 tff(8067,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.55 tff(8068,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8067])).
% 1.35/1.55 tff(8069,plain,
% 1.35/1.55 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8068])).
% 1.35/1.55 tff(8070,plain,
% 1.35/1.55 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.55 tff(8071,plain,
% 1.35/1.55 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8070])).
% 1.35/1.55 tff(8072,plain,
% 1.35/1.55 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8071])).
% 1.35/1.55 tff(8073,plain,
% 1.35/1.55 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8072])).
% 1.35/1.55 tff(8074,plain,
% 1.35/1.55 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8073])).
% 1.35/1.55 tff(8075,plain,
% 1.35/1.55 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[5165, 8074])).
% 1.35/1.55 tff(8076,plain,
% 1.35/1.55 (~b(s(s(elem!1)), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5399, 8066, 64])).
% 1.35/1.55 tff(8077,plain,
% 1.35/1.55 (r(s(s(elem!1)), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[112, 8076])).
% 1.35/1.55 tff(8078,plain,
% 1.35/1.55 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.55 tff(8079,plain,
% 1.35/1.55 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8078])).
% 1.35/1.55 tff(8080,plain,
% 1.35/1.55 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1291, 8079])).
% 1.35/1.55 tff(8081,plain,
% 1.35/1.55 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.55 tff(8082,plain,
% 1.35/1.55 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8081])).
% 1.35/1.55 tff(8083,plain,
% 1.35/1.55 (r(s(s(elem!1)), s(elem!1))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8077, 8082])).
% 1.35/1.55 tff(8084,plain,
% 1.35/1.55 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.55 tff(8085,plain,
% 1.35/1.55 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8084])).
% 1.35/1.55 tff(8086,plain,
% 1.35/1.55 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8085])).
% 1.35/1.55 tff(8087,plain,
% 1.35/1.55 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[41, 8086])).
% 1.35/1.55 tff(8088,plain,
% 1.35/1.55 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.55 inference(symmetry,[status(thm)],[4243])).
% 1.35/1.55 tff(8089,plain,
% 1.35/1.55 (r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[161, 8088])).
% 1.35/1.55 tff(8090,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[223, 219, 4087])).
% 1.35/1.55 tff(8091,plain,
% 1.35/1.55 (r(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5701, 5695])).
% 1.35/1.55 tff(8092,plain,
% 1.35/1.55 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.35/1.55 inference(monotonicity,[status(thm)],[353])).
% 1.35/1.55 tff(8093,plain,
% 1.35/1.55 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 1.35/1.55 inference(symmetry,[status(thm)],[8092])).
% 1.35/1.55 tff(8094,plain,
% 1.35/1.55 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3762])).
% 1.35/1.55 tff(8095,plain,
% 1.35/1.55 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.35/1.55 inference(symmetry,[status(thm)],[8094])).
% 1.35/1.55 tff(8096,plain,
% 1.35/1.55 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 1.35/1.55 inference(transitivity,[status(thm)],[8095, 8093])).
% 1.35/1.55 tff(8097,plain,
% 1.35/1.55 ((~b(s(z), z)) <=> (~b(s(elem!1), elem!1))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8096])).
% 1.35/1.55 tff(8098,plain,
% 1.35/1.55 (~b(s(elem!1), elem!1)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[5695, 8097])).
% 1.35/1.55 tff(8099,plain,
% 1.35/1.55 (r(s(elem!1), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[408, 8098, 7203])).
% 1.35/1.55 tff(8100,plain,
% 1.35/1.55 (~r(elem!1, s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3315, 8099, 542])).
% 1.35/1.55 tff(8101,plain,
% 1.35/1.55 (b(elem!1, s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1319, 8100, 4084])).
% 1.35/1.55 tff(8102,plain,
% 1.35/1.55 (~r(s(s(elem!1)), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[403, 8099, 307])).
% 1.35/1.55 tff(8103,plain,
% 1.35/1.55 (r(elem!1, s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[615, 8102, 7119, 226, 8101])).
% 1.35/1.55 tff(8104,plain,
% 1.35/1.55 (r(z, s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7136, 8103, 353])).
% 1.35/1.55 tff(8105,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6136, 124, 160, 8104, 8091])).
% 1.35/1.55 tff(8106,plain,(b(s(z), z) | (~r(s(z), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8107,plain,
% 1.35/1.55 (b(s(z), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8106, 160, 353, 8090, 7104, 8089])).
% 1.35/1.55 tff(8108,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[353])).
% 1.35/1.55 tff(8109,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8108])).
% 1.35/1.55 tff(8110,plain,
% 1.35/1.55 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8109])).
% 1.35/1.55 tff(8111,plain,
% 1.35/1.55 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[1775, 8110])).
% 1.35/1.55 tff(8112,plain,
% 1.35/1.55 (r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1781, 1775])).
% 1.35/1.55 tff(8113,plain,
% 1.35/1.55 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1826, 8112, 161])).
% 1.35/1.55 tff(8114,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1814, 8113, 5782])).
% 1.35/1.55 tff(8115,plain,
% 1.35/1.55 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5264, 8112, 162])).
% 1.35/1.55 tff(8116,plain,
% 1.35/1.55 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7528, 8115, 7481, 226, 8114])).
% 1.35/1.55 tff(8117,plain,
% 1.35/1.55 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4361, 8116, 7104])).
% 1.35/1.55 tff(8118,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4351, 8117, 3926])).
% 1.35/1.55 tff(8119,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8118, 8111])).
% 1.35/1.55 tff(8120,plain,(b(s(s(s(s(s(z))))), s(z)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8121,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8120, 8090, 353, 162, 161])).
% 1.35/1.55 tff(8122,plain,
% 1.35/1.55 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[3762])).
% 1.35/1.55 tff(8123,plain,
% 1.35/1.55 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8122])).
% 1.35/1.55 tff(8124,plain,
% 1.35/1.55 (b(z, s(z)) <=> b(elem!1, s(elem!1))),
% 1.35/1.55 inference(transitivity,[status(thm)],[8123, 4093])).
% 1.35/1.55 tff(8125,plain,
% 1.35/1.55 (b(s(s(elem!1)), z)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[4905, 5033])).
% 1.35/1.55 tff(8126,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(8127,plain,
% 1.35/1.55 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(8128,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8127])).
% 1.35/1.55 tff(8129,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[8128, 8126])).
% 1.35/1.55 tff(8130,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(8131,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8130, 8129])).
% 1.35/1.55 tff(8132,plain,
% 1.35/1.55 (~b(z, s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8131, 238, 226, 5036, 8125])).
% 1.35/1.55 tff(8133,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(8134,plain,
% 1.35/1.55 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(8135,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8134])).
% 1.35/1.55 tff(8136,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.35/1.55 inference(transitivity,[status(thm)],[8135, 8133])).
% 1.35/1.55 tff(8137,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(8138,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8137, 8136])).
% 1.35/1.55 tff(8139,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8138, 124, 160, 5517, 161, 1545])).
% 1.35/1.55 tff(8140,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8141,plain,
% 1.35/1.55 (~r(z, s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8140, 1545, 161, 160])).
% 1.35/1.55 tff(8142,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3795, 51, 8141, 3785, 8132])).
% 1.35/1.55 tff(8143,plain,((~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8144,plain,
% 1.35/1.55 (~r(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8143, 8090, 161, 162, 160])).
% 1.35/1.55 tff(8145,plain,
% 1.35/1.55 (b(z, s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1542, 8144])).
% 1.35/1.55 tff(8146,plain,
% 1.35/1.55 (b(elem!1, s(elem!1))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8145, 8124])).
% 1.35/1.55 tff(8147,plain,
% 1.35/1.55 (r(s(elem!1), s(s(elem!1)))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[160, 3872])).
% 1.35/1.55 tff(8148,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[529, 8147])).
% 1.35/1.55 tff(8149,plain,((~r(s(z), s(s(elem!1)))) | r(s(elem!1), s(s(elem!1))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8150,plain,
% 1.35/1.55 (r(s(elem!1), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8149, 160, 353])).
% 1.35/1.55 tff(8151,plain,
% 1.35/1.55 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[2893, 5782])).
% 1.35/1.55 tff(8152,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5236, 51, 8151, 2959])).
% 1.35/1.55 tff(8153,plain,
% 1.35/1.55 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[7429, 238, 226, 8152, 7241])).
% 1.35/1.55 tff(8154,plain,
% 1.35/1.55 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.35/1.55 inference(commutativity,[status(thm)],[])).
% 1.35/1.55 tff(8155,plain,
% 1.35/1.55 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8154])).
% 1.35/1.55 tff(8156,plain,
% 1.35/1.55 (s(z) = s(elem!1)),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[353, 8155])).
% 1.35/1.55 tff(8157,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[353])).
% 1.35/1.55 tff(8158,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.55 inference(symmetry,[status(thm)],[8157])).
% 1.35/1.55 tff(8159,plain,
% 1.35/1.55 (~r(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5185, 1544, 169])).
% 1.35/1.55 tff(8160,plain,
% 1.35/1.55 (b(s(s(s(z))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[5118, 8159])).
% 1.35/1.55 tff(8161,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3886, 8160, 804])).
% 1.35/1.55 tff(8162,plain,
% 1.35/1.55 (b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8161, 8158])).
% 1.35/1.55 tff(8163,plain,
% 1.35/1.55 (~b(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1222, 8162, 7110, 226, 7115, 631])).
% 1.35/1.55 tff(8164,plain,
% 1.35/1.55 (r(s(s(s(elem!1))), elem!1)),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[647, 8163, 7122])).
% 1.35/1.55 tff(8165,plain,
% 1.35/1.55 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[915, 8164, 542, 518, 8156, 631])).
% 1.35/1.55 tff(8166,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[2974, 51, 8165, 8153, 7101])).
% 1.35/1.55 tff(8167,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8168,plain,
% 1.35/1.55 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8167, 8090, 8089, 8150, 8146, 162, 353, 169])).
% 1.35/1.55 tff(8169,plain,
% 1.35/1.55 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1624, 8168])).
% 1.35/1.55 tff(8170,plain,
% 1.35/1.55 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[2798, 8169, 8145, 8121])).
% 1.35/1.55 tff(8171,plain,
% 1.35/1.55 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[6600, 8170])).
% 1.35/1.55 tff(8172,plain,
% 1.35/1.55 (~b(s(z), s(s(s(s(s(z))))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3641, 8169, 8145, 8121])).
% 1.35/1.55 tff(8173,plain,
% 1.35/1.55 (r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1709, 8172])).
% 1.35/1.55 tff(8174,plain,
% 1.35/1.55 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1660, 8173, 8171])).
% 1.35/1.55 tff(8175,plain,
% 1.35/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[1904, 8174])).
% 1.35/1.55 tff(8176,plain,
% 1.35/1.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.55 inference(rewrite,[status(thm)],[])).
% 1.35/1.55 tff(8177,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.35/1.55 inference(quant_inst,[status(thm)],[])).
% 1.35/1.55 tff(8178,plain,
% 1.35/1.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.35/1.55 inference(modus_ponens,[status(thm)],[8177, 8176])).
% 1.35/1.55 tff(8179,plain,
% 1.35/1.55 ($false),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8178, 238, 8175, 8169, 8121, 8107])).
% 1.35/1.55 tff(8180,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.55 tff(8181,plain,
% 1.35/1.55 (~r(s(z), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[8180, 8077, 8065, 80, 7580])).
% 1.35/1.55 tff(8182,plain,
% 1.35/1.55 (~r(s(elem!1), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[3876, 8181, 8065])).
% 1.35/1.55 tff(8183,plain,
% 1.35/1.55 (b(s(elem!1), s(s(elem!1)))),
% 1.35/1.55 inference(unit_resolution,[status(thm)],[534, 8182, 8087])).
% 1.35/1.55 tff(8184,plain,
% 1.35/1.55 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.35/1.55 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.55 tff(8185,plain,
% 1.35/1.55 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8184])).
% 1.35/1.56 tff(8186,plain,
% 1.35/1.56 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.56 tff(8187,plain,
% 1.35/1.56 (elem!1 = z),
% 1.35/1.56 inference(transitivity,[status(thm)],[155, 8186, 26])).
% 1.35/1.56 tff(8188,plain,
% 1.35/1.56 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8187])).
% 1.35/1.56 tff(8189,plain,
% 1.35/1.56 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.35/1.56 inference(transitivity,[status(thm)],[8188, 2036])).
% 1.35/1.56 tff(8190,plain,
% 1.35/1.56 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8189])).
% 1.35/1.56 tff(8191,plain,
% 1.35/1.56 ((s(z) = z) <=> (elem!1 = s(elem!1))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8190, 8185])).
% 1.35/1.56 tff(8192,plain,
% 1.35/1.56 ((~(s(z) = z)) <=> (~(elem!1 = s(elem!1)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8191])).
% 1.35/1.56 tff(8193,plain,
% 1.35/1.56 (~(elem!1 = s(elem!1))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[72, 8192])).
% 1.35/1.56 tff(8194,plain,
% 1.35/1.56 (b(s(z), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[56, 8181])).
% 1.35/1.56 tff(8195,plain,
% 1.35/1.56 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.56 tff(8196,plain,
% 1.35/1.56 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8195, 3730])).
% 1.35/1.56 tff(8197,plain,
% 1.35/1.56 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8196])).
% 1.35/1.56 tff(8198,plain,
% 1.35/1.56 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[4960, 8066])).
% 1.35/1.56 tff(8199,plain,
% 1.35/1.56 (~(s(s(z)) = elem!1)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1385, 8198])).
% 1.35/1.56 tff(8200,plain,
% 1.35/1.56 (~(elem!1 = s(s(elem!1)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8199, 8197])).
% 1.35/1.56 tff(8201,plain,
% 1.35/1.56 (~r(s(s(s(z))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[7584, 1545, 169])).
% 1.35/1.56 tff(8202,plain,
% 1.35/1.56 (b(s(s(s(z))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[5118, 8201])).
% 1.35/1.56 tff(8203,plain,
% 1.35/1.56 (~r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1773, 1545, 169])).
% 1.35/1.56 tff(8204,plain,
% 1.35/1.56 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1781, 8203])).
% 1.35/1.56 tff(8205,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[7606, 8204, 4851, 1137, 8202])).
% 1.35/1.56 tff(8206,plain,((~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8207,plain,
% 1.35/1.56 (~r(z, s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8206, 8194, 80])).
% 1.35/1.56 tff(8208,plain,
% 1.35/1.56 (b(z, s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1542, 8207])).
% 1.35/1.56 tff(8209,plain,
% 1.35/1.56 (b(elem!1, s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[6376, 8208, 8065])).
% 1.35/1.56 tff(8210,plain,
% 1.35/1.56 (~r(elem!1, s(elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1149, 8209, 8200, 8194, 8083])).
% 1.35/1.56 tff(8211,plain,
% 1.35/1.56 (b(elem!1, s(elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[629, 8210, 8193])).
% 1.35/1.56 tff(8212,plain,
% 1.35/1.56 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[7142, 8211, 8183, 8065, 8083])).
% 1.35/1.56 tff(8213,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[223, 8212, 8080])).
% 1.35/1.56 tff(8214,plain,
% 1.35/1.56 (b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8120, 8213, 8065, 8077, 7580])).
% 1.35/1.56 tff(8215,plain,
% 1.35/1.56 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8070])).
% 1.35/1.56 tff(8216,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8215])).
% 1.35/1.56 tff(8217,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.56 tff(8218,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8217, 8216])).
% 1.35/1.56 tff(8219,plain,
% 1.35/1.56 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8218])).
% 1.35/1.56 tff(8220,plain,
% 1.35/1.56 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8065])).
% 1.35/1.56 tff(8221,plain,
% 1.35/1.56 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8220])).
% 1.35/1.56 tff(8222,plain,
% 1.35/1.56 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.56 tff(8223,plain,
% 1.35/1.56 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8222])).
% 1.35/1.56 tff(8224,plain,
% 1.35/1.56 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8223, 8221])).
% 1.35/1.56 tff(8225,plain,
% 1.35/1.56 (b(s(elem!1), s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8194, 8224])).
% 1.35/1.56 tff(8226,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.56 tff(8227,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8226])).
% 1.35/1.56 tff(8228,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8213, 8227])).
% 1.35/1.56 tff(8229,plain,
% 1.35/1.56 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1243, 8228, 7690, 8225])).
% 1.35/1.56 tff(8230,plain,
% 1.35/1.56 (~b(s(s(s(z))), s(z))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8229, 8219])).
% 1.35/1.56 tff(8231,plain,
% 1.35/1.56 (r(s(s(s(z))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[5118, 8230])).
% 1.35/1.56 tff(8232,plain,
% 1.35/1.56 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[5185, 8231, 80])).
% 1.35/1.56 tff(8233,plain,
% 1.35/1.56 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1624, 8232])).
% 1.35/1.56 tff(8234,plain,
% 1.35/1.56 (~b(s(z), s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2798, 8233, 8208, 8214])).
% 1.35/1.56 tff(8235,plain,
% 1.35/1.56 (r(s(z), s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[6600, 8234])).
% 1.35/1.56 tff(8236,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8237,plain,
% 1.35/1.56 (((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8238,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8237])).
% 1.35/1.56 tff(8239,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8238, 8236])).
% 1.35/1.56 tff(8240,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(8241,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8240, 8239])).
% 1.35/1.56 tff(8242,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8241, 124, 1650, 861, 161])).
% 1.35/1.56 tff(8243,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8244,plain,
% 1.35/1.56 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8243, 8235, 7580])).
% 1.35/1.56 tff(8245,assumption,(~r(s(s(s(s(z)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.35/1.56 tff(8246,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2974, 51, 8245, 4221, 3797])).
% 1.35/1.56 tff(8247,plain,(r(s(s(s(s(z)))), s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8248,plain,
% 1.35/1.56 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8247, 8244, 8075])).
% 1.35/1.56 tff(8249,plain,
% 1.35/1.56 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.56 tff(8250,plain,
% 1.35/1.56 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[7690, 8249])).
% 1.35/1.56 tff(8251,plain,
% 1.35/1.56 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[2978, 238, 8213, 8250, 8248])).
% 1.35/1.56 tff(8252,plain,
% 1.35/1.56 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8251, 8069])).
% 1.35/1.56 tff(8253,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8254,plain,
% 1.35/1.56 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8255,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8254])).
% 1.35/1.56 tff(8256,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8255, 8253])).
% 1.35/1.56 tff(8257,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(8258,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8257, 8256])).
% 1.35/1.56 tff(8259,plain,
% 1.35/1.56 (~b(z, s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8258, 238, 8194, 8208, 8233])).
% 1.35/1.56 tff(8260,plain,
% 1.35/1.56 (r(z, s(s(s(s(z)))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1487, 51, 8259, 7182])).
% 1.35/1.56 tff(8261,plain,
% 1.35/1.56 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066])).
% 1.35/1.56 tff(8262,plain,
% 1.35/1.56 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8261])).
% 1.35/1.56 tff(8263,plain,
% 1.35/1.56 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8066, 8070])).
% 1.35/1.56 tff(8264,plain,
% 1.35/1.56 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.35/1.56 inference(symmetry,[status(thm)],[8263])).
% 1.35/1.56 tff(8265,plain,
% 1.35/1.56 (b(s(s(z)), s(s(s(z))))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8250, 8264])).
% 1.35/1.56 tff(8266,plain,
% 1.35/1.56 (b(s(z), s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8194, 8223])).
% 1.35/1.56 tff(8267,plain,
% 1.35/1.56 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.35/1.56 inference(transitivity,[status(thm)],[8190, 2465])).
% 1.35/1.56 tff(8268,plain,
% 1.35/1.56 ((~(s(z) = z)) <=> (~(s(z) = elem!1))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8267])).
% 1.35/1.56 tff(8269,plain,
% 1.35/1.56 (~(s(z) = elem!1)),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[72, 8268])).
% 1.35/1.56 tff(8270,plain,
% 1.35/1.56 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8187])).
% 1.35/1.56 tff(8271,plain,
% 1.35/1.56 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.35/1.56 inference(symmetry,[status(thm)],[8270])).
% 1.35/1.56 tff(8272,plain,
% 1.35/1.56 ((~r(s(z), z)) <=> (~r(s(z), elem!1))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8271])).
% 1.35/1.56 tff(8273,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8274,plain,
% 1.35/1.56 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8275,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8274])).
% 1.35/1.56 tff(8276,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8275, 8273])).
% 1.35/1.56 tff(8277,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(8278,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8277, 8276])).
% 1.35/1.56 tff(8279,plain,
% 1.35/1.56 (~r(s(z), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8278, 124, 8235, 8260])).
% 1.35/1.56 tff(8280,plain,
% 1.35/1.56 (~r(s(z), elem!1)),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8279, 8272])).
% 1.35/1.56 tff(8281,plain,
% 1.35/1.56 (b(s(z), elem!1)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[351, 8280, 8269])).
% 1.35/1.56 tff(8282,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8283,plain,
% 1.35/1.56 (((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8284,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8283])).
% 1.35/1.56 tff(8285,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8284, 8282])).
% 1.35/1.56 tff(8286,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 1.35/1.56 inference(quant_inst,[status(thm)],[])).
% 1.35/1.56 tff(8287,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8286, 8285])).
% 1.35/1.56 tff(8288,plain,
% 1.35/1.56 ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8287, 238])).
% 1.35/1.56 tff(8289,plain,
% 1.35/1.56 (~b(elem!1, s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8288, 8281, 8266, 8265])).
% 1.35/1.56 tff(8290,plain,
% 1.35/1.56 (b(elem!1, s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[1185, 742])).
% 1.35/1.56 tff(8291,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[757, 8290])).
% 1.35/1.56 tff(8292,plain,((~b(elem!1, s(s(elem!1)))) | b(elem!1, s(s(z))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8293,plain,
% 1.35/1.56 (~b(elem!1, s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8292, 8289, 8066])).
% 1.35/1.56 tff(8294,plain,
% 1.35/1.56 (r(elem!1, s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[606, 8293, 8200])).
% 1.35/1.56 tff(8295,plain,
% 1.35/1.56 (r(z, s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[7136, 8294, 8065])).
% 1.35/1.56 tff(8296,plain,
% 1.35/1.56 (r(z, s(s(z)))),
% 1.35/1.56 inference(modus_ponens,[status(thm)],[8295, 8262])).
% 1.35/1.56 tff(8297,plain,
% 1.35/1.56 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3484, 8296, 8260])).
% 1.35/1.56 tff(8298,plain,
% 1.35/1.56 (b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1564, 8297])).
% 1.35/1.56 tff(8299,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8298, 8252])).
% 1.35/1.56 tff(8300,plain,(b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8301,plain,
% 1.35/1.56 (~(s(elem!1) = s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[5343, 8043])).
% 1.35/1.56 tff(8302,plain,
% 1.35/1.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[223, 8043, 5616])).
% 1.35/1.56 tff(8303,plain,
% 1.35/1.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3182, 192, 210])).
% 1.35/1.56 tff(8304,plain,
% 1.35/1.56 (b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[190, 8303])).
% 1.35/1.56 tff(8305,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3242, 238, 1817, 546, 8304, 4423])).
% 1.35/1.56 tff(8306,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8307,plain,
% 1.35/1.56 (~r(s(s(z)), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8306, 210, 8300, 546])).
% 1.35/1.56 tff(8308,plain,
% 1.35/1.56 (b(s(s(z)), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[135, 8307, 22])).
% 1.35/1.56 tff(8309,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3221, 238, 1817, 227, 546, 23])).
% 1.35/1.56 tff(8310,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8311,plain,
% 1.35/1.56 (~b(s(s(elem!1)), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8310, 8308, 8300, 546])).
% 1.35/1.56 tff(8312,plain,
% 1.35/1.56 (r(s(s(elem!1)), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[112, 8311])).
% 1.35/1.56 tff(8313,plain,
% 1.35/1.56 (~r(s(s(s(elem!1))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[6920, 8312, 210])).
% 1.35/1.56 tff(8314,plain,
% 1.35/1.56 (b(s(s(s(elem!1))), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[576, 51, 94, 8313])).
% 1.35/1.56 tff(8315,plain,
% 1.35/1.56 (~b(s(elem!1), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[5637, 528, 546, 150, 5616])).
% 1.35/1.56 tff(8316,plain,
% 1.35/1.56 (r(s(elem!1), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[534, 528, 206])).
% 1.35/1.56 tff(8317,plain,
% 1.35/1.56 (~r(s(elem!1), s(z))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[526, 8316, 160])).
% 1.35/1.56 tff(8318,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[473, 8317, 8315, 1])).
% 1.35/1.56 tff(8319,plain,(b(s(elem!1), s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8320,plain,
% 1.35/1.56 (b(s(elem!1), s(s(elem!1)))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8319, 150, 160, 546, 1, 5616, 206])).
% 1.35/1.56 tff(8321,plain,
% 1.35/1.56 (~r(z, s(elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3111, 124, 306, 1545])).
% 1.35/1.56 tff(8322,plain,
% 1.35/1.56 (b(z, s(elem!1))),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[3115, 51, 8321, 4923])).
% 1.35/1.56 tff(8323,plain,
% 1.35/1.56 (~r(s(elem!1), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1880, 124, 306, 1545])).
% 1.35/1.56 tff(8324,plain,
% 1.35/1.56 (b(s(elem!1), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[6772, 8323])).
% 1.35/1.56 tff(8325,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.35/1.56 tff(8326,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.35/1.56 tff(8327,plain,
% 1.35/1.56 ($false),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[1499, 51, 726, 8326, 8325])).
% 1.35/1.56 tff(8328,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.35/1.56 tff(8329,plain,
% 1.35/1.56 (b(s(s(s(s(z)))), z)),
% 1.35/1.56 inference(unit_resolution,[status(thm)],[8328, 4039])).
% 1.35/1.56 tff(8330,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8331,plain,
% 1.35/1.56 (((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.35/1.56 inference(rewrite,[status(thm)],[])).
% 1.35/1.56 tff(8332,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.35/1.56 inference(monotonicity,[status(thm)],[8331])).
% 1.35/1.56 tff(8333,plain,
% 1.35/1.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.35/1.56 inference(transitivity,[status(thm)],[8332, 8330])).
% 1.35/1.56 tff(8334,plain,
% 1.35/1.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8335,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8334, 8333])).
% 1.35/1.57 tff(8336,plain,
% 1.35/1.57 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8335, 238, 8329, 8324, 8322])).
% 1.35/1.57 tff(8337,plain,
% 1.35/1.57 ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[1960, 51, 2115])).
% 1.35/1.57 tff(8338,plain,
% 1.35/1.57 (s(elem!1) = s(s(s(s(z))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8337, 8336])).
% 1.35/1.57 tff(8339,plain,
% 1.35/1.57 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8338])).
% 1.35/1.57 tff(8340,plain,
% 1.35/1.57 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.35/1.57 inference(symmetry,[status(thm)],[8339])).
% 1.35/1.57 tff(8341,plain,
% 1.35/1.57 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(elem!1)))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8340])).
% 1.35/1.57 tff(8342,plain,
% 1.35/1.57 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(s(z))))))),
% 1.35/1.57 inference(symmetry,[status(thm)],[8341])).
% 1.35/1.57 tff(8343,plain,
% 1.35/1.57 (b(s(s(elem!1)), s(elem!1))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[323, 7959, 275])).
% 1.35/1.57 tff(8344,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.35/1.57 tff(8345,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.35/1.57 tff(8346,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), z)))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8347,plain,
% 1.35/1.57 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8348,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), z))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8347])).
% 1.35/1.57 tff(8349,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), z)))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8348, 8346])).
% 1.35/1.57 tff(8350,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8351,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8350, 8349])).
% 1.35/1.57 tff(8352,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8351, 238, 289, 2078, 8345, 8344])).
% 1.35/1.57 tff(8353,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8354,plain,
% 1.35/1.57 (~b(z, s(s(elem!1)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8353, 8322, 8343, 8324])).
% 1.35/1.57 tff(8355,plain,
% 1.35/1.57 (r(z, s(s(elem!1)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[2071, 8354])).
% 1.35/1.57 tff(8356,plain,
% 1.35/1.57 (r(z, s(s(s(s(s(z))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8355, 8342])).
% 1.35/1.57 tff(8357,plain,
% 1.35/1.57 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8339])).
% 1.35/1.57 tff(8358,plain,
% 1.35/1.57 (r(s(z), s(s(s(s(s(z))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[160, 8357])).
% 1.35/1.57 tff(8359,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8360,plain,
% 1.35/1.57 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8361,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8360])).
% 1.35/1.57 tff(8362,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8361, 8359])).
% 1.35/1.57 tff(8363,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8364,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8363, 8362])).
% 1.35/1.57 tff(8365,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8364, 124, 8358, 1545, 8356])).
% 1.35/1.57 tff(8366,plain,((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8367,plain,
% 1.35/1.57 (~r(s(elem!1), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8366, 1544, 160, 1545, 275, 8312])).
% 1.35/1.57 tff(8368,plain,
% 1.35/1.57 (b(s(elem!1), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[473, 8367, 1])).
% 1.35/1.57 tff(8369,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8370,plain,
% 1.35/1.57 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8371,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8370])).
% 1.35/1.57 tff(8372,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8371, 8369])).
% 1.35/1.57 tff(8373,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8374,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8373, 8372])).
% 1.35/1.57 tff(8375,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8374, 238, 1817, 564, 546, 225])).
% 1.35/1.57 tff(8376,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8377,plain,
% 1.35/1.57 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8376, 564, 8300, 546])).
% 1.35/1.57 tff(8378,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8379,plain,
% 1.35/1.57 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8380,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8379])).
% 1.35/1.57 tff(8381,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8380, 8378])).
% 1.35/1.57 tff(8382,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8383,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8382, 8381])).
% 1.35/1.57 tff(8384,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8383, 238, 1817, 490, 1152, 546])).
% 1.35/1.57 tff(8385,plain,((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8386,plain,
% 1.35/1.57 (~b(s(elem!1), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8385, 1152, 8300, 546])).
% 1.35/1.57 tff(8387,plain,
% 1.35/1.57 (r(s(elem!1), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[488, 8386, 278])).
% 1.35/1.57 tff(8388,plain,
% 1.35/1.57 (r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[188, 51, 185, 179])).
% 1.35/1.57 tff(8389,plain,
% 1.35/1.57 (r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[539, 415, 505])).
% 1.35/1.57 tff(8390,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8391,plain,
% 1.35/1.57 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8392,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8391])).
% 1.35/1.57 tff(8393,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8392, 8390])).
% 1.35/1.57 tff(8394,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8395,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8394, 8393])).
% 1.35/1.57 tff(8396,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8395, 124, 8389, 475, 8388])).
% 1.35/1.57 tff(8397,plain,((elem!1 = s(s(elem!1))) | (~r(s(elem!1), s(s(z)))) | b(s(elem!1), s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8398,plain,
% 1.35/1.57 (b(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8397, 8387, 8377, 150])).
% 1.35/1.57 tff(8399,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8400,plain,
% 1.35/1.57 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8401,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8400])).
% 1.35/1.57 tff(8402,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8401, 8399])).
% 1.35/1.57 tff(8403,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8404,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 1.35/1.57 tff(8405,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8404, 238, 8398, 1152, 564, 546])).
% 1.35/1.57 tff(8406,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8407,plain,
% 1.35/1.57 (s(elem!1) = s(s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8406, 8368, 546, 150, 8314])).
% 1.35/1.57 tff(8408,plain,
% 1.35/1.57 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8407])).
% 1.35/1.57 tff(8409,plain,
% 1.35/1.57 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 1.35/1.57 inference(symmetry,[status(thm)],[8408])).
% 1.35/1.57 tff(8410,plain,
% 1.35/1.57 ((~b(s(z), s(s(z)))) <=> (~b(s(z), s(elem!1)))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8409])).
% 1.35/1.57 tff(8411,plain,
% 1.35/1.57 (b(z, s(s(s(s(z)))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[1487, 51, 1572, 7182])).
% 1.35/1.57 tff(8412,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8413,plain,
% 1.35/1.57 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8414,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8413])).
% 1.35/1.57 tff(8415,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8414, 8412])).
% 1.35/1.57 tff(8416,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8417,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8416, 8415])).
% 1.35/1.57 tff(8418,plain,
% 1.35/1.57 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8417, 238, 3818, 8329, 8411])).
% 1.35/1.57 tff(8419,plain,
% 1.35/1.57 ($false),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[5176, 8418, 5175])).
% 1.35/1.57 tff(8420,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.57 tff(8421,plain,
% 1.35/1.57 (~r(s(s(s(z))), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8420, 1544, 1545])).
% 1.35/1.57 tff(8422,plain,
% 1.35/1.57 (b(s(s(s(z))), s(z))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[5118, 8421])).
% 1.35/1.57 tff(8423,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8424,plain,
% 1.35/1.57 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(rewrite,[status(thm)],[])).
% 1.35/1.57 tff(8425,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.57 inference(monotonicity,[status(thm)],[8424])).
% 1.35/1.57 tff(8426,plain,
% 1.35/1.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.57 inference(transitivity,[status(thm)],[8425, 8423])).
% 1.35/1.57 tff(8427,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.35/1.57 inference(quant_inst,[status(thm)],[])).
% 1.35/1.57 tff(8428,plain,
% 1.35/1.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.57 inference(modus_ponens,[status(thm)],[8427, 8426])).
% 1.35/1.57 tff(8429,plain,
% 1.35/1.57 (~b(s(s(s(z))), s(s(z)))),
% 1.35/1.57 inference(unit_resolution,[status(thm)],[8428, 238, 8300, 546, 8422])).
% 1.35/1.57 tff(8430,plain,
% 1.35/1.57 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.35/1.57 inference(commutativity,[status(thm)],[])).
% 1.35/1.57 tff(8431,plain,
% 1.35/1.57 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.35/1.58 inference(symmetry,[status(thm)],[8430])).
% 1.35/1.58 tff(8432,plain,
% 1.35/1.58 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8431])).
% 1.35/1.58 tff(8433,plain,
% 1.35/1.58 (~(s(s(s(z))) = s(s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[147, 8432])).
% 1.35/1.58 tff(8434,plain,
% 1.35/1.58 ((~r(s(s(elem!1)), s(elem!1))) <=> (~r(s(s(s(z))), s(s(z))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1438])).
% 1.35/1.58 tff(8435,plain,
% 1.35/1.58 (~r(s(s(s(z))), s(s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[318, 8434])).
% 1.35/1.58 tff(8436,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.35/1.58 tff(8437,plain,
% 1.35/1.58 ((s(s(s(z))) = s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2298, 51, 8436])).
% 1.35/1.58 tff(8438,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8437, 8435, 8433])).
% 1.35/1.58 tff(8439,plain,(b(s(s(s(z))), s(s(z))) | r(s(s(elem!1)), s(elem!1)) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8440,plain,
% 1.35/1.58 (r(s(s(elem!1)), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8439, 8407, 8429])).
% 1.35/1.58 tff(8441,plain,
% 1.35/1.58 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1397, 8440, 210])).
% 1.35/1.58 tff(8442,plain,
% 1.35/1.58 (b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[459, 8441, 421])).
% 1.35/1.58 tff(8443,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8444,plain,
% 1.35/1.58 (((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8445,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8444])).
% 1.35/1.58 tff(8446,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[8445, 8443])).
% 1.35/1.58 tff(8447,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(8448,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 1.35/1.58 tff(8449,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8448, 238, 491, 1152, 564, 2258])).
% 1.35/1.58 tff(8450,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8451,plain,
% 1.35/1.58 (~b(s(z), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8450, 8442, 8368, 8314])).
% 1.35/1.58 tff(8452,plain,
% 1.35/1.58 (~b(s(z), s(elem!1))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8451, 8410])).
% 1.35/1.58 tff(8453,plain,
% 1.35/1.58 (~r(s(z), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[6009, 8440, 160])).
% 1.35/1.58 tff(8454,plain,
% 1.35/1.58 (b(s(z), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[439, 8453, 426])).
% 1.35/1.58 tff(8455,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8454, 8452])).
% 1.35/1.58 tff(8456,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8457,plain,
% 1.35/1.58 (~r(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8456, 1545, 160, 546, 150, 1, 210, 275])).
% 1.35/1.58 tff(8458,plain,
% 1.35/1.58 (b(s(s(s(s(z)))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1624, 8457])).
% 1.35/1.58 tff(8459,plain,
% 1.35/1.58 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[2359])).
% 1.35/1.58 tff(8460,plain,
% 1.35/1.58 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 1.35/1.58 inference(symmetry,[status(thm)],[8459])).
% 1.35/1.58 tff(8461,plain,
% 1.35/1.58 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8460])).
% 1.35/1.58 tff(8462,plain,
% 1.35/1.58 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[82, 8461])).
% 1.35/1.58 tff(8463,plain,
% 1.35/1.58 (~r(s(s(s(elem!1))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[6920, 113, 210])).
% 1.35/1.58 tff(8464,plain,
% 1.35/1.58 (b(s(s(s(elem!1))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[576, 51, 94, 8463])).
% 1.35/1.58 tff(8465,plain,
% 1.35/1.58 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8376, 8464, 8300, 546])).
% 1.35/1.58 tff(8466,plain,
% 1.35/1.58 (r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[190, 8465])).
% 1.35/1.58 tff(8467,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1435])).
% 1.35/1.58 tff(8468,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.58 inference(symmetry,[status(thm)],[8467])).
% 1.35/1.58 tff(8469,plain,
% 1.35/1.58 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1626, 1435])).
% 1.35/1.58 tff(8470,plain,
% 1.35/1.58 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[210, 8469])).
% 1.35/1.58 tff(8471,plain,
% 1.35/1.58 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[2999, 238, 8300, 546, 1784])).
% 1.35/1.58 tff(8472,plain,
% 1.35/1.58 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1632, 375, 8471])).
% 1.35/1.58 tff(8473,plain,
% 1.35/1.58 (r(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[459, 8472, 453])).
% 1.35/1.58 tff(8474,plain,
% 1.35/1.58 (~r(s(s(elem!1)), s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1397, 8473, 210])).
% 1.35/1.58 tff(8475,plain,
% 1.35/1.58 (b(s(s(s(z))), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8439, 8474, 375])).
% 1.35/1.58 tff(8476,plain,
% 1.35/1.58 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[375])).
% 1.35/1.58 tff(8477,plain,
% 1.35/1.58 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.58 inference(symmetry,[status(thm)],[8476])).
% 1.35/1.58 tff(8478,plain,
% 1.35/1.58 (r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[168, 8477])).
% 1.35/1.58 tff(8479,plain,
% 1.35/1.58 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.35/1.58 inference(symmetry,[status(thm)],[2347])).
% 1.35/1.58 tff(8480,plain,
% 1.35/1.58 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8479])).
% 1.35/1.58 tff(8481,plain,
% 1.35/1.58 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[1092, 8480])).
% 1.35/1.58 tff(8482,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.35/1.58 tff(8483,plain,
% 1.35/1.58 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1648])).
% 1.35/1.58 tff(8484,plain,
% 1.35/1.58 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.35/1.58 inference(transitivity,[status(thm)],[8483, 1727])).
% 1.35/1.58 tff(8485,plain,
% 1.35/1.58 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(s(z))))) = s(s(z))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8484])).
% 1.35/1.58 tff(8486,assumption,(s(s(z)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.35/1.58 tff(8487,plain,
% 1.35/1.58 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.35/1.58 inference(symmetry,[status(thm)],[8486])).
% 1.35/1.58 tff(8488,plain,
% 1.35/1.58 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8487])).
% 1.35/1.58 tff(8489,plain,
% 1.35/1.58 (s(s(s(elem!1))) = s(z)),
% 1.35/1.58 inference(transitivity,[status(thm)],[826, 8488, 12])).
% 1.35/1.58 tff(8490,plain,
% 1.35/1.58 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8489])).
% 1.35/1.58 tff(8491,plain,
% 1.35/1.58 (s(s(elem!1)) = z),
% 1.35/1.58 inference(transitivity,[status(thm)],[89, 8490, 26])).
% 1.35/1.58 tff(8492,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[92, 8491])).
% 1.35/1.58 tff(8493,plain,(~(s(s(z)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8494,plain,
% 1.35/1.58 (~(s(s(s(s(s(z))))) = s(s(z)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8493, 8485])).
% 1.35/1.58 tff(8495,plain,
% 1.35/1.58 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1434, 1662])).
% 1.35/1.58 tff(8496,plain,
% 1.35/1.58 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.58 inference(symmetry,[status(thm)],[8495])).
% 1.35/1.58 tff(8497,plain,
% 1.35/1.58 (r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[542, 8496])).
% 1.35/1.58 tff(8498,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8499,plain,
% 1.35/1.58 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8500,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8499])).
% 1.35/1.58 tff(8501,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[8500, 8498])).
% 1.35/1.58 tff(8502,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(8503,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8502, 8501])).
% 1.35/1.58 tff(8504,plain,
% 1.35/1.58 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8503, 124, 1717, 1652])).
% 1.35/1.58 tff(8505,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8504, 8497])).
% 1.35/1.58 tff(8506,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~(s(elem!1) = s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8507,plain,
% 1.35/1.58 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8506, 1652, 542, 375])).
% 1.35/1.58 tff(8508,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1737, 8507, 8494])).
% 1.35/1.58 tff(8509,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8510,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(8511,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8510, 8509])).
% 1.35/1.58 tff(8512,plain,
% 1.35/1.58 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8511, 238, 1817, 8508, 8482])).
% 1.35/1.58 tff(8513,plain,
% 1.35/1.58 ((s(s(s(s(s(z))))) = s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1099, 51, 8512])).
% 1.35/1.58 tff(8514,plain,
% 1.35/1.58 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8513, 8481])).
% 1.35/1.58 tff(8515,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3657, 124, 1652, 1477, 8514])).
% 1.35/1.58 tff(8516,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~(s(elem!1) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8517,plain,
% 1.35/1.58 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8516, 8478, 8300, 375, 8475, 8470])).
% 1.35/1.58 tff(8518,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1904, 8517])).
% 1.35/1.58 tff(8519,plain,
% 1.35/1.58 (~b(s(s(s(s(s(z))))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4153, 8518, 546, 1784])).
% 1.35/1.58 tff(8520,plain,
% 1.35/1.58 (r(s(s(s(s(s(z))))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1781, 8519])).
% 1.35/1.58 tff(8521,plain,
% 1.35/1.58 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3580, 124, 8520, 2288])).
% 1.35/1.58 tff(8522,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1101, 8521])).
% 1.35/1.58 tff(8523,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8522, 8468])).
% 1.35/1.58 tff(8524,plain,
% 1.35/1.58 (b(z, s(s(s(z))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1475, 2817])).
% 1.35/1.58 tff(8525,plain,
% 1.35/1.58 (b(z, s(s(elem!1)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8524, 3344])).
% 1.35/1.58 tff(8526,plain,
% 1.35/1.58 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.35/1.58 inference(monotonicity,[status(thm)],[1435])).
% 1.35/1.58 tff(8527,plain,
% 1.35/1.58 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 1.35/1.58 inference(symmetry,[status(thm)],[8526])).
% 1.35/1.58 tff(8528,plain,
% 1.35/1.58 (b(s(s(elem!1)), z)),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[3818, 8527])).
% 1.35/1.58 tff(8529,plain,
% 1.35/1.58 (~r(s(s(s(s(s(z))))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3947, 124, 8520, 1545])).
% 1.35/1.58 tff(8530,plain,
% 1.35/1.58 (b(s(s(s(s(s(z))))), z)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 8529])).
% 1.35/1.58 tff(8531,plain,
% 1.35/1.58 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[7343, 8530, 8528, 8525])).
% 1.35/1.58 tff(8532,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8531, 8523])).
% 1.35/1.58 tff(8533,plain,((~(s(elem!1) = s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8534,plain,
% 1.35/1.58 (~r(s(s(s(z))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8533, 375, 1545, 546, 1784, 210, 8466, 453])).
% 1.35/1.58 tff(8535,plain,
% 1.35/1.58 (b(s(s(s(z))), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[5118, 8534])).
% 1.35/1.58 tff(8536,plain,
% 1.35/1.58 (b(s(s(elem!1)), elem!1)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[7971, 8535, 2359])).
% 1.35/1.58 tff(8537,plain,
% 1.35/1.58 ($false),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8536, 8462])).
% 1.35/1.58 tff(8538,plain,((~(s(elem!1) = s(s(z)))) | b(s(s(elem!1)), s(z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.58 tff(8539,plain,
% 1.35/1.58 (~(s(elem!1) = s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8538, 1545, 8311, 546, 8458, 210, 421])).
% 1.35/1.58 tff(8540,plain,
% 1.35/1.58 (~b(s(elem!1), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8406, 8539, 546, 150, 8314])).
% 1.35/1.58 tff(8541,plain,
% 1.35/1.58 (r(s(elem!1), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[473, 8540, 1])).
% 1.35/1.58 tff(8542,plain,
% 1.35/1.58 (~(s(s(z)) = elem!1)),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4855, 8458, 8311])).
% 1.35/1.58 tff(8543,plain,
% 1.35/1.58 (~(elem!1 = s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[4995, 8542])).
% 1.35/1.58 tff(8544,plain,
% 1.35/1.58 (~b(s(elem!1), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8406, 278, 546, 150, 8314])).
% 1.35/1.58 tff(8545,plain,
% 1.35/1.58 (r(s(elem!1), s(z))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[473, 8544, 1])).
% 1.35/1.58 tff(8546,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8547,plain,
% 1.35/1.58 (((~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(elem!1), s(s(z))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8548,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8547])).
% 1.35/1.58 tff(8549,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[8548, 8546])).
% 1.35/1.58 tff(8550,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(elem!1), s(s(z)))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(8551,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8550, 8549])).
% 1.35/1.58 tff(8552,plain,
% 1.35/1.58 (~b(s(elem!1), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8551, 238, 289, 288, 8308])).
% 1.35/1.58 tff(8553,plain,
% 1.35/1.58 (r(s(elem!1), s(s(z)))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[488, 278, 8552])).
% 1.35/1.58 tff(8554,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8555,plain,
% 1.35/1.58 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8556,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))))),
% 1.35/1.58 inference(monotonicity,[status(thm)],[8555])).
% 1.35/1.58 tff(8557,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.35/1.58 inference(transitivity,[status(thm)],[8556, 8554])).
% 1.35/1.58 tff(8558,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))),
% 1.35/1.58 inference(quant_inst,[status(thm)],[])).
% 1.35/1.58 tff(8559,plain,
% 1.35/1.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))),
% 1.35/1.58 inference(modus_ponens,[status(thm)],[8558, 8557])).
% 1.35/1.58 tff(8560,plain,
% 1.35/1.58 (~r(z, s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8559, 124, 8553, 8545, 1545])).
% 1.35/1.58 tff(8561,plain,
% 1.35/1.58 (b(z, s(elem!1))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[3115, 51, 8560, 4923])).
% 1.35/1.58 tff(8562,plain,
% 1.35/1.58 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[8376, 8314, 8300, 546])).
% 1.35/1.58 tff(8563,plain,
% 1.35/1.58 (r(s(s(z)), s(s(s(elem!1))))),
% 1.35/1.58 inference(unit_resolution,[status(thm)],[190, 8562])).
% 1.35/1.58 tff(8564,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8565,plain,
% 1.35/1.58 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.58 inference(rewrite,[status(thm)],[])).
% 1.35/1.58 tff(8566,plain,
% 1.35/1.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8565])).
% 1.35/1.59 tff(8567,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8566, 8564])).
% 1.35/1.59 tff(8568,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8569,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8568, 8567])).
% 1.35/1.59 tff(8570,plain,
% 1.35/1.59 (~b(s(s(z)), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8569, 238, 289, 288, 8308])).
% 1.35/1.59 tff(8571,plain,
% 1.35/1.59 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[1260, 51, 8570])).
% 1.35/1.59 tff(8572,plain,
% 1.35/1.59 (r(s(s(z)), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8571, 1250])).
% 1.35/1.59 tff(8573,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8574,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8575,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8574, 8573])).
% 1.35/1.59 tff(8576,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8575, 124, 210, 442, 4689, 168])).
% 1.35/1.59 tff(8577,plain,((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(8578,plain,
% 1.35/1.59 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8577, 8572, 8563, 210])).
% 1.35/1.59 tff(8579,plain,
% 1.35/1.59 (b(s(s(s(elem!1))), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[459, 8578, 421])).
% 1.35/1.59 tff(8580,plain,
% 1.35/1.59 (b(s(elem!1), s(s(s(elem!1))))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8397, 8553, 8562, 150])).
% 1.35/1.59 tff(8581,plain,
% 1.35/1.59 ((z = s(elem!1)) | b(z, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[3115, 51, 8321])).
% 1.35/1.59 tff(8582,plain,
% 1.35/1.59 (b(z, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8581, 3105])).
% 1.35/1.59 tff(8583,plain,
% 1.35/1.59 (~r(elem!1, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[5000, 1370, 306])).
% 1.35/1.59 tff(8584,plain,
% 1.35/1.59 (b(elem!1, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[629, 8583, 391])).
% 1.35/1.59 tff(8585,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8586,plain,
% 1.35/1.59 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8587,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8586])).
% 1.35/1.59 tff(8588,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8587, 8585])).
% 1.35/1.59 tff(8589,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8590,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)) | (~b(z, s(elem!1)))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8589, 8588])).
% 1.35/1.59 tff(8591,plain,
% 1.35/1.59 (~b(elem!1, z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8590, 238, 8584, 290, 8582])).
% 1.35/1.59 tff(8592,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[4843, 51, 8591, 4840, 4839])).
% 1.35/1.59 tff(8593,plain,((~r(elem!1, s(z))) | (elem!1 = z) | (~b(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(z))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(8594,plain,
% 1.35/1.59 (~r(elem!1, s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8593, 8580, 1545, 4831, 391, 8545])).
% 1.35/1.59 tff(8595,plain,
% 1.35/1.59 (b(elem!1, s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[363, 8594, 4576])).
% 1.35/1.59 tff(8596,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8597,plain,
% 1.35/1.59 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8598,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8597])).
% 1.35/1.59 tff(8599,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8598, 8596])).
% 1.35/1.59 tff(8600,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8601,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8600, 8599])).
% 1.35/1.59 tff(8602,plain,
% 1.35/1.59 (~b(elem!1, s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8601, 238, 8300, 8595, 546])).
% 1.35/1.59 tff(8603,plain,
% 1.35/1.59 (r(elem!1, s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[763, 8602, 541])).
% 1.35/1.59 tff(8604,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8605,plain,
% 1.35/1.59 (((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8606,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8605])).
% 1.35/1.59 tff(8607,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8606, 8604])).
% 1.35/1.59 tff(8608,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8609,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8608, 8607])).
% 1.35/1.59 tff(8610,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8609, 124, 590, 475, 939])).
% 1.35/1.59 tff(8611,plain,((~r(s(elem!1), s(s(z)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(8612,plain,
% 1.35/1.59 (~r(elem!1, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8611, 8603, 8553])).
% 1.35/1.59 tff(8613,plain,
% 1.35/1.59 (b(elem!1, s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[629, 8612, 391])).
% 1.35/1.59 tff(8614,plain,
% 1.35/1.59 (~b(s(s(s(elem!1))), elem!1)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[639, 8613, 8579, 288])).
% 1.35/1.59 tff(8615,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8616,plain,
% 1.35/1.59 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8617,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8616])).
% 1.35/1.59 tff(8618,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8617, 8615])).
% 1.35/1.59 tff(8619,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8620,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8619, 8618])).
% 1.35/1.59 tff(8621,plain,
% 1.35/1.59 (~b(s(s(elem!1)), elem!1)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8620, 238, 8613, 8580, 289])).
% 1.35/1.59 tff(8622,plain,
% 1.35/1.59 (r(s(s(elem!1)), elem!1)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[255, 8621, 167])).
% 1.35/1.59 tff(8623,plain,
% 1.35/1.59 (~r(s(s(s(elem!1))), elem!1)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[1182, 8622, 210])).
% 1.35/1.59 tff(8624,plain,
% 1.35/1.59 (s(s(s(elem!1))) = elem!1),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[647, 8623, 8614])).
% 1.35/1.59 tff(8625,plain,
% 1.35/1.59 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8624])).
% 1.35/1.59 tff(8626,plain,
% 1.35/1.59 (~r(s(elem!1), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[1880, 124, 8545, 1545])).
% 1.35/1.59 tff(8627,plain,
% 1.35/1.59 (b(s(elem!1), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[6772, 8626])).
% 1.35/1.59 tff(8628,plain,
% 1.35/1.59 (~b(z, s(s(elem!1)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8353, 8561, 289, 8627])).
% 1.35/1.59 tff(8629,plain,
% 1.35/1.59 (r(z, s(s(elem!1)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[2071, 8628])).
% 1.35/1.59 tff(8630,plain,
% 1.35/1.59 (~r(s(s(s(elem!1))), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[3520, 8629, 210])).
% 1.35/1.59 tff(8631,plain,
% 1.35/1.59 (b(s(s(s(elem!1))), z)),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[6952, 8630])).
% 1.35/1.59 tff(8632,plain,
% 1.35/1.59 (b(elem!1, z)),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8631, 8625])).
% 1.35/1.59 tff(8633,plain,
% 1.35/1.59 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8624])).
% 1.35/1.59 tff(8634,plain,
% 1.35/1.59 (b(s(elem!1), elem!1)),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8580, 8633])).
% 1.35/1.59 tff(8635,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8636,plain,
% 1.35/1.59 (((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8637,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1)))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8636])).
% 1.35/1.59 tff(8638,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8637, 8635])).
% 1.35/1.59 tff(8639,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, z)))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8640,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~b(z, s(elem!1)))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8639, 8638])).
% 1.35/1.59 tff(8641,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8640, 238, 8613, 8634, 8632, 8561])).
% 1.35/1.59 tff(8642,plain,((s(elem!1) = s(s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(8643,plain,
% 1.35/1.59 (~b(s(s(elem!1)), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8642, 8539, 210, 288, 391, 8543, 546, 1545, 150, 1])).
% 1.35/1.59 tff(8644,plain,
% 1.35/1.59 (r(s(s(elem!1)), s(elem!1))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[323, 8643, 275])).
% 1.35/1.59 tff(8645,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[315, 8644, 8541, 8312])).
% 1.35/1.59 tff(8646,plain,((~r(z, s(z))) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.35/1.59 tff(8647,plain,
% 1.35/1.59 (~r(z, s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8646, 8320, 1, 210, 3294, 1212, 546, 150, 160])).
% 1.35/1.59 tff(8648,plain,
% 1.35/1.59 (b(z, s(z))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[1542, 8647])).
% 1.35/1.59 tff(8649,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8650,plain,
% 1.35/1.59 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8651,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8650])).
% 1.35/1.59 tff(8652,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8651, 8649])).
% 1.35/1.59 tff(8653,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8654,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8653, 8652])).
% 1.35/1.59 tff(8655,plain,
% 1.35/1.59 (~b(z, s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8654, 238, 8300, 546, 8648])).
% 1.35/1.59 tff(8656,plain,
% 1.35/1.59 (r(z, s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[1511, 51, 8655, 4848])).
% 1.35/1.59 tff(8657,plain,
% 1.35/1.59 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[6869, 8656, 546, 8648])).
% 1.35/1.59 tff(8658,plain,
% 1.35/1.59 (b(s(s(s(elem!1))), s(s(z)))),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[3233, 8657])).
% 1.35/1.59 tff(8659,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8660,plain,
% 1.35/1.59 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(rewrite,[status(thm)],[])).
% 1.35/1.59 tff(8661,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.35/1.59 inference(monotonicity,[status(thm)],[8660])).
% 1.35/1.59 tff(8662,plain,
% 1.35/1.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(transitivity,[status(thm)],[8661, 8659])).
% 1.35/1.59 tff(8663,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.35/1.59 inference(quant_inst,[status(thm)],[])).
% 1.35/1.59 tff(8664,plain,
% 1.35/1.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.35/1.59 inference(modus_ponens,[status(thm)],[8663, 8662])).
% 1.35/1.59 tff(8665,plain,
% 1.35/1.59 ($false),
% 1.35/1.59 inference(unit_resolution,[status(thm)],[8664, 238, 1817, 546, 2258, 1235])).
% 1.35/1.59 tff(8666,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(8667,plain,
% 1.45/1.60 (~b(s(z), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8666, 8658, 8300, 546])).
% 1.45/1.60 tff(8668,plain,
% 1.45/1.60 (r(s(z), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[4557, 51, 8667, 7947])).
% 1.45/1.60 tff(8669,plain,
% 1.45/1.60 (~b(z, s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8654, 238, 8300, 546, 1457])).
% 1.45/1.60 tff(8670,plain,
% 1.45/1.60 (r(z, s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1511, 51, 8669, 4848])).
% 1.45/1.60 tff(8671,plain,
% 1.45/1.60 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1564, 8471])).
% 1.45/1.60 tff(8672,plain,
% 1.45/1.60 (~r(z, s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[3484, 8671, 8670])).
% 1.45/1.60 tff(8673,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1487, 51, 8672, 7400, 7182])).
% 1.45/1.60 tff(8674,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(8675,plain,
% 1.45/1.60 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8674, 8648, 546])).
% 1.45/1.60 tff(8676,plain,
% 1.45/1.60 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1624, 8675])).
% 1.45/1.60 tff(8677,plain,
% 1.45/1.60 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8428, 238, 8300, 546, 1456])).
% 1.45/1.60 tff(8678,plain,
% 1.45/1.60 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2298, 51, 8677, 149])).
% 1.45/1.60 tff(8679,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8680,plain,
% 1.45/1.60 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8681,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8680])).
% 1.45/1.60 tff(8682,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[8681, 8679])).
% 1.45/1.60 tff(8683,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8684,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8683, 8682])).
% 1.45/1.60 tff(8685,plain,
% 1.45/1.60 (~b(z, s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8684, 238, 546, 1457, 1456])).
% 1.45/1.60 tff(8686,plain,
% 1.45/1.60 (r(z, s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1475, 8685])).
% 1.45/1.60 tff(8687,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8688,plain,
% 1.45/1.60 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8689,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8688])).
% 1.45/1.60 tff(8690,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[8689, 8687])).
% 1.45/1.60 tff(8691,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8692,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8691, 8690])).
% 1.45/1.60 tff(8693,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8692, 124, 8686, 8670, 8678])).
% 1.45/1.60 tff(8694,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(8695,plain,
% 1.45/1.60 (~b(s(s(s(z))), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8694, 8648, 546])).
% 1.45/1.60 tff(8696,plain,
% 1.45/1.60 (~b(s(elem!1), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8406, 278, 546, 150, 564])).
% 1.45/1.60 tff(8697,plain,
% 1.45/1.60 (r(s(elem!1), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[473, 8696, 1])).
% 1.45/1.60 tff(8698,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8699,plain,
% 1.45/1.60 (((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8700,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8699])).
% 1.45/1.60 tff(8701,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[8700, 8698])).
% 1.45/1.60 tff(8702,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8703,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8702, 8701])).
% 1.45/1.60 tff(8704,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8703, 124, 475, 306, 4560])).
% 1.45/1.60 tff(8705,plain,((~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(8706,plain,
% 1.45/1.60 (~r(s(elem!1), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8705, 8697, 4560])).
% 1.45/1.60 tff(8707,plain,
% 1.45/1.60 (b(s(elem!1), s(s(z)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[488, 8706, 278])).
% 1.45/1.60 tff(8708,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8709,plain,
% 1.45/1.60 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8710,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8709])).
% 1.45/1.60 tff(8711,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[8710, 8708])).
% 1.45/1.60 tff(8712,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8713,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8712, 8711])).
% 1.45/1.60 tff(8714,plain,
% 1.45/1.60 (~r(s(elem!1), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8713, 124, 8697, 7853])).
% 1.45/1.60 tff(8715,plain,
% 1.45/1.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2320, 124, 7853, 1544])).
% 1.45/1.60 tff(8716,plain,
% 1.45/1.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[5167, 8715])).
% 1.45/1.60 tff(8717,plain,
% 1.45/1.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[5174, 124, 7853, 1544])).
% 1.45/1.60 tff(8718,plain,
% 1.45/1.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[5176, 8717])).
% 1.45/1.60 tff(8719,plain,
% 1.45/1.60 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[1956, 124, 8697, 1544])).
% 1.45/1.60 tff(8720,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.45/1.60 tff(8721,plain,
% 1.45/1.60 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8720])).
% 1.45/1.60 tff(8722,plain,
% 1.45/1.60 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.45/1.60 inference(symmetry,[status(thm)],[8721])).
% 1.45/1.60 tff(8723,plain,
% 1.45/1.60 (s(s(z)) = elem!1),
% 1.45/1.60 inference(transitivity,[status(thm)],[144, 8722, 154])).
% 1.45/1.60 tff(8724,plain,
% 1.45/1.60 ($false),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[374, 8723])).
% 1.45/1.60 tff(8725,plain,((~(s(elem!1) = s(s(s(z))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.60 tff(8726,plain,
% 1.45/1.60 (~(s(elem!1) = s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8725, 374])).
% 1.45/1.60 tff(8727,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.45/1.60 tff(8728,plain,
% 1.45/1.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8729,plain,
% 1.45/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8730,plain,
% 1.45/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8729, 8728])).
% 1.45/1.60 tff(8731,plain,
% 1.45/1.60 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8730, 51, 8727])).
% 1.45/1.60 tff(8732,plain,
% 1.45/1.60 (b(s(elem!1), s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8731, 8726])).
% 1.45/1.60 tff(8733,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.45/1.60 tff(8734,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8735,plain,
% 1.45/1.60 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8736,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8735])).
% 1.45/1.60 tff(8737,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.45/1.60 inference(transitivity,[status(thm)],[8736, 8734])).
% 1.45/1.60 tff(8738,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.45/1.60 inference(quant_inst,[status(thm)],[])).
% 1.45/1.60 tff(8739,plain,
% 1.45/1.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[8738, 8737])).
% 1.45/1.60 tff(8740,plain,
% 1.45/1.60 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8739, 238, 2389, 8733, 8732])).
% 1.45/1.60 tff(8741,plain,
% 1.45/1.60 (s(elem!1) = s(s(s(s(z))))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[6476, 8740])).
% 1.45/1.60 tff(8742,plain,
% 1.45/1.60 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8741])).
% 1.45/1.60 tff(8743,plain,
% 1.45/1.60 (elem!1 = s(s(s(z)))),
% 1.45/1.60 inference(transitivity,[status(thm)],[155, 8742, 715])).
% 1.45/1.60 tff(8744,plain,
% 1.45/1.60 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8743])).
% 1.45/1.60 tff(8745,plain,
% 1.45/1.60 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.45/1.60 inference(symmetry,[status(thm)],[8744])).
% 1.45/1.60 tff(8746,plain,
% 1.45/1.60 ((~b(s(s(s(z))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8745])).
% 1.45/1.60 tff(8747,plain,
% 1.45/1.60 (~b(elem!1, s(z))),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[1425, 8746])).
% 1.45/1.60 tff(8748,plain,
% 1.45/1.60 (~b(s(elem!1), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8385, 490, 546, 1817])).
% 1.45/1.60 tff(8749,plain,
% 1.45/1.60 (r(s(elem!1), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[473, 8748, 1])).
% 1.45/1.60 tff(8750,plain,
% 1.45/1.60 (~r(s(elem!1), s(s(elem!1)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[526, 8749, 160])).
% 1.45/1.60 tff(8751,plain,
% 1.45/1.60 (b(s(elem!1), s(s(elem!1)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[534, 8750, 159])).
% 1.45/1.60 tff(8752,plain,
% 1.45/1.60 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[2644, 8751, 1370, 8749, 387])).
% 1.45/1.60 tff(8753,plain,
% 1.45/1.60 (r(s(s(elem!1)), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[255, 8752, 167])).
% 1.45/1.60 tff(8754,plain,
% 1.45/1.60 (~r(s(s(elem!1)), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[263, 8753, 1370])).
% 1.45/1.60 tff(8755,plain,
% 1.45/1.60 (b(s(s(elem!1)), s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[110, 51, 8754, 106])).
% 1.45/1.60 tff(8756,plain,
% 1.45/1.60 (~(s(z) = elem!1)),
% 1.45/1.60 inference(modus_ponens,[status(thm)],[330, 2466])).
% 1.45/1.60 tff(8757,plain,
% 1.45/1.60 (r(s(s(elem!1)), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[255, 167, 249])).
% 1.45/1.60 tff(8758,plain,
% 1.45/1.60 (~r(s(z), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[342, 8757, 160])).
% 1.45/1.60 tff(8759,plain,
% 1.45/1.60 ((s(z) = elem!1) | b(s(z), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[349, 51, 8758])).
% 1.45/1.60 tff(8760,plain,
% 1.45/1.60 (b(s(z), elem!1)),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[8759, 8756])).
% 1.45/1.60 tff(8761,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.45/1.60 tff(8762,plain,
% 1.45/1.60 (r(elem!1, s(s(elem!1)))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[606, 150, 8761])).
% 1.45/1.60 tff(8763,plain,
% 1.45/1.60 (~r(elem!1, s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[5841, 124, 8762, 160])).
% 1.45/1.60 tff(8764,plain,
% 1.45/1.60 (b(elem!1, s(z))),
% 1.45/1.60 inference(unit_resolution,[status(thm)],[363, 8763, 330])).
% 1.45/1.60 tff(8765,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8766,plain,
% 1.45/1.60 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 1.45/1.60 inference(rewrite,[status(thm)],[])).
% 1.45/1.60 tff(8767,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))))),
% 1.45/1.60 inference(monotonicity,[status(thm)],[8766])).
% 1.45/1.60 tff(8768,plain,
% 1.45/1.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8767, 8765])).
% 1.45/1.61 tff(8769,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8770,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8769, 8768])).
% 1.45/1.61 tff(8771,plain,
% 1.45/1.61 (~b(s(s(z)), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8770, 238, 1817, 8764, 8760])).
% 1.45/1.61 tff(8772,plain,
% 1.45/1.61 (r(s(s(z)), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1275, 8771, 374])).
% 1.45/1.61 tff(8773,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8774,plain,
% 1.45/1.61 (((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8775,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8774])).
% 1.45/1.61 tff(8776,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8775, 8773])).
% 1.45/1.61 tff(8777,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8778,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8777, 8776])).
% 1.45/1.61 tff(8779,plain,
% 1.45/1.61 (~r(s(s(elem!1)), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8778, 124, 8757, 8772])).
% 1.45/1.61 tff(8780,plain,
% 1.45/1.61 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5230, 51, 8779])).
% 1.45/1.61 tff(8781,plain,
% 1.45/1.61 (b(s(s(elem!1)), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8780, 5226])).
% 1.45/1.61 tff(8782,plain,
% 1.45/1.61 (b(s(elem!1), s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[534, 159, 529])).
% 1.45/1.61 tff(8783,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8784,plain,
% 1.45/1.61 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8785,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8784])).
% 1.45/1.61 tff(8786,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8785, 8783])).
% 1.45/1.61 tff(8787,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8788,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8787, 8786])).
% 1.45/1.61 tff(8789,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8788, 238, 1817, 8782, 490, 8781])).
% 1.45/1.61 tff(8790,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (s(s(z)) = elem!1) | (elem!1 = s(z)) | (~r(s(z), s(s(elem!1)))) | b(s(s(elem!1)), elem!1) | r(s(elem!1), s(s(elem!1))) | b(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8791,plain,
% 1.45/1.61 (b(elem!1, s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8790, 8752, 150, 374, 1817, 490, 22, 330, 160, 8750])).
% 1.45/1.61 tff(8792,plain,
% 1.45/1.61 (~r(s(elem!1), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[2626, 124, 1370, 8749])).
% 1.45/1.61 tff(8793,plain,
% 1.45/1.61 (b(s(elem!1), elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[408, 8792, 394])).
% 1.45/1.61 tff(8794,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8795,plain,
% 1.45/1.61 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8796,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8795])).
% 1.45/1.61 tff(8797,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8796, 8794])).
% 1.45/1.61 tff(8798,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8799,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8798, 8797])).
% 1.45/1.61 tff(8800,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8799, 238, 8793, 8791, 8751, 8755])).
% 1.45/1.61 tff(8801,plain,((~b(s(elem!1), s(s(z)))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(z)) = elem!1) | (~b(s(s(z)), s(z))) | (elem!1 = s(z)) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8802,plain,
% 1.45/1.61 (~r(elem!1, s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8801, 374, 8300, 150, 1, 160, 490, 330, 546])).
% 1.45/1.61 tff(8803,plain,
% 1.45/1.61 (b(elem!1, s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[363, 8802, 330])).
% 1.45/1.61 tff(8804,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8803, 8747])).
% 1.45/1.61 tff(8805,plain,((s(s(z)) = elem!1) | b(s(s(s(z))), s(z)) | r(s(elem!1), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (elem!1 = s(z)) | r(s(elem!1), s(s(s(z)))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8806,plain,
% 1.45/1.61 (s(s(z)) = elem!1),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8805, 8719, 1425, 8718, 8716, 4576, 8714, 150, 1, 160, 8707, 546])).
% 1.45/1.61 tff(8807,plain,
% 1.45/1.61 (elem!1 = s(s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1231, 8806])).
% 1.45/1.61 tff(8808,plain,
% 1.45/1.61 (s(elem!1) = s(s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8807])).
% 1.45/1.61 tff(8809,plain,
% 1.45/1.61 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8808])).
% 1.45/1.61 tff(8810,plain,
% 1.45/1.61 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(symmetry,[status(thm)],[8809])).
% 1.45/1.61 tff(8811,plain,
% 1.45/1.61 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(elem!1), s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8810])).
% 1.45/1.61 tff(8812,plain,
% 1.45/1.61 (b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5877, 8807, 227])).
% 1.45/1.61 tff(8813,plain,
% 1.45/1.61 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5183, 238, 8718, 8812, 8716])).
% 1.45/1.61 tff(8814,plain,
% 1.45/1.61 (~b(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8813, 8811])).
% 1.45/1.61 tff(8815,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8707, 8814])).
% 1.45/1.61 tff(8816,plain,((s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(elem!1)))) | b(s(s(s(z))), s(z)) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8817,plain,
% 1.45/1.61 (s(elem!1) = s(s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8816, 8695, 8308, 150, 1, 160, 546, 8676, 8668, 8314])).
% 1.45/1.61 tff(8818,plain,
% 1.45/1.61 (s(s(elem!1)) = s(s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8817])).
% 1.45/1.61 tff(8819,plain,
% 1.45/1.61 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8818])).
% 1.45/1.61 tff(8820,plain,
% 1.45/1.61 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8819, 8818])).
% 1.45/1.61 tff(8821,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.61 inference(symmetry,[status(thm)],[8820])).
% 1.45/1.61 tff(8822,plain,
% 1.45/1.61 (r(s(s(s(z))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5118, 8695])).
% 1.45/1.61 tff(8823,plain,
% 1.45/1.61 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5174, 124, 8822, 8676])).
% 1.45/1.61 tff(8824,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5176, 8823])).
% 1.45/1.61 tff(8825,plain,
% 1.45/1.61 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8824, 8821])).
% 1.45/1.61 tff(8826,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5616, 8825])).
% 1.45/1.61 tff(8827,plain,((elem!1 = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8828,plain,
% 1.45/1.61 (elem!1 = s(s(elem!1))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8827, 544, 1, 5616, 546, 8302, 8301])).
% 1.45/1.61 tff(8829,plain,
% 1.45/1.61 (s(elem!1) = s(s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[2097, 8828])).
% 1.45/1.61 tff(8830,plain,
% 1.45/1.61 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8829])).
% 1.45/1.61 tff(8831,plain,
% 1.45/1.61 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.45/1.61 inference(symmetry,[status(thm)],[8830])).
% 1.45/1.61 tff(8832,plain,
% 1.45/1.61 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8831])).
% 1.45/1.61 tff(8833,plain,
% 1.45/1.61 (~(s(elem!1) = s(s(z)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[1291, 8832])).
% 1.45/1.61 tff(8834,plain,
% 1.45/1.61 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8829])).
% 1.45/1.61 tff(8835,plain,
% 1.45/1.61 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.45/1.61 inference(symmetry,[status(thm)],[8834])).
% 1.45/1.61 tff(8836,plain,
% 1.45/1.61 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8306, 8302, 8300, 546])).
% 1.45/1.61 tff(8837,plain,
% 1.45/1.61 (b(s(s(z)), s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[135, 8836, 22])).
% 1.45/1.61 tff(8838,plain,
% 1.45/1.61 (~b(s(s(elem!1)), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8310, 8837, 8300, 546])).
% 1.45/1.61 tff(8839,plain,
% 1.45/1.61 (r(s(s(elem!1)), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[112, 8838])).
% 1.45/1.61 tff(8840,plain,
% 1.45/1.61 (~r(s(s(s(elem!1))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[6920, 8839, 8302])).
% 1.45/1.61 tff(8841,plain,
% 1.45/1.61 (b(s(s(s(elem!1))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[576, 51, 94, 8840])).
% 1.45/1.61 tff(8842,plain,
% 1.45/1.61 (b(s(elem!1), s(z))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8841, 8835])).
% 1.45/1.61 tff(8843,plain,
% 1.45/1.61 (~b(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8385, 8842, 8300, 546])).
% 1.45/1.61 tff(8844,plain,
% 1.45/1.61 (r(s(elem!1), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[488, 8843, 8833])).
% 1.45/1.61 tff(8845,plain,
% 1.45/1.61 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[3017, 8844, 8829])).
% 1.45/1.61 tff(8846,plain,
% 1.45/1.61 (~r(z, s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[6869, 1457, 546, 3002])).
% 1.45/1.61 tff(8847,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1511, 51, 8669, 8846, 4848])).
% 1.45/1.61 tff(8848,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8849,plain,
% 1.45/1.61 (~b(z, s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8848, 8845, 546])).
% 1.45/1.61 tff(8850,plain,
% 1.45/1.61 (r(z, s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1542, 8849])).
% 1.45/1.61 tff(8851,plain,
% 1.45/1.61 (~r(s(s(elem!1)), z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4026, 124, 8839, 8850])).
% 1.45/1.61 tff(8852,plain,
% 1.45/1.61 (b(s(s(elem!1)), z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[4905, 8851])).
% 1.45/1.61 tff(8853,plain,
% 1.45/1.61 (s(s(elem!1)) = elem!1),
% 1.45/1.61 inference(symmetry,[status(thm)],[8828])).
% 1.45/1.61 tff(8854,plain,
% 1.45/1.61 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8853])).
% 1.45/1.61 tff(8855,plain,
% 1.45/1.61 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.61 inference(symmetry,[status(thm)],[8854])).
% 1.45/1.61 tff(8856,plain,
% 1.45/1.61 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8855])).
% 1.45/1.61 tff(8857,plain,
% 1.45/1.61 (~(s(s(s(z))) = elem!1)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[7046, 8828])).
% 1.45/1.61 tff(8858,plain,
% 1.45/1.61 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8857, 8856])).
% 1.45/1.61 tff(8859,plain,
% 1.45/1.61 (~r(z, s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[2057, 124, 8839, 8850])).
% 1.45/1.61 tff(8860,plain,
% 1.45/1.61 (b(z, s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[2071, 8859])).
% 1.45/1.61 tff(8861,plain,
% 1.45/1.61 (~r(s(s(s(z))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5741, 8860, 8839, 8858, 8850, 8852])).
% 1.45/1.61 tff(8862,plain,
% 1.45/1.61 (b(s(s(s(z))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5118, 8861])).
% 1.45/1.61 tff(8863,plain,
% 1.45/1.61 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8428, 238, 8300, 546, 8862])).
% 1.45/1.61 tff(8864,plain,
% 1.45/1.61 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[2298, 51, 8863, 149])).
% 1.45/1.61 tff(8865,plain,
% 1.45/1.61 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5222, 8829, 22])).
% 1.45/1.61 tff(8866,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), z)),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1499, 51, 726, 4039])).
% 1.45/1.61 tff(8867,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8868,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8869,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8868, 8867])).
% 1.45/1.61 tff(8870,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8869, 238, 2078, 4047, 8866, 5237])).
% 1.45/1.61 tff(8871,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.61 tff(8872,plain,
% 1.45/1.61 (~r(s(s(s(s(z)))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8871, 8852, 8850, 8860, 8865, 8839])).
% 1.45/1.61 tff(8873,plain,
% 1.45/1.61 (b(s(s(s(s(z)))), s(z))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1624, 8872])).
% 1.45/1.61 tff(8874,plain,
% 1.45/1.61 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[3059, 238, 8300, 546, 8873])).
% 1.45/1.61 tff(8875,plain,
% 1.45/1.61 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[1604, 8874])).
% 1.45/1.61 tff(8876,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8877,plain,
% 1.45/1.61 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8878,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8877])).
% 1.45/1.61 tff(8879,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8878, 8876])).
% 1.45/1.61 tff(8880,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8881,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8880, 8879])).
% 1.45/1.61 tff(8882,plain,
% 1.45/1.61 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8881, 238, 546, 8873, 8862])).
% 1.45/1.61 tff(8883,plain,
% 1.45/1.61 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[5167, 8882])).
% 1.45/1.61 tff(8884,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8885,plain,
% 1.45/1.61 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.61 inference(rewrite,[status(thm)],[])).
% 1.45/1.61 tff(8886,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.45/1.61 inference(monotonicity,[status(thm)],[8885])).
% 1.45/1.61 tff(8887,plain,
% 1.45/1.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.61 inference(transitivity,[status(thm)],[8886, 8884])).
% 1.45/1.61 tff(8888,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.61 inference(quant_inst,[status(thm)],[])).
% 1.45/1.61 tff(8889,plain,
% 1.45/1.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.45/1.61 inference(modus_ponens,[status(thm)],[8888, 8887])).
% 1.45/1.61 tff(8890,plain,
% 1.45/1.61 ($false),
% 1.45/1.61 inference(unit_resolution,[status(thm)],[8889, 124, 8883, 8875, 8864])).
% 1.45/1.62 tff(8891,plain,(b(s(z), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | b(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(8892,plain,
% 1.45/1.62 (b(s(z), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8891, 5616, 1, 4225])).
% 1.45/1.62 tff(8893,plain,
% 1.45/1.62 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8306, 5617, 8300, 4225])).
% 1.45/1.62 tff(8894,plain,
% 1.45/1.62 (b(s(s(z)), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[135, 8893, 22])).
% 1.45/1.62 tff(8895,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8896,plain,
% 1.45/1.62 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8897,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8896])).
% 1.45/1.62 tff(8898,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8897, 8895])).
% 1.45/1.62 tff(8899,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8900,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8899, 8898])).
% 1.45/1.62 tff(8901,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8900, 238, 1817, 289, 1137, 227])).
% 1.45/1.62 tff(8902,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(8903,plain,
% 1.45/1.62 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8902, 8894, 8300, 8892])).
% 1.45/1.62 tff(8904,plain,
% 1.45/1.62 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[323, 8903, 272])).
% 1.45/1.62 tff(8905,plain,
% 1.45/1.62 (~b(s(s(z)), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8310, 4225, 1817, 23])).
% 1.45/1.62 tff(8906,plain,
% 1.45/1.62 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[2595, 209])).
% 1.45/1.62 tff(8907,plain,
% 1.45/1.62 (r(s(s(z)), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[135, 114, 2213])).
% 1.45/1.62 tff(8908,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8909,plain,
% 1.45/1.62 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8910,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8909])).
% 1.45/1.62 tff(8911,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8910, 8908])).
% 1.45/1.62 tff(8912,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8913,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8912, 8911])).
% 1.45/1.62 tff(8914,plain,
% 1.45/1.62 (~r(s(z), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8913, 124, 160, 8907])).
% 1.45/1.62 tff(8915,plain,
% 1.45/1.62 (b(s(z), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4557, 51, 8914, 7947])).
% 1.45/1.62 tff(8916,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8917,plain,
% 1.45/1.62 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8918,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8917])).
% 1.45/1.62 tff(8919,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8918, 8916])).
% 1.45/1.62 tff(8920,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8921,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 1.45/1.62 tff(8922,plain,
% 1.45/1.62 (~b(s(s(elem!1)), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8921, 238, 1817, 8915, 23])).
% 1.45/1.62 tff(8923,plain,
% 1.45/1.62 ((s(s(elem!1)) = s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[5230, 51, 8922])).
% 1.45/1.62 tff(8924,plain,
% 1.45/1.62 (r(s(s(elem!1)), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8923, 5226])).
% 1.45/1.62 tff(8925,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8926,plain,
% 1.45/1.62 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8927,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8926])).
% 1.45/1.62 tff(8928,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8927, 8925])).
% 1.45/1.62 tff(8929,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8930,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8929, 8928])).
% 1.45/1.62 tff(8931,plain,
% 1.45/1.62 (~b(elem!1, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8930, 238, 1817, 370, 2258])).
% 1.45/1.62 tff(8932,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8933,plain,
% 1.45/1.62 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8934,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8933])).
% 1.45/1.62 tff(8935,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8934, 8932])).
% 1.45/1.62 tff(8936,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8937,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8936, 8935])).
% 1.45/1.62 tff(8938,plain,
% 1.45/1.62 (~b(elem!1, s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8937, 238, 370, 2258, 23])).
% 1.45/1.62 tff(8939,plain,
% 1.45/1.62 (r(elem!1, s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[606, 8938, 150])).
% 1.45/1.62 tff(8940,plain,
% 1.45/1.62 (~r(elem!1, s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4484, 8939, 192])).
% 1.45/1.62 tff(8941,plain,
% 1.45/1.62 (elem!1 = s(s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[763, 8940, 8931])).
% 1.45/1.62 tff(8942,plain,
% 1.45/1.62 (s(elem!1) = s(s(s(z)))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8941])).
% 1.45/1.62 tff(8943,plain,
% 1.45/1.62 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8942])).
% 1.45/1.62 tff(8944,plain,
% 1.45/1.62 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8943])).
% 1.45/1.62 tff(8945,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8944])).
% 1.45/1.62 tff(8946,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.62 inference(symmetry,[status(thm)],[8945])).
% 1.45/1.62 tff(8947,plain,
% 1.45/1.62 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8944])).
% 1.45/1.62 tff(8948,plain,
% 1.45/1.62 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8947])).
% 1.45/1.62 tff(8949,plain,
% 1.45/1.62 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8666, 2258, 1817, 546])).
% 1.45/1.62 tff(8950,plain,
% 1.45/1.62 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[3233, 8949])).
% 1.45/1.62 tff(8951,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8952,plain,
% 1.45/1.62 (((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8953,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8952])).
% 1.45/1.62 tff(8954,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8953, 8951])).
% 1.45/1.62 tff(8955,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8956,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8955, 8954])).
% 1.45/1.62 tff(8957,plain,
% 1.45/1.62 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8956, 238, 370, 2258, 23])).
% 1.45/1.62 tff(8958,plain,
% 1.45/1.62 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[4979, 8941, 8957])).
% 1.45/1.62 tff(8959,plain,
% 1.45/1.62 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1564, 8958])).
% 1.45/1.62 tff(8960,plain,
% 1.45/1.62 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[3010, 8959, 8950])).
% 1.45/1.62 tff(8961,plain,
% 1.45/1.62 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8960, 8948])).
% 1.45/1.62 tff(8962,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1051, 51, 8961, 2782])).
% 1.45/1.62 tff(8963,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8962, 8946])).
% 1.45/1.62 tff(8964,plain,
% 1.45/1.62 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8943])).
% 1.45/1.62 tff(8965,plain,
% 1.45/1.62 (b(s(s(s(s(z)))), s(z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[23, 8964])).
% 1.45/1.62 tff(8966,plain,
% 1.45/1.62 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[2991, 8965, 546, 226])).
% 1.45/1.62 tff(8967,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8966, 8963])).
% 1.45/1.62 tff(8968,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(8969,plain,
% 1.45/1.62 (~b(elem!1, s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8968, 8907, 226, 23, 4225, 150, 8915, 1817])).
% 1.45/1.62 tff(8970,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.45/1.62 tff(8971,plain,
% 1.45/1.62 (r(elem!1, s(z))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[363, 1400, 330])).
% 1.45/1.62 tff(8972,plain,
% 1.45/1.62 (b(elem!1, s(z))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[1817, 367])).
% 1.45/1.62 tff(8973,plain,
% 1.45/1.62 ($false),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1400, 8972])).
% 1.45/1.62 tff(8974,plain,((~(elem!1 = s(s(z)))) | b(elem!1, s(z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.62 tff(8975,plain,
% 1.45/1.62 (~(elem!1 = s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8974, 1400, 1817])).
% 1.45/1.62 tff(8976,plain,
% 1.45/1.62 (~(s(s(z)) = elem!1)),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[1231, 8975])).
% 1.45/1.62 tff(8977,plain,
% 1.45/1.62 (~b(s(elem!1), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8801, 8976, 1817, 150, 160, 330, 8971, 1, 546])).
% 1.45/1.62 tff(8978,plain,
% 1.45/1.62 (r(s(elem!1), s(s(z)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[488, 8977, 3258])).
% 1.45/1.62 tff(8979,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8980,plain,
% 1.45/1.62 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8981,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8980])).
% 1.45/1.62 tff(8982,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8981, 8979])).
% 1.45/1.62 tff(8983,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8984,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8983, 8982])).
% 1.45/1.62 tff(8985,plain,
% 1.45/1.62 (~r(s(elem!1), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[8984, 124, 8978, 8970])).
% 1.45/1.62 tff(8986,plain,
% 1.45/1.62 (b(s(elem!1), s(s(elem!1)))),
% 1.45/1.62 inference(unit_resolution,[status(thm)],[534, 8985, 159])).
% 1.45/1.62 tff(8987,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8988,plain,
% 1.45/1.62 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(rewrite,[status(thm)],[])).
% 1.45/1.62 tff(8989,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.45/1.62 inference(monotonicity,[status(thm)],[8988])).
% 1.45/1.62 tff(8990,plain,
% 1.45/1.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.45/1.62 inference(transitivity,[status(thm)],[8989, 8987])).
% 1.45/1.62 tff(8991,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.45/1.62 inference(quant_inst,[status(thm)],[])).
% 1.45/1.62 tff(8992,plain,
% 1.45/1.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.45/1.62 inference(modus_ponens,[status(thm)],[8991, 8990])).
% 1.45/1.62 tff(8993,plain,
% 1.45/1.62 (~r(s(s(elem!1)), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[8992, 124, 8978, 8970])).
% 1.45/1.63 tff(8994,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[323, 8993, 272])).
% 1.45/1.63 tff(8995,plain,
% 1.45/1.63 (~b(s(elem!1), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5832, 8994, 546, 23])).
% 1.45/1.63 tff(8996,plain,
% 1.45/1.63 (r(s(elem!1), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[473, 8995, 1])).
% 1.45/1.63 tff(8997,plain,
% 1.45/1.63 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2644, 8996, 8971, 387, 8986])).
% 1.45/1.63 tff(8998,plain,
% 1.45/1.63 (r(s(s(elem!1)), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[255, 8997, 167])).
% 1.45/1.63 tff(8999,plain,
% 1.45/1.63 (~r(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5843, 8971, 160])).
% 1.45/1.63 tff(9000,plain,
% 1.45/1.63 (b(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[606, 8999, 150])).
% 1.45/1.63 tff(9001,plain,
% 1.45/1.63 (~r(elem!1, s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5000, 8996, 8971])).
% 1.45/1.63 tff(9002,plain,
% 1.45/1.63 (b(elem!1, s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[629, 9001, 387])).
% 1.45/1.63 tff(9003,plain,
% 1.45/1.63 (~b(s(elem!1), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5551, 9002, 9000, 8994])).
% 1.45/1.63 tff(9004,plain,
% 1.45/1.63 (r(s(elem!1), elem!1)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[408, 9003, 394])).
% 1.45/1.63 tff(9005,plain,
% 1.45/1.63 (elem!1 = s(s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3317, 9004, 226, 415, 9000, 8998, 159])).
% 1.45/1.63 tff(9006,plain,
% 1.45/1.63 (s(s(s(elem!1))) = elem!1),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2002, 9005])).
% 1.45/1.63 tff(9007,plain,
% 1.45/1.63 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9006])).
% 1.45/1.63 tff(9008,plain,
% 1.45/1.63 (b(elem!1, s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.45/1.63 inference(symmetry,[status(thm)],[9007])).
% 1.45/1.63 tff(9009,plain,
% 1.45/1.63 (b(s(s(s(elem!1))), s(elem!1))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9002, 9008])).
% 1.45/1.63 tff(9010,plain,
% 1.45/1.63 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[298, 8986, 226, 8994])).
% 1.45/1.63 tff(9011,plain,
% 1.45/1.63 (b(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[8397, 9010, 150, 8978])).
% 1.45/1.63 tff(9012,plain,
% 1.45/1.63 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3172, 9011, 1817, 546])).
% 1.45/1.63 tff(9013,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9012, 9009])).
% 1.45/1.63 tff(9014,plain,(b(elem!1, s(z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9015,plain,
% 1.45/1.63 (elem!1 = s(z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9014, 8969, 1817, 4225, 150, 358, 23, 8924, 160, 226])).
% 1.45/1.63 tff(9016,plain,
% 1.45/1.63 (s(elem!1) = s(s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[280, 9015])).
% 1.45/1.63 tff(9017,plain,
% 1.45/1.63 (s(s(elem!1)) = s(s(s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9016])).
% 1.45/1.63 tff(9018,plain,
% 1.45/1.63 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9017])).
% 1.45/1.63 tff(9019,plain,
% 1.45/1.63 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9018])).
% 1.45/1.63 tff(9020,plain,
% 1.45/1.63 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9019])).
% 1.45/1.63 tff(9021,plain,
% 1.45/1.63 (~b(s(s(s(elem!1))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3895, 226, 4225, 23])).
% 1.45/1.63 tff(9022,plain,
% 1.45/1.63 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9021, 9020])).
% 1.45/1.63 tff(9023,plain,
% 1.45/1.63 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1624, 9022])).
% 1.45/1.63 tff(9024,plain,
% 1.45/1.63 (~r(s(s(s(s(z)))), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1938, 124, 9023, 1545])).
% 1.45/1.63 tff(9025,plain,
% 1.45/1.63 (b(s(s(s(s(z)))), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1499, 51, 726, 9024])).
% 1.45/1.63 tff(9026,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9017])).
% 1.45/1.63 tff(9027,plain,
% 1.45/1.63 (b(s(s(s(z))), s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[23, 9026])).
% 1.45/1.63 tff(9028,plain,
% 1.45/1.63 (b(s(elem!1), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2858, 9016, 1817])).
% 1.45/1.63 tff(9029,plain,
% 1.45/1.63 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5832, 9028, 4225, 23])).
% 1.45/1.63 tff(9030,plain,
% 1.45/1.63 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[323, 9029, 272])).
% 1.45/1.63 tff(9031,plain,
% 1.45/1.63 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1442, 9030, 9016])).
% 1.45/1.63 tff(9032,plain,
% 1.45/1.63 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.45/1.63 inference(symmetry,[status(thm)],[9018])).
% 1.45/1.63 tff(9033,plain,
% 1.45/1.63 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9032])).
% 1.45/1.63 tff(9034,plain,
% 1.45/1.63 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.63 inference(symmetry,[status(thm)],[9033])).
% 1.45/1.63 tff(9035,plain,
% 1.45/1.63 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[8666, 8915, 1817, 4225])).
% 1.45/1.63 tff(9036,plain,
% 1.45/1.63 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3233, 9035])).
% 1.45/1.63 tff(9037,plain,
% 1.45/1.63 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9036, 9034])).
% 1.45/1.63 tff(9038,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9039,plain,
% 1.45/1.63 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9040,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9039])).
% 1.45/1.63 tff(9041,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[9040, 9038])).
% 1.45/1.63 tff(9042,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(9043,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9042, 9041])).
% 1.45/1.63 tff(9044,plain,
% 1.45/1.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9043, 124, 9037, 9031])).
% 1.45/1.63 tff(9045,plain,
% 1.45/1.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5167, 9044])).
% 1.45/1.63 tff(9046,plain,
% 1.45/1.63 (~r(s(z), s(s(s(s(z)))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3396, 9016, 63])).
% 1.45/1.63 tff(9047,plain,
% 1.45/1.63 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[6600, 9046])).
% 1.45/1.63 tff(9048,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9049,plain,
% 1.45/1.63 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9050,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9049])).
% 1.45/1.63 tff(9051,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[9050, 9048])).
% 1.45/1.63 tff(9052,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(9053,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9052, 9051])).
% 1.45/1.63 tff(9054,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9053, 238, 9047, 9045, 9027, 9025])).
% 1.45/1.63 tff(9055,plain,((s(s(z)) = s(s(elem!1))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(z))) | r(s(z), s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9056,plain,
% 1.45/1.63 (s(s(z)) = s(s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9055, 5390, 23, 63, 1817, 150, 160, 226, 2213])).
% 1.45/1.63 tff(9057,plain,
% 1.45/1.63 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9056])).
% 1.45/1.63 tff(9058,plain,
% 1.45/1.63 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9057])).
% 1.45/1.63 tff(9059,plain,
% 1.45/1.63 (~b(s(s(s(z))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3886, 9056, 9021])).
% 1.45/1.63 tff(9060,plain,
% 1.45/1.63 (r(s(s(s(z))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5118, 9059])).
% 1.45/1.63 tff(9061,plain,
% 1.45/1.63 (~r(s(s(s(z))), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2827, 9060, 5390])).
% 1.45/1.63 tff(9062,plain,
% 1.45/1.63 (b(s(s(s(z))), z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1524, 9061])).
% 1.45/1.63 tff(9063,plain,
% 1.45/1.63 (b(s(s(s(elem!1))), z)),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9062, 9058])).
% 1.45/1.63 tff(9064,plain,
% 1.45/1.63 (s(elem!1) = s(z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[21, 9056])).
% 1.45/1.63 tff(9065,plain,
% 1.45/1.63 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9064])).
% 1.45/1.63 tff(9066,plain,
% 1.45/1.63 (elem!1 = z),
% 1.45/1.63 inference(transitivity,[status(thm)],[155, 9065, 26])).
% 1.45/1.63 tff(9067,plain,
% 1.45/1.63 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9066])).
% 1.45/1.63 tff(9068,plain,
% 1.45/1.63 (~b(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5709, 9064, 5389])).
% 1.45/1.63 tff(9069,plain,
% 1.45/1.63 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[804])).
% 1.45/1.63 tff(9070,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 1.45/1.63 inference(symmetry,[status(thm)],[9069])).
% 1.45/1.63 tff(9071,plain,
% 1.45/1.63 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(z)), s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9070])).
% 1.45/1.63 tff(9072,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[353])).
% 1.45/1.63 tff(9073,plain,
% 1.45/1.63 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9072])).
% 1.45/1.63 tff(9074,plain,
% 1.45/1.63 (~b(s(s(elem!1)), s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[317, 9073])).
% 1.45/1.63 tff(9075,plain,
% 1.45/1.63 (~b(s(s(z)), s(z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9074, 9071])).
% 1.45/1.63 tff(9076,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1817, 9075])).
% 1.45/1.63 tff(9077,plain,((~(s(elem!1) = s(z))) | (~b(s(s(z)), s(z))) | b(s(s(elem!1)), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9078,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9077, 9064, 1817])).
% 1.45/1.63 tff(9079,plain,
% 1.45/1.63 (~b(s(elem!1), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5832, 9078, 4225, 23])).
% 1.45/1.63 tff(9080,plain,
% 1.45/1.63 (~(s(elem!1) = s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2858, 9079, 1817])).
% 1.45/1.63 tff(9081,plain,
% 1.45/1.63 (~(elem!1 = s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[280, 9080])).
% 1.45/1.63 tff(9082,plain,
% 1.45/1.63 (r(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[363, 9081, 9068])).
% 1.45/1.63 tff(9083,plain,
% 1.45/1.63 (~r(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[5843, 9082, 160])).
% 1.45/1.63 tff(9084,plain,
% 1.45/1.63 (b(elem!1, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[606, 9083, 150])).
% 1.45/1.63 tff(9085,plain,
% 1.45/1.63 (b(z, s(s(elem!1)))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9084, 9067])).
% 1.45/1.63 tff(9086,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9087,plain,
% 1.45/1.63 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(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(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9088,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9087])).
% 1.45/1.63 tff(9089,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.63 inference(transitivity,[status(thm)],[9088, 9086])).
% 1.45/1.63 tff(9090,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(9091,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9090, 9089])).
% 1.45/1.63 tff(9092,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9091, 238, 226, 9085, 23, 9063])).
% 1.45/1.63 tff(9093,plain,(b(z, s(z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | r(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9094,plain,
% 1.45/1.63 (b(z, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9093, 226, 23, 150, 160, 1817, 63, 2213])).
% 1.45/1.63 tff(9095,plain,
% 1.45/1.63 (~b(z, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[6999, 238, 4225, 23, 9094])).
% 1.45/1.63 tff(9096,plain,
% 1.45/1.63 (r(z, s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2071, 9095])).
% 1.45/1.63 tff(9097,plain,
% 1.45/1.63 (~b(z, s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[8654, 238, 1817, 4225, 9094])).
% 1.45/1.63 tff(9098,plain,
% 1.45/1.63 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1511, 51, 9097])).
% 1.45/1.63 tff(9099,plain,
% 1.45/1.63 (r(z, s(s(z)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9098, 1450])).
% 1.45/1.63 tff(9100,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[6411, 124, 192, 2026, 1575])).
% 1.45/1.63 tff(9101,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9102,plain,
% 1.45/1.63 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9101, 9099, 9096])).
% 1.45/1.63 tff(9103,plain,
% 1.45/1.63 (s(s(z)) = s(s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[135, 9102, 2213])).
% 1.45/1.63 tff(9104,plain,
% 1.45/1.63 (s(elem!1) = s(z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[21, 9103])).
% 1.45/1.63 tff(9105,plain,
% 1.45/1.63 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9104])).
% 1.45/1.63 tff(9106,plain,
% 1.45/1.63 (elem!1 = z),
% 1.45/1.63 inference(transitivity,[status(thm)],[155, 9105, 26])).
% 1.45/1.63 tff(9107,plain,
% 1.45/1.63 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9106])).
% 1.45/1.63 tff(9108,plain,
% 1.45/1.63 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9107])).
% 1.45/1.63 tff(9109,plain,
% 1.45/1.63 (b(elem!1, s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[6376, 9104, 9094])).
% 1.45/1.63 tff(9110,plain,
% 1.45/1.63 (~b(elem!1, s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[578, 9109, 4225, 160, 209])).
% 1.45/1.63 tff(9111,plain,
% 1.45/1.63 (~b(z, s(s(s(elem!1))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9110, 9108])).
% 1.45/1.63 tff(9112,plain,
% 1.45/1.63 (r(z, s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3795, 51, 3785, 9111])).
% 1.45/1.63 tff(9113,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.45/1.63 tff(9114,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9115,plain,
% 1.45/1.63 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9116,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9115])).
% 1.45/1.63 tff(9117,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[9116, 9114])).
% 1.45/1.63 tff(9118,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(9119,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9118, 9117])).
% 1.45/1.63 tff(9120,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9119, 124, 2026, 5517, 9113])).
% 1.45/1.63 tff(9121,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9122,plain,
% 1.45/1.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9121, 9096, 9112])).
% 1.45/1.63 tff(9123,plain,
% 1.45/1.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2549, 51, 9122, 8906])).
% 1.45/1.63 tff(9124,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9125,plain,
% 1.45/1.63 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(rewrite,[status(thm)],[])).
% 1.45/1.63 tff(9126,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9125])).
% 1.45/1.63 tff(9127,plain,
% 1.45/1.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.45/1.63 inference(transitivity,[status(thm)],[9126, 9124])).
% 1.45/1.63 tff(9128,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.45/1.63 inference(quant_inst,[status(thm)],[])).
% 1.45/1.63 tff(9129,plain,
% 1.45/1.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.45/1.63 inference(modus_ponens,[status(thm)],[9128, 9127])).
% 1.45/1.63 tff(9130,plain,
% 1.45/1.63 ($false),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9129, 238, 226, 4225, 23, 9123])).
% 1.45/1.63 tff(9131,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | b(s(s(z)), s(s(elem!1))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.63 tff(9132,plain,
% 1.45/1.63 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[9131, 2213, 160, 23, 1817, 150, 63])).
% 1.45/1.63 tff(9133,plain,
% 1.45/1.63 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[223, 9132, 209])).
% 1.45/1.63 tff(9134,plain,
% 1.45/1.63 (~r(s(s(s(elem!1))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[562, 124, 160, 9133])).
% 1.45/1.63 tff(9135,plain,
% 1.45/1.63 (b(s(s(s(elem!1))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[576, 51, 94, 9134])).
% 1.45/1.63 tff(9136,plain,
% 1.45/1.63 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[8376, 9135, 1817, 4225])).
% 1.45/1.63 tff(9137,plain,
% 1.45/1.63 (r(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[190, 9136])).
% 1.45/1.63 tff(9138,plain,
% 1.45/1.63 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3182, 9137, 9133])).
% 1.45/1.63 tff(9139,plain,
% 1.45/1.63 (s(s(z)) = s(s(elem!1))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[135, 9138, 2213])).
% 1.45/1.63 tff(9140,plain,
% 1.45/1.63 (s(elem!1) = s(z)),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[21, 9139])).
% 1.45/1.63 tff(9141,plain,
% 1.45/1.63 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[4960, 9139])).
% 1.45/1.63 tff(9142,plain,
% 1.45/1.63 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[3850, 9139])).
% 1.45/1.63 tff(9143,plain,
% 1.45/1.63 (~b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[2441, 9142, 9133, 23, 160, 9141])).
% 1.45/1.63 tff(9144,plain,
% 1.45/1.63 (r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.63 inference(unit_resolution,[status(thm)],[1781, 9143])).
% 1.45/1.63 tff(9145,plain,
% 1.45/1.63 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.63 inference(monotonicity,[status(thm)],[9139])).
% 1.45/1.63 tff(9146,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9145])).
% 1.45/1.64 tff(9147,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9133, 9146])).
% 1.45/1.64 tff(9148,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[7267, 9139, 4225, 9135, 160, 9147])).
% 1.45/1.64 tff(9149,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5643, 9148, 23, 4225])).
% 1.45/1.64 tff(9150,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1624, 9149])).
% 1.45/1.64 tff(9151,plain,
% 1.45/1.64 (~r(z, s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3973, 9150, 9144, 9140])).
% 1.45/1.64 tff(9152,plain,
% 1.45/1.64 (b(z, s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1542, 9151])).
% 1.45/1.64 tff(9153,plain,
% 1.45/1.64 (~r(s(s(s(elem!1))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3520, 2026, 210])).
% 1.45/1.64 tff(9154,plain,
% 1.45/1.64 (b(s(s(s(elem!1))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[6058, 51, 821, 9153])).
% 1.45/1.64 tff(9155,plain,
% 1.45/1.64 (~r(s(z), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[6136, 124, 160, 2026])).
% 1.45/1.64 tff(9156,plain,
% 1.45/1.64 (b(s(z), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5699, 51, 72, 9155])).
% 1.45/1.64 tff(9157,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9158,plain,
% 1.45/1.64 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9159,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9158])).
% 1.45/1.64 tff(9160,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9159, 9157])).
% 1.45/1.64 tff(9161,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(9162,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9161, 9160])).
% 1.45/1.64 tff(9163,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9162, 238, 546, 1457, 9156, 9154])).
% 1.45/1.64 tff(9164,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(9165,plain,
% 1.45/1.64 (~r(z, s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9164, 9152, 4225, 160, 9133])).
% 1.45/1.64 tff(9166,plain,
% 1.45/1.64 (b(z, s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2071, 9165])).
% 1.45/1.64 tff(9167,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[6999, 238, 4225, 9166, 23, 9152])).
% 1.45/1.64 tff(9168,plain,(b(s(s(z)), s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(elem!1))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(9169,plain,
% 1.45/1.64 (~r(s(z), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9168, 8905, 23, 1817, 150, 63])).
% 1.45/1.64 tff(9170,plain,
% 1.45/1.64 (b(s(z), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[56, 9169])).
% 1.45/1.64 tff(9171,plain,
% 1.45/1.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3192, 9170, 4225, 23])).
% 1.45/1.64 tff(9172,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[223, 9171, 209])).
% 1.45/1.64 tff(9173,plain,
% 1.45/1.64 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[8306, 4225, 1817, 9172])).
% 1.45/1.64 tff(9174,plain,
% 1.45/1.64 (s(s(z)) = s(s(elem!1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[135, 9173, 8905])).
% 1.45/1.64 tff(9175,plain,
% 1.45/1.64 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9174])).
% 1.45/1.64 tff(9176,plain,
% 1.45/1.64 ((~r(z, s(s(z)))) <=> (~r(z, s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9175])).
% 1.45/1.64 tff(9177,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9174])).
% 1.45/1.64 tff(9178,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9177])).
% 1.45/1.64 tff(9179,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9172, 9178])).
% 1.45/1.64 tff(9180,plain,
% 1.45/1.64 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[8306, 4225, 1817, 210])).
% 1.45/1.64 tff(9181,plain,
% 1.45/1.64 (s(s(z)) = s(s(elem!1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[135, 9180, 8905])).
% 1.45/1.64 tff(9182,plain,
% 1.45/1.64 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9181])).
% 1.45/1.64 tff(9183,plain,
% 1.45/1.64 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.64 tff(9184,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9183])).
% 1.45/1.64 tff(9185,plain,
% 1.45/1.64 (r(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[210, 9184])).
% 1.45/1.64 tff(9186,plain,
% 1.45/1.64 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4960, 9181])).
% 1.45/1.64 tff(9187,plain,
% 1.45/1.64 (s(elem!1) = s(z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[21, 9181])).
% 1.45/1.64 tff(9188,plain,
% 1.45/1.64 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3850, 9181])).
% 1.45/1.64 tff(9189,plain,
% 1.45/1.64 (b(s(s(elem!1)), s(elem!1))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9077, 9187, 1817])).
% 1.45/1.64 tff(9190,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9181])).
% 1.45/1.64 tff(9191,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9190])).
% 1.45/1.64 tff(9192,plain,
% 1.45/1.64 (r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[210, 9191])).
% 1.45/1.64 tff(9193,plain,
% 1.45/1.64 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[5165, 3700])).
% 1.45/1.64 tff(9194,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[4276, 1784, 63, 13, 1545])).
% 1.45/1.64 tff(9195,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[13])).
% 1.45/1.64 tff(9196,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9195])).
% 1.45/1.64 tff(9197,plain,
% 1.45/1.64 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9196])).
% 1.45/1.64 tff(9198,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5643, 1784, 23, 4225])).
% 1.45/1.64 tff(9199,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9198, 9197])).
% 1.45/1.64 tff(9200,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1564, 9199])).
% 1.45/1.64 tff(9201,plain,
% 1.45/1.64 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3010, 9200, 3002])).
% 1.45/1.64 tff(9202,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2974, 51, 9201, 9194, 9193])).
% 1.45/1.64 tff(9203,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | r(s(z), s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(9204,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9203, 1545, 9181, 23, 63, 9192])).
% 1.45/1.64 tff(9205,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1624, 9204])).
% 1.45/1.64 tff(9206,plain,
% 1.45/1.64 (~r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3973, 9205, 1545, 9187])).
% 1.45/1.64 tff(9207,plain,
% 1.45/1.64 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3937, 9206, 23, 210, 9189, 9188, 9187, 9186])).
% 1.45/1.64 tff(9208,plain,
% 1.45/1.64 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3867, 9207, 9185])).
% 1.45/1.64 tff(9209,plain,
% 1.45/1.64 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1101, 9208])).
% 1.45/1.64 tff(9210,plain,
% 1.45/1.64 (b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1781, 9206])).
% 1.45/1.64 tff(9211,plain,
% 1.45/1.64 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.64 tff(9212,plain,
% 1.45/1.64 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.45/1.64 inference(symmetry,[status(thm)],[9211])).
% 1.45/1.64 tff(9213,plain,
% 1.45/1.64 (b(s(z), s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[4225, 9212])).
% 1.45/1.64 tff(9214,plain,
% 1.45/1.64 (~b(s(s(s(z))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5745, 9209, 9213, 9210])).
% 1.45/1.64 tff(9215,plain,
% 1.45/1.64 (r(s(s(s(z))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5118, 9214])).
% 1.45/1.64 tff(9216,plain,
% 1.45/1.64 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3719])).
% 1.45/1.64 tff(9217,plain,
% 1.45/1.64 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1075])).
% 1.45/1.64 tff(9218,plain,
% 1.45/1.64 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9217, 9216])).
% 1.45/1.64 tff(9219,plain,
% 1.45/1.64 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.45/1.64 inference(symmetry,[status(thm)],[5081])).
% 1.45/1.64 tff(9220,plain,
% 1.45/1.64 ((s(s(s(z))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1075])).
% 1.45/1.64 tff(9221,plain,
% 1.45/1.64 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9220, 511])).
% 1.45/1.64 tff(9222,plain,
% 1.45/1.64 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.45/1.64 inference(symmetry,[status(thm)],[9221])).
% 1.45/1.64 tff(9223,plain,
% 1.45/1.64 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[3722, 9222, 9219])).
% 1.45/1.64 tff(9224,plain,
% 1.45/1.64 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9223])).
% 1.45/1.64 tff(9225,plain,
% 1.45/1.64 (~(elem!1 = s(s(s(z))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[821, 9224])).
% 1.45/1.64 tff(9226,plain,
% 1.45/1.64 (~r(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[3791, 124, 3741, 1545])).
% 1.45/1.64 tff(9227,plain,
% 1.45/1.64 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3719])).
% 1.45/1.64 tff(9228,plain,
% 1.45/1.64 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[1075])).
% 1.45/1.64 tff(9229,plain,
% 1.45/1.64 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9228, 9227])).
% 1.45/1.64 tff(9230,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.45/1.64 tff(9231,plain,
% 1.45/1.64 (r(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9230, 9229])).
% 1.45/1.64 tff(9232,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.45/1.64 tff(9233,plain,
% 1.45/1.64 ($false),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9232, 9231])).
% 1.45/1.64 tff(9234,plain,((~r(elem!1, s(s(s(z))))) | r(z, s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.64 tff(9235,plain,
% 1.45/1.64 (~r(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9234, 9226, 13])).
% 1.45/1.64 tff(9236,plain,
% 1.45/1.64 (b(elem!1, s(s(s(z))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[5079, 9235, 9225])).
% 1.45/1.64 tff(9237,plain,
% 1.45/1.64 (b(z, s(s(s(elem!1))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9236, 9218])).
% 1.45/1.64 tff(9238,plain,
% 1.45/1.64 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.45/1.64 inference(monotonicity,[status(thm)],[3719])).
% 1.45/1.64 tff(9239,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9240,plain,
% 1.45/1.64 (((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9241,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9240])).
% 1.45/1.64 tff(9242,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9241, 9239])).
% 1.45/1.64 tff(9243,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(9244,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9243, 9242])).
% 1.45/1.64 tff(9245,plain,
% 1.45/1.64 ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9244, 238])).
% 1.45/1.64 tff(9246,plain,
% 1.45/1.64 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9245, 9236, 1079, 3818])).
% 1.45/1.64 tff(9247,plain,
% 1.45/1.64 (r(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1064, 9246, 3823])).
% 1.45/1.64 tff(9248,plain,
% 1.45/1.64 (r(s(s(s(s(s(z))))), z)),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9247, 9238])).
% 1.45/1.64 tff(9249,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9250,plain,
% 1.45/1.64 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9251,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9250])).
% 1.45/1.64 tff(9252,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9251, 9249])).
% 1.45/1.64 tff(9253,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(9254,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9253, 9252])).
% 1.45/1.64 tff(9255,plain,
% 1.45/1.64 (~r(s(z), s(s(s(s(s(z))))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9254, 124, 4278, 9248])).
% 1.45/1.64 tff(9256,plain,
% 1.45/1.64 (b(s(z), s(s(s(s(s(z))))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1709, 9255])).
% 1.45/1.64 tff(9257,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9258,plain,
% 1.45/1.64 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9259,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9258])).
% 1.45/1.64 tff(9260,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9259, 9257])).
% 1.45/1.64 tff(9261,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(9262,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9261, 9260])).
% 1.45/1.64 tff(9263,plain,
% 1.45/1.64 (~r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9262, 124, 4278, 9248])).
% 1.45/1.64 tff(9264,plain,
% 1.45/1.64 (b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1781, 9263])).
% 1.45/1.64 tff(9265,plain,
% 1.45/1.64 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1930, 9264, 1817, 9256])).
% 1.45/1.64 tff(9266,plain,
% 1.45/1.64 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1624, 9265])).
% 1.45/1.64 tff(9267,plain,
% 1.45/1.64 (~r(s(s(s(s(z)))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1938, 124, 9266, 1545])).
% 1.45/1.64 tff(9268,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), z)),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[1499, 51, 726, 9267])).
% 1.45/1.64 tff(9269,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9270,plain,
% 1.45/1.64 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.45/1.64 inference(rewrite,[status(thm)],[])).
% 1.45/1.64 tff(9271,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.45/1.64 inference(monotonicity,[status(thm)],[9270])).
% 1.45/1.64 tff(9272,plain,
% 1.45/1.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.45/1.64 inference(transitivity,[status(thm)],[9271, 9269])).
% 1.45/1.64 tff(9273,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.45/1.64 inference(quant_inst,[status(thm)],[])).
% 1.45/1.64 tff(9274,plain,
% 1.45/1.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.45/1.64 inference(modus_ponens,[status(thm)],[9273, 9272])).
% 1.45/1.64 tff(9275,plain,
% 1.45/1.64 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[9274, 124, 210, 9266, 3741])).
% 1.45/1.64 tff(9276,plain,
% 1.45/1.64 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.64 inference(unit_resolution,[status(thm)],[2974, 51, 9275, 9193])).
% 1.45/1.65 tff(9277,plain,
% 1.45/1.65 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1075])).
% 1.45/1.65 tff(9278,plain,
% 1.45/1.65 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[1076])).
% 1.45/1.65 tff(9279,plain,
% 1.45/1.65 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9278])).
% 1.45/1.65 tff(9280,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9281,plain,
% 1.45/1.65 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9282,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9281])).
% 1.45/1.65 tff(9283,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9282, 9280])).
% 1.45/1.65 tff(9284,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9285,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9284, 9283])).
% 1.45/1.65 tff(9286,plain,
% 1.45/1.65 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9285, 124, 9266, 3741])).
% 1.45/1.65 tff(9287,plain,
% 1.45/1.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9286, 9279])).
% 1.45/1.65 tff(9288,plain,
% 1.45/1.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[5167, 9287])).
% 1.45/1.65 tff(9289,plain,
% 1.45/1.65 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9288, 9277])).
% 1.45/1.65 tff(9290,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9291,plain,
% 1.45/1.65 (((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9292,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9291])).
% 1.45/1.65 tff(9293,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9292, 9290])).
% 1.45/1.65 tff(9294,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9295,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9294, 9293])).
% 1.45/1.65 tff(9296,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9295, 238, 9289, 9276, 9268, 9237])).
% 1.45/1.65 tff(9297,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9298,plain,
% 1.45/1.65 (~r(s(z), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9297, 9215, 1545, 210, 1817, 9181, 9209])).
% 1.45/1.65 tff(9299,plain,
% 1.45/1.65 (b(s(z), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[5701, 9298])).
% 1.45/1.65 tff(9300,plain,
% 1.45/1.65 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.65 tff(9301,plain,
% 1.45/1.65 (~r(s(s(s(z))), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2827, 9215, 1545])).
% 1.45/1.65 tff(9302,plain,
% 1.45/1.65 (b(s(s(s(z))), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1524, 9301])).
% 1.45/1.65 tff(9303,plain,
% 1.45/1.65 (b(s(s(s(elem!1))), z)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9302, 9300])).
% 1.45/1.65 tff(9304,plain,
% 1.45/1.65 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9187])).
% 1.45/1.65 tff(9305,plain,
% 1.45/1.65 (elem!1 = z),
% 1.45/1.65 inference(transitivity,[status(thm)],[155, 9304, 26])).
% 1.45/1.65 tff(9306,plain,
% 1.45/1.65 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9305])).
% 1.45/1.65 tff(9307,plain,
% 1.45/1.65 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.65 tff(9308,plain,
% 1.45/1.65 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9307, 9306])).
% 1.45/1.65 tff(9309,plain,
% 1.45/1.65 ((s(s(s(z))) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.65 tff(9310,plain,
% 1.45/1.65 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9309, 511])).
% 1.45/1.65 tff(9311,plain,
% 1.45/1.65 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(z))) = elem!1)),
% 1.45/1.65 inference(symmetry,[status(thm)],[9310])).
% 1.45/1.65 tff(9312,plain,
% 1.45/1.65 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9305])).
% 1.45/1.65 tff(9313,plain,
% 1.45/1.65 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.45/1.65 inference(transitivity,[status(thm)],[9312, 3716])).
% 1.45/1.65 tff(9314,plain,
% 1.45/1.65 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.45/1.65 inference(symmetry,[status(thm)],[9313])).
% 1.45/1.65 tff(9315,plain,
% 1.45/1.65 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9314, 9311, 9219])).
% 1.45/1.65 tff(9316,plain,
% 1.45/1.65 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9315])).
% 1.45/1.65 tff(9317,plain,
% 1.45/1.65 (~(elem!1 = s(s(s(z))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[821, 9316])).
% 1.45/1.65 tff(9318,plain,
% 1.45/1.65 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9182])).
% 1.45/1.65 tff(9319,plain,
% 1.45/1.65 (r(s(s(s(elem!1))), s(z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9215, 9318])).
% 1.45/1.65 tff(9320,plain,
% 1.45/1.65 (~r(z, s(s(s(elem!1))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3791, 124, 9319, 1545])).
% 1.45/1.65 tff(9321,plain,
% 1.45/1.65 (~r(elem!1, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9234, 9320, 9181])).
% 1.45/1.65 tff(9322,plain,
% 1.45/1.65 (b(elem!1, s(s(s(z))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[5079, 9321, 9317])).
% 1.45/1.65 tff(9323,plain,
% 1.45/1.65 (b(z, s(s(s(elem!1))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9322, 9308])).
% 1.45/1.65 tff(9324,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9325,plain,
% 1.45/1.65 (((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9326,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9325])).
% 1.45/1.65 tff(9327,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9326, 9324])).
% 1.45/1.65 tff(9328,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9329,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 1.45/1.65 tff(9330,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9329, 238, 4225, 9323, 9303, 9299])).
% 1.45/1.65 tff(9331,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9332,plain,
% 1.45/1.65 (~r(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9331, 9172, 1817, 23, 63])).
% 1.45/1.65 tff(9333,plain,
% 1.45/1.65 (b(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1542, 9332])).
% 1.45/1.65 tff(9334,plain,
% 1.45/1.65 (~r(z, s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[6869, 9333, 9179, 4225])).
% 1.45/1.65 tff(9335,plain,
% 1.45/1.65 (~r(z, s(s(elem!1)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9334, 9176])).
% 1.45/1.65 tff(9336,plain,
% 1.45/1.65 (~b(z, s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4875, 9333, 23, 9170])).
% 1.45/1.65 tff(9337,plain,
% 1.45/1.65 (r(z, s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2071, 9336])).
% 1.45/1.65 tff(9338,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9337, 9335])).
% 1.45/1.65 tff(9339,plain,(r(s(z), s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9340,plain,
% 1.45/1.65 (~b(s(s(elem!1)), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9339, 150, 8300, 63])).
% 1.45/1.65 tff(9341,plain,
% 1.45/1.65 (r(s(s(elem!1)), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[112, 9340])).
% 1.45/1.65 tff(9342,plain,
% 1.45/1.65 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3161, 8894, 8300, 8892])).
% 1.45/1.65 tff(9343,plain,
% 1.45/1.65 (r(s(s(elem!1)), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[255, 9342, 167])).
% 1.45/1.65 tff(9344,plain,
% 1.45/1.65 (~r(elem!1, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[263, 9343, 9341])).
% 1.45/1.65 tff(9345,plain,
% 1.45/1.65 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8902, 1137, 1817, 227])).
% 1.45/1.65 tff(9346,plain,
% 1.45/1.65 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[323, 9345, 275])).
% 1.45/1.65 tff(9347,plain,
% 1.45/1.65 (~b(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[7927, 1137, 9346, 1, 162, 275])).
% 1.45/1.65 tff(9348,plain,
% 1.45/1.65 (r(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1542, 9347])).
% 1.45/1.65 tff(9349,plain,
% 1.45/1.65 (~r(s(s(elem!1)), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4026, 124, 162, 9348])).
% 1.45/1.65 tff(9350,plain,
% 1.45/1.65 (b(s(s(elem!1)), z)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[4905, 9349])).
% 1.45/1.65 tff(9351,plain,
% 1.45/1.65 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3161, 1137, 1817, 227])).
% 1.45/1.65 tff(9352,plain,
% 1.45/1.65 (r(s(s(elem!1)), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[255, 9351, 248])).
% 1.45/1.65 tff(9353,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), 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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9354,plain,
% 1.45/1.65 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9355,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9354])).
% 1.45/1.65 tff(9356,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9355, 9353])).
% 1.45/1.65 tff(9357,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9358,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9357, 9356])).
% 1.45/1.65 tff(9359,plain,
% 1.45/1.65 (~r(z, s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9358, 124, 9352, 162, 9348])).
% 1.45/1.65 tff(9360,plain,
% 1.45/1.65 (b(z, s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2071, 9359])).
% 1.45/1.65 tff(9361,plain,
% 1.45/1.65 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8871, 9360, 9348, 1544, 9350, 162])).
% 1.45/1.65 tff(9362,plain,
% 1.45/1.65 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9361])).
% 1.45/1.65 tff(9363,plain,
% 1.45/1.65 (s(s(s(z))) = s(elem!1)),
% 1.45/1.65 inference(transitivity,[status(thm)],[716, 9362, 17])).
% 1.45/1.65 tff(9364,plain,
% 1.45/1.65 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9363])).
% 1.45/1.65 tff(9365,plain,
% 1.45/1.65 (s(s(z)) = elem!1),
% 1.45/1.65 inference(transitivity,[status(thm)],[144, 9364, 154])).
% 1.45/1.65 tff(9366,plain,
% 1.45/1.65 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9365])).
% 1.45/1.65 tff(9367,plain,
% 1.45/1.65 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 1.45/1.65 inference(symmetry,[status(thm)],[9366])).
% 1.45/1.65 tff(9368,plain,
% 1.45/1.65 (~r(s(elem!1), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[403, 9346, 9352])).
% 1.45/1.65 tff(9369,plain,
% 1.45/1.65 (b(s(elem!1), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[408, 9368, 632])).
% 1.45/1.65 tff(9370,plain,
% 1.45/1.65 (b(s(elem!1), s(s(z)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9369, 9367])).
% 1.45/1.65 tff(9371,plain,
% 1.45/1.65 (~r(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[315, 9346, 162])).
% 1.45/1.65 tff(9372,plain,
% 1.45/1.65 (b(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[473, 9371, 1])).
% 1.45/1.65 tff(9373,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9374,plain,
% 1.45/1.65 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9375,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9374])).
% 1.45/1.65 tff(9376,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9375, 9373])).
% 1.45/1.65 tff(9377,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9378,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9377, 9376])).
% 1.45/1.65 tff(9379,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9378, 238, 1817, 1137, 490, 1152])).
% 1.45/1.65 tff(9380,plain,((~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9381,plain,
% 1.45/1.65 (~b(s(elem!1), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9380, 9372, 1817, 1137])).
% 1.45/1.65 tff(9382,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9381, 9370])).
% 1.45/1.65 tff(9383,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(s(z)), s(z))) | (s(elem!1) = elem!1) | (s(s(elem!1)) = elem!1) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9384,plain,
% 1.45/1.65 (~r(s(s(s(s(z)))), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9383, 8894, 8300, 1, 8892, 272, 394, 167, 9341])).
% 1.45/1.65 tff(9385,plain,
% 1.45/1.65 (b(s(s(s(s(z)))), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1624, 9384])).
% 1.45/1.65 tff(9386,plain,
% 1.45/1.65 (~b(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[7927, 8904, 1, 8892, 9341, 272])).
% 1.45/1.65 tff(9387,plain,
% 1.45/1.65 (r(z, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1542, 9386])).
% 1.45/1.65 tff(9388,plain,
% 1.45/1.65 (~(s(elem!1) = s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8538, 9387, 9340, 4225, 9385, 5617, 421])).
% 1.45/1.65 tff(9389,plain,
% 1.45/1.65 (~(elem!1 = s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[280, 9388])).
% 1.45/1.65 tff(9390,plain,
% 1.45/1.65 (b(elem!1, s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[363, 9389, 9344])).
% 1.45/1.65 tff(9391,plain,
% 1.45/1.65 (~r(elem!1, s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1149, 9390, 8892, 150, 8904])).
% 1.45/1.65 tff(9392,plain,
% 1.45/1.65 (~r(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[315, 8904, 9341])).
% 1.45/1.65 tff(9393,plain,
% 1.45/1.65 (b(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[473, 9392, 1])).
% 1.45/1.65 tff(9394,plain,
% 1.45/1.65 (~b(elem!1, s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1160, 9390, 8892, 9393])).
% 1.45/1.65 tff(9395,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[629, 9394, 9391, 387])).
% 1.45/1.65 tff(9396,plain,((elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(9397,plain,
% 1.45/1.65 (elem!1 = s(s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9396, 5616, 1, 63])).
% 1.45/1.65 tff(9398,plain,
% 1.45/1.65 (b(s(z), elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3083, 9397, 8892])).
% 1.45/1.65 tff(9399,plain,
% 1.45/1.65 (s(elem!1) = s(s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[2097, 9397])).
% 1.45/1.65 tff(9400,plain,
% 1.45/1.65 (s(s(elem!1)) = elem!1),
% 1.45/1.65 inference(symmetry,[status(thm)],[9397])).
% 1.45/1.65 tff(9401,plain,
% 1.45/1.65 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9400])).
% 1.45/1.65 tff(9402,plain,
% 1.45/1.65 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.65 inference(symmetry,[status(thm)],[9401])).
% 1.45/1.65 tff(9403,plain,
% 1.45/1.65 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9402])).
% 1.45/1.65 tff(9404,plain,
% 1.45/1.65 (~(s(s(s(z))) = elem!1)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[7046, 9397])).
% 1.45/1.65 tff(9405,plain,
% 1.45/1.65 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9404, 9403])).
% 1.45/1.65 tff(9406,plain,
% 1.45/1.65 (~b(s(s(elem!1)), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[6413, 1457, 8300, 22, 427])).
% 1.45/1.65 tff(9407,plain,
% 1.45/1.65 (r(s(s(elem!1)), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[112, 9406])).
% 1.45/1.65 tff(9408,plain,
% 1.45/1.65 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[410])).
% 1.45/1.65 tff(9409,plain,
% 1.45/1.65 (b(s(z), s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8891, 5616, 1, 546])).
% 1.45/1.65 tff(9410,plain,
% 1.45/1.65 (~(elem!1 = s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[1802, 427])).
% 1.45/1.65 tff(9411,plain,
% 1.45/1.65 (~(s(elem!1) = s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[379, 9410])).
% 1.45/1.65 tff(9412,plain,
% 1.45/1.65 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8848, 1457, 546])).
% 1.45/1.65 tff(9413,plain,
% 1.45/1.65 (~r(s(elem!1), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[3017, 9412, 410])).
% 1.45/1.65 tff(9414,plain,
% 1.45/1.65 (b(s(elem!1), s(s(z)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[488, 9413, 9411])).
% 1.45/1.65 tff(9415,plain,
% 1.45/1.65 (~b(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[9380, 9414, 8300, 9409])).
% 1.45/1.65 tff(9416,plain,
% 1.45/1.65 (r(s(elem!1), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[473, 9415, 1])).
% 1.45/1.65 tff(9417,plain,
% 1.45/1.65 (r(s(s(s(elem!1))), s(z))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[9416, 9408])).
% 1.45/1.65 tff(9418,plain,
% 1.45/1.65 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[6920, 9417, 9407])).
% 1.45/1.65 tff(9419,plain,
% 1.45/1.65 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[223, 9418, 5616])).
% 1.45/1.65 tff(9420,plain,
% 1.45/1.65 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9419])).
% 1.45/1.65 tff(9421,plain,
% 1.45/1.65 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9420])).
% 1.45/1.65 tff(9422,plain,
% 1.45/1.65 (~b(s(s(s(z))), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[8694, 1457, 546])).
% 1.45/1.65 tff(9423,plain,
% 1.45/1.65 (r(s(s(s(z))), s(z))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[5118, 9422])).
% 1.45/1.65 tff(9424,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9425,plain,
% 1.45/1.65 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9426,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))))),
% 1.45/1.65 inference(monotonicity,[status(thm)],[9425])).
% 1.45/1.65 tff(9427,plain,
% 1.45/1.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[9426, 9424])).
% 1.45/1.65 tff(9428,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(9429,plain,
% 1.45/1.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9428, 9427])).
% 1.45/1.66 tff(9430,plain,
% 1.45/1.66 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9429, 124, 9423, 9417])).
% 1.45/1.66 tff(9431,plain,
% 1.45/1.66 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9430, 9421])).
% 1.45/1.66 tff(9432,plain,
% 1.45/1.66 (b(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5739, 51, 9431, 5729])).
% 1.45/1.66 tff(9433,plain,
% 1.45/1.66 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9419])).
% 1.45/1.66 tff(9434,plain,
% 1.45/1.66 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2879, 410])).
% 1.45/1.66 tff(9435,plain,
% 1.45/1.66 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[8674, 1457, 546])).
% 1.45/1.66 tff(9436,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1624, 9435])).
% 1.45/1.66 tff(9437,plain,
% 1.45/1.66 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2970, 124, 9436, 9417])).
% 1.45/1.66 tff(9438,plain,
% 1.45/1.66 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[8247, 9437, 9434])).
% 1.45/1.66 tff(9439,plain,
% 1.45/1.66 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9438, 9433])).
% 1.45/1.66 tff(9440,plain,
% 1.45/1.66 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9419])).
% 1.45/1.66 tff(9441,plain,
% 1.45/1.66 (b(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[3233, 9412])).
% 1.45/1.66 tff(9442,plain,
% 1.45/1.66 (b(s(s(elem!1)), s(s(z)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9441, 9440])).
% 1.45/1.66 tff(9443,plain,
% 1.45/1.66 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5174, 124, 9423, 9436])).
% 1.45/1.66 tff(9444,plain,
% 1.45/1.66 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5176, 9443])).
% 1.45/1.66 tff(9445,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9446,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9447,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9446, 9445])).
% 1.45/1.66 tff(9448,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9447, 238, 9444, 9442, 9439, 9432])).
% 1.45/1.66 tff(9449,plain,((~b(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~(s(elem!1) = s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(9450,plain,
% 1.45/1.66 (~b(z, s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9449, 9405, 5616, 9399, 1, 9398, 4225])).
% 1.45/1.66 tff(9451,plain,
% 1.45/1.66 (r(z, s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1542, 9450])).
% 1.45/1.66 tff(9452,plain,
% 1.45/1.66 (~(elem!1 = s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1802, 9398])).
% 1.45/1.66 tff(9453,plain,
% 1.45/1.66 (~(s(elem!1) = s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[379, 9452])).
% 1.45/1.66 tff(9454,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9455,plain,
% 1.45/1.66 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9456,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9455])).
% 1.45/1.66 tff(9457,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9456, 9454])).
% 1.45/1.66 tff(9458,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9459,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9458, 9457])).
% 1.45/1.66 tff(9460,plain,
% 1.45/1.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9459, 238, 8300, 1137, 1784])).
% 1.45/1.66 tff(9461,plain,
% 1.45/1.66 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1604, 9460])).
% 1.45/1.66 tff(9462,plain,
% 1.45/1.66 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2575])).
% 1.45/1.66 tff(9463,plain,
% 1.45/1.66 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.66 inference(symmetry,[status(thm)],[9462])).
% 1.45/1.66 tff(9464,plain,
% 1.45/1.66 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9463])).
% 1.45/1.66 tff(9465,plain,
% 1.45/1.66 (~(s(s(s(z))) = elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[7046, 2073])).
% 1.45/1.66 tff(9466,plain,
% 1.45/1.66 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9465, 9464])).
% 1.45/1.66 tff(9467,plain,
% 1.45/1.66 (~b(s(s(z)), s(s(elem!1)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[8310, 23, 8300, 546])).
% 1.45/1.66 tff(9468,plain,
% 1.45/1.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2575])).
% 1.45/1.66 tff(9469,plain,
% 1.45/1.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9468, 767])).
% 1.45/1.66 tff(9470,plain,
% 1.45/1.66 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.45/1.66 inference(transitivity,[status(thm)],[9469, 789])).
% 1.45/1.66 tff(9471,plain,
% 1.45/1.66 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9470])).
% 1.45/1.66 tff(9472,plain,
% 1.45/1.66 (~(s(s(s(s(z)))) = elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[6832, 9471])).
% 1.45/1.66 tff(9473,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2073])).
% 1.45/1.66 tff(9474,plain,
% 1.45/1.66 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[2948])).
% 1.45/1.66 tff(9475,plain,
% 1.45/1.66 (~b(s(s(s(s(z)))), elem!1)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[7882, 9474])).
% 1.45/1.66 tff(9476,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), elem!1)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2131, 9475, 2950])).
% 1.45/1.66 tff(9477,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9476, 9473])).
% 1.45/1.66 tff(9478,plain,
% 1.45/1.66 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9459, 238, 1817, 1137, 1784])).
% 1.45/1.66 tff(9479,plain,
% 1.45/1.66 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1604, 9478])).
% 1.45/1.66 tff(9480,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9481,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9482,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9481, 9480])).
% 1.45/1.66 tff(9483,plain,
% 1.45/1.66 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9482, 238, 1817, 1137, 1784])).
% 1.45/1.66 tff(9484,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1564, 9483])).
% 1.45/1.66 tff(9485,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9486,plain,
% 1.45/1.66 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9487,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9486])).
% 1.45/1.66 tff(9488,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9487, 9485])).
% 1.45/1.66 tff(9489,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9490,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9489, 9488])).
% 1.45/1.66 tff(9491,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9490, 124, 192, 9484, 9479, 9477])).
% 1.45/1.66 tff(9492,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(9493,plain,
% 1.45/1.66 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9492, 23, 8300, 1137, 2073, 9472, 1784])).
% 1.45/1.66 tff(9494,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[135, 9493, 9467, 114])).
% 1.45/1.66 tff(9495,plain,((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(9496,plain,
% 1.45/1.66 (~b(s(s(elem!1)), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9495, 1784, 1137, 2073, 114, 546])).
% 1.45/1.66 tff(9497,plain,
% 1.45/1.66 (r(s(s(elem!1)), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[112, 9496])).
% 1.45/1.66 tff(9498,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5741, 8125, 5036, 1545, 5729, 2288, 162])).
% 1.45/1.66 tff(9499,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(9500,plain,
% 1.45/1.66 (~r(s(s(s(z))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9499, 9497, 9466, 1545])).
% 1.45/1.66 tff(9501,plain,
% 1.45/1.66 (b(s(s(s(z))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5118, 9500])).
% 1.45/1.66 tff(9502,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9503,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9504,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9503, 9502])).
% 1.45/1.66 tff(9505,plain,
% 1.45/1.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9504, 238, 1137, 1784, 9501])).
% 1.45/1.66 tff(9506,plain,
% 1.45/1.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5167, 9505])).
% 1.45/1.66 tff(9507,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9508,plain,
% 1.45/1.66 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9509,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9508])).
% 1.45/1.66 tff(9510,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9509, 9507])).
% 1.45/1.66 tff(9511,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9512,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9511, 9510])).
% 1.45/1.66 tff(9513,plain,
% 1.45/1.66 (~b(s(s(z)), s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9512, 238, 8300, 1137, 9501])).
% 1.45/1.66 tff(9514,plain,
% 1.45/1.66 (r(s(s(z)), s(s(s(z))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[4334, 9513])).
% 1.45/1.66 tff(9515,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9516,plain,
% 1.45/1.66 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9517,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9516])).
% 1.45/1.66 tff(9518,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9517, 9515])).
% 1.45/1.66 tff(9519,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9520,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9519, 9518])).
% 1.45/1.66 tff(9521,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9520, 124, 9514, 9506, 9461])).
% 1.45/1.66 tff(9522,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(9523,plain,
% 1.45/1.66 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9522, 8892, 9451, 9397, 22, 4225])).
% 1.45/1.66 tff(9524,plain,
% 1.45/1.66 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[1624, 9523])).
% 1.45/1.66 tff(9525,plain,
% 1.45/1.66 (~r(s(s(s(z))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[8420, 9524, 9451])).
% 1.45/1.66 tff(9526,plain,
% 1.45/1.66 (b(s(s(s(z))), s(z))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[5118, 9525])).
% 1.45/1.66 tff(9527,plain,
% 1.45/1.66 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9331, 23, 8300, 1545, 63])).
% 1.45/1.66 tff(9528,plain,
% 1.45/1.66 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[223, 9527, 5616])).
% 1.45/1.66 tff(9529,plain,
% 1.45/1.66 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9528])).
% 1.45/1.66 tff(9530,plain,
% 1.45/1.66 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[410])).
% 1.45/1.66 tff(9531,plain,
% 1.45/1.66 (r(s(elem!1), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9530, 9529])).
% 1.45/1.66 tff(9532,plain,
% 1.45/1.66 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[9528])).
% 1.45/1.66 tff(9533,plain,
% 1.45/1.66 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.45/1.66 inference(symmetry,[status(thm)],[9532])).
% 1.45/1.66 tff(9534,plain,
% 1.45/1.66 (b(s(s(elem!1)), s(z)) <=> b(s(elem!1), s(z))),
% 1.45/1.66 inference(transitivity,[status(thm)],[9533, 5660])).
% 1.45/1.66 tff(9535,plain,
% 1.45/1.66 (b(s(elem!1), s(z))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[23, 9534])).
% 1.45/1.66 tff(9536,plain,
% 1.45/1.66 (~b(s(elem!1), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[8385, 9535, 8300, 4225])).
% 1.45/1.66 tff(9537,plain,
% 1.45/1.66 (r(s(elem!1), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[488, 9536, 278])).
% 1.45/1.66 tff(9538,plain,
% 1.45/1.66 (r(s(s(elem!1)), s(s(z)))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9537, 9531])).
% 1.45/1.66 tff(9539,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9540,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(9541,plain,
% 1.45/1.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[9540, 9539])).
% 1.45/1.66 tff(9542,plain,
% 1.45/1.66 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[9541, 238, 8300, 1137, 1456])).
% 1.45/1.66 tff(9543,plain,
% 1.45/1.66 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[2298, 51, 9542, 149])).
% 1.45/1.66 tff(9544,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9545,plain,
% 1.45/1.66 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(9546,plain,
% 1.45/1.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9545])).
% 1.45/1.67 tff(9547,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9546, 9544])).
% 1.45/1.67 tff(9548,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9549,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9548, 9547])).
% 1.45/1.67 tff(9550,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9549, 124, 9543, 9538])).
% 1.45/1.67 tff(9551,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5739, 51, 9550, 5729, 7770])).
% 1.45/1.67 tff(9552,plain,((~b(s(s(elem!1)), s(z))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(s(s(elem!1))))) | (s(elem!1) = s(s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(z, s(z))) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9553,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9552, 9405, 8892, 9526, 9399, 9453, 5616, 9451, 63])).
% 1.45/1.67 tff(9554,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[112, 9553])).
% 1.45/1.67 tff(9555,plain,
% 1.45/1.67 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5222, 9399, 22])).
% 1.45/1.67 tff(9556,plain,
% 1.45/1.67 (~r(z, s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2057, 124, 9554, 9451])).
% 1.45/1.67 tff(9557,plain,
% 1.45/1.67 (b(z, s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2071, 9556])).
% 1.45/1.67 tff(9558,plain,
% 1.45/1.67 (~r(s(s(elem!1)), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4026, 124, 9554, 9451])).
% 1.45/1.67 tff(9559,plain,
% 1.45/1.67 (b(s(s(elem!1)), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4905, 9558])).
% 1.45/1.67 tff(9560,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8871, 9559, 9557, 9451, 9524, 9555, 9554])).
% 1.45/1.67 tff(9561,plain,(b(s(s(s(elem!1))), s(s(elem!1))) | r(s(z), s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9562,plain,
% 1.45/1.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9561, 1, 63])).
% 1.45/1.67 tff(9563,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2320, 124, 9423, 9436])).
% 1.45/1.67 tff(9564,plain,
% 1.45/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5167, 9563])).
% 1.45/1.67 tff(9565,plain,
% 1.45/1.67 (~b(s(s(z)), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9383, 1137, 8300, 1, 3294, 1544, 1213, 248, 162])).
% 1.45/1.67 tff(9566,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9567,plain,
% 1.45/1.67 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9568,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9567])).
% 1.45/1.67 tff(9569,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9568, 9566])).
% 1.45/1.67 tff(9570,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9571,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9570, 9569])).
% 1.45/1.67 tff(9572,plain,
% 1.45/1.67 (~b(z, s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9571, 238, 1817, 1137, 1457])).
% 1.45/1.67 tff(9573,plain,
% 1.45/1.67 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1511, 51, 9572])).
% 1.45/1.67 tff(9574,plain,
% 1.45/1.67 (r(z, s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9573, 1450])).
% 1.45/1.67 tff(9575,plain,
% 1.45/1.67 (~r(z, s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9101, 8907, 9574])).
% 1.45/1.67 tff(9576,plain,
% 1.45/1.67 (b(z, s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2071, 9575])).
% 1.45/1.67 tff(9577,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4875, 9576, 1137, 1457])).
% 1.45/1.67 tff(9578,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[110, 51, 9577, 106])).
% 1.45/1.67 tff(9579,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4881, 9576, 1137, 1457])).
% 1.45/1.67 tff(9580,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[323, 9579, 3294])).
% 1.45/1.67 tff(9581,plain,
% 1.45/1.67 (~r(s(elem!1), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[315, 9580, 9578])).
% 1.45/1.67 tff(9582,plain,
% 1.45/1.67 (b(s(elem!1), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[473, 9581, 358])).
% 1.45/1.67 tff(9583,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9584,plain,
% 1.45/1.67 (((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9585,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9584])).
% 1.45/1.67 tff(9586,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9585, 9583])).
% 1.45/1.67 tff(9587,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9588,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z)))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9587, 9586])).
% 1.45/1.67 tff(9589,plain,
% 1.45/1.67 (~b(s(s(z)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9588, 238, 1817, 1137, 9582])).
% 1.45/1.67 tff(9590,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9591,plain,
% 1.45/1.67 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9592,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9591])).
% 1.45/1.67 tff(9593,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9592, 9590])).
% 1.45/1.67 tff(9594,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9595,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9594, 9593])).
% 1.45/1.67 tff(9596,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9595, 124, 518, 192, 4689])).
% 1.45/1.67 tff(9597,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9598,plain,
% 1.45/1.67 (~r(s(elem!1), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9597, 4689, 192])).
% 1.45/1.67 tff(9599,plain,
% 1.45/1.67 (b(s(elem!1), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[534, 9598, 206])).
% 1.45/1.67 tff(9600,plain,
% 1.45/1.67 (~b(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4533, 9599, 1137, 1152])).
% 1.45/1.67 tff(9601,plain,
% 1.45/1.67 (r(s(s(elem!1)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[323, 9600, 3294])).
% 1.45/1.67 tff(9602,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9603,plain,
% 1.45/1.67 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9604,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9603])).
% 1.45/1.67 tff(9605,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9604, 9602])).
% 1.45/1.67 tff(9606,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9607,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9606, 9605])).
% 1.45/1.67 tff(9608,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9607, 124, 9601, 192, 4689])).
% 1.45/1.67 tff(9609,plain,((~r(s(s(z)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9610,plain,
% 1.45/1.67 (~r(s(s(z)), s(elem!1))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9609, 9582, 1137, 206, 8907])).
% 1.45/1.67 tff(9611,plain,
% 1.45/1.67 (s(s(z)) = s(elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1260, 51, 9610, 9589])).
% 1.45/1.67 tff(9612,plain,
% 1.45/1.67 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9611])).
% 1.45/1.67 tff(9613,plain,
% 1.45/1.67 (r(z, s(elem!1))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9574, 9612])).
% 1.45/1.67 tff(9614,plain,
% 1.45/1.67 (~r(s(s(elem!1)), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4900, 124, 9580, 9613])).
% 1.45/1.67 tff(9615,plain,
% 1.45/1.67 (b(s(s(elem!1)), z)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4030, 51, 92, 9614])).
% 1.45/1.67 tff(9616,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4912, 238, 1137, 9576, 9615, 1457])).
% 1.45/1.67 tff(9617,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9618,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9617, 9565, 1137, 8300, 206, 22, 1457])).
% 1.45/1.67 tff(9619,plain,((~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(z)))), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9620,plain,
% 1.45/1.67 (~b(s(z), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9619, 1457, 159, 1, 9436, 167, 162])).
% 1.45/1.67 tff(9621,plain,
% 1.45/1.67 (r(s(z), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[56, 9620])).
% 1.45/1.67 tff(9622,plain,
% 1.45/1.67 (~b(s(z), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8666, 9441, 8300, 546])).
% 1.45/1.67 tff(9623,plain,
% 1.45/1.67 (r(s(z), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[4557, 51, 9622, 7947])).
% 1.45/1.67 tff(9624,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8913, 124, 160, 192, 4560])).
% 1.45/1.67 tff(9625,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9626,plain,
% 1.45/1.67 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9625, 160, 9623])).
% 1.45/1.67 tff(9627,plain,
% 1.45/1.67 (b(s(s(z)), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[135, 9626, 22])).
% 1.45/1.67 tff(9628,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(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(z)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9629,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(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(z)))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9630,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9629, 9628])).
% 1.45/1.67 tff(9631,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9630, 238, 228, 227, 226, 1235])).
% 1.45/1.67 tff(9632,plain,((~b(s(s(elem!1)), elem!1)) | (~b(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(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9633,plain,
% 1.45/1.67 (~b(s(s(elem!1)), elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9632, 9627, 226, 9441])).
% 1.45/1.67 tff(9634,plain,
% 1.45/1.67 (r(s(s(elem!1)), elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[255, 9633, 167])).
% 1.45/1.67 tff(9635,plain,
% 1.45/1.67 (~r(elem!1, s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[263, 9634, 162])).
% 1.45/1.67 tff(9636,plain,
% 1.45/1.67 (b(elem!1, s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[363, 9635, 4576])).
% 1.45/1.67 tff(9637,plain,
% 1.45/1.67 (~r(s(elem!1), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8705, 306, 4560])).
% 1.45/1.67 tff(9638,plain,
% 1.45/1.67 (b(s(elem!1), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[488, 9637, 278])).
% 1.45/1.67 tff(9639,plain,
% 1.45/1.67 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9625, 160, 4560])).
% 1.45/1.67 tff(9640,plain,
% 1.45/1.67 (b(s(s(z)), s(s(elem!1)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[135, 9639, 22])).
% 1.45/1.67 tff(9641,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9642,plain,
% 1.45/1.67 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9643,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[9642])).
% 1.45/1.67 tff(9644,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.45/1.67 inference(transitivity,[status(thm)],[9643, 9641])).
% 1.45/1.67 tff(9645,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(9646,plain,
% 1.45/1.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[9645, 9644])).
% 1.45/1.67 tff(9647,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9646, 124, 160, 2288, 4560, 1444])).
% 1.45/1.67 tff(9648,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9649,plain,
% 1.45/1.67 (~r(s(s(s(z))), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9648, 160, 7853, 4560])).
% 1.45/1.67 tff(9650,plain,
% 1.45/1.67 (b(s(s(s(z))), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[2298, 51, 9649, 149])).
% 1.45/1.67 tff(9651,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5183, 238, 2389, 1501, 8733, 8482])).
% 1.45/1.67 tff(9652,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9653,plain,
% 1.45/1.67 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9652, 9650, 8716, 8718])).
% 1.45/1.67 tff(9654,plain,
% 1.45/1.67 (~(elem!1 = s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[5877, 9653, 9640])).
% 1.45/1.67 tff(9655,plain,
% 1.45/1.67 (~(s(s(z)) = elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[1231, 9654])).
% 1.45/1.67 tff(9656,plain,
% 1.45/1.67 (~r(s(elem!1), s(s(s(z))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8713, 124, 306, 7853])).
% 1.45/1.67 tff(9657,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8805, 2115, 9656, 9655, 8718, 8716, 4576, 9638, 150, 1, 160, 1425, 546])).
% 1.45/1.67 tff(9658,plain,((~r(s(elem!1), s(z))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | b(s(s(s(z))), s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.67 tff(9659,plain,
% 1.45/1.67 (~r(s(elem!1), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[9658, 160, 1, 150, 9422, 546, 9436, 278, 9623])).
% 1.45/1.67 tff(9660,plain,
% 1.45/1.67 (b(s(elem!1), s(z))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[473, 9659, 1])).
% 1.45/1.67 tff(9661,plain,
% 1.45/1.67 (~r(s(z), elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[342, 9634, 160])).
% 1.45/1.67 tff(9662,plain,
% 1.45/1.67 (b(s(z), elem!1)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[351, 9661, 6098])).
% 1.45/1.67 tff(9663,plain,
% 1.45/1.67 (~b(s(elem!1), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[8385, 9660, 8300, 546])).
% 1.45/1.67 tff(9664,plain,
% 1.45/1.67 (r(s(elem!1), s(s(z)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[488, 9663, 278])).
% 1.45/1.67 tff(9665,plain,
% 1.45/1.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(9666,plain,
% 1.45/1.67 (((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9667,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9666])).
% 1.45/1.68 tff(9668,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9667, 9665])).
% 1.45/1.68 tff(9669,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9670,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9669, 9668])).
% 1.45/1.68 tff(9671,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9670, 238, 631, 370, 1152, 427])).
% 1.45/1.68 tff(9672,plain,((~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9673,plain,
% 1.45/1.68 (~b(elem!1, s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9672, 427, 1152, 370])).
% 1.45/1.68 tff(9674,plain,
% 1.45/1.68 (r(elem!1, s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[629, 9673, 391])).
% 1.45/1.68 tff(9675,plain,
% 1.45/1.68 (~r(elem!1, s(s(z)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[8611, 9674, 475])).
% 1.45/1.68 tff(9676,plain,
% 1.45/1.68 (elem!1 = s(s(z))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[763, 9675, 757])).
% 1.45/1.68 tff(9677,plain,
% 1.45/1.68 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.45/1.68 inference(symmetry,[status(thm)],[4811])).
% 1.45/1.68 tff(9678,plain,
% 1.45/1.68 (s(elem!1) = s(s(s(z)))),
% 1.45/1.68 inference(transitivity,[status(thm)],[18, 9677, 715])).
% 1.45/1.68 tff(9679,plain,
% 1.45/1.68 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9678])).
% 1.45/1.68 tff(9680,plain,
% 1.45/1.68 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.45/1.68 inference(symmetry,[status(thm)],[9679])).
% 1.45/1.68 tff(9681,plain,
% 1.45/1.68 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9678])).
% 1.45/1.68 tff(9682,plain,
% 1.45/1.68 ((~b(z, s(elem!1))) <=> (~b(z, s(s(s(z)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9681])).
% 1.45/1.68 tff(9683,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9684,plain,
% 1.45/1.68 (((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9685,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9684])).
% 1.45/1.68 tff(9686,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9685, 9683])).
% 1.45/1.68 tff(9687,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9688,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9687, 9686])).
% 1.45/1.68 tff(9689,plain,
% 1.45/1.68 (~b(z, s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9688, 238, 1152, 427, 1457])).
% 1.45/1.68 tff(9690,plain,
% 1.45/1.68 (~b(z, s(s(s(z))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9689, 9682])).
% 1.45/1.68 tff(9691,plain,
% 1.45/1.68 (r(z, s(s(s(z))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1474, 9690, 1470])).
% 1.45/1.68 tff(9692,plain,
% 1.45/1.68 (r(z, s(elem!1))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9691, 9680])).
% 1.45/1.68 tff(9693,plain,
% 1.45/1.68 ((z = elem!1) <=> (z = s(s(z)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[5512])).
% 1.45/1.68 tff(9694,plain,
% 1.45/1.68 ((z = elem!1) <=> (s(s(z)) = z)),
% 1.45/1.68 inference(transitivity,[status(thm)],[9693, 1445])).
% 1.45/1.68 tff(9695,plain,
% 1.45/1.68 ((s(s(z)) = z) <=> (z = elem!1)),
% 1.45/1.68 inference(symmetry,[status(thm)],[9694])).
% 1.45/1.68 tff(9696,plain,
% 1.45/1.68 ((~(s(s(z)) = z)) <=> (~(z = elem!1))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9695])).
% 1.45/1.68 tff(9697,plain,
% 1.45/1.68 (~(z = elem!1)),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[1449, 9696])).
% 1.45/1.68 tff(9698,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9699,plain,
% 1.45/1.68 (((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9700,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9699])).
% 1.45/1.68 tff(9701,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9700, 9698])).
% 1.45/1.68 tff(9702,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9703,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9702, 9701])).
% 1.45/1.68 tff(9704,plain,
% 1.45/1.68 (~b(z, elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9703, 238, 370, 427, 1457])).
% 1.45/1.68 tff(9705,plain,
% 1.45/1.68 ((z = elem!1) | r(z, elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[3134, 51, 9704])).
% 1.45/1.68 tff(9706,plain,
% 1.45/1.68 (r(z, elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9705, 9697])).
% 1.45/1.68 tff(9707,plain,
% 1.45/1.68 (~r(z, s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[6217, 9706])).
% 1.45/1.68 tff(9708,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9707, 9692])).
% 1.45/1.68 tff(9709,plain,((~b(z, s(z))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9710,plain,
% 1.45/1.68 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9709, 9674, 1457, 1152, 370, 427])).
% 1.45/1.68 tff(9711,plain,
% 1.45/1.68 (~(s(s(z)) = elem!1)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1385, 9710])).
% 1.45/1.68 tff(9712,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[4995, 9711, 9676])).
% 1.45/1.68 tff(9713,plain,((~b(s(z), elem!1)) | b(elem!1, s(s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~r(s(elem!1), s(s(z)))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9714,plain,
% 1.45/1.68 (b(elem!1, s(s(z)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9713, 9664, 1457, 9662, 9660, 9636, 387])).
% 1.45/1.68 tff(9715,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9716,plain,
% 1.45/1.68 (((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9717,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9716])).
% 1.45/1.68 tff(9718,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9717, 9715])).
% 1.45/1.68 tff(9719,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9720,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(elem!1)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9719, 9718])).
% 1.45/1.68 tff(9721,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9720, 238, 1817, 370, 753, 660])).
% 1.45/1.68 tff(9722,plain,((~b(s(z), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9723,plain,
% 1.45/1.68 (~b(s(z), s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9722, 9714, 8300, 9636])).
% 1.45/1.68 tff(9724,plain,
% 1.45/1.68 (r(s(z), s(elem!1))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[439, 9723, 426])).
% 1.45/1.68 tff(9725,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9726,plain,
% 1.45/1.68 (((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9727,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1)))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9726])).
% 1.45/1.68 tff(9728,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9727, 9725])).
% 1.45/1.68 tff(9729,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(elem!1))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9730,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(elem!1)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9729, 9728])).
% 1.45/1.68 tff(9731,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9730, 124, 9664, 9724, 9623])).
% 1.45/1.68 tff(9732,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (s(elem!1) = s(s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9733,plain,
% 1.45/1.68 (s(elem!1) = s(s(z))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9732, 9621, 1457, 546, 1, 150, 162, 226])).
% 1.45/1.68 tff(9734,plain,
% 1.45/1.68 (s(s(elem!1)) = s(s(s(z)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9733])).
% 1.45/1.68 tff(9735,plain,
% 1.45/1.68 (s(s(s(z))) = s(s(elem!1))),
% 1.45/1.68 inference(symmetry,[status(thm)],[9734])).
% 1.45/1.68 tff(9736,plain,
% 1.45/1.68 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9735])).
% 1.45/1.68 tff(9737,plain,
% 1.45/1.68 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 1.45/1.68 inference(symmetry,[status(thm)],[9736])).
% 1.45/1.68 tff(9738,plain,
% 1.45/1.68 (~r(s(s(z)), s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9625, 9621, 9623])).
% 1.45/1.68 tff(9739,plain,
% 1.45/1.68 (b(s(s(z)), s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[135, 9738, 22])).
% 1.45/1.68 tff(9740,plain,
% 1.45/1.68 (b(s(s(z)), s(s(s(z))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9739, 9737])).
% 1.45/1.68 tff(9741,plain,
% 1.45/1.68 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9734])).
% 1.45/1.68 tff(9742,plain,
% 1.45/1.68 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9741])).
% 1.45/1.68 tff(9743,plain,
% 1.45/1.68 (b(s(s(s(s(z)))), s(s(z)))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9441, 9742])).
% 1.45/1.68 tff(9744,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9745,plain,
% 1.45/1.68 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9746,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9745])).
% 1.45/1.68 tff(9747,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9746, 9744])).
% 1.45/1.68 tff(9748,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9749,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.45/1.68 inference(modus_ponens,[status(thm)],[9748, 9747])).
% 1.45/1.68 tff(9750,plain,
% 1.45/1.68 ($false),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9749, 238, 9444, 9743, 9740, 9564])).
% 1.45/1.68 tff(9751,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.68 tff(9752,plain,
% 1.45/1.68 (~b(z, s(z))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[9751, 150, 1, 4225, 9341, 9562])).
% 1.45/1.68 tff(9753,plain,
% 1.45/1.68 (r(z, s(z))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[1542, 9752])).
% 1.45/1.68 tff(9754,plain,
% 1.45/1.68 (~r(s(s(elem!1)), z)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[4026, 124, 9341, 9753])).
% 1.45/1.68 tff(9755,plain,
% 1.45/1.68 (b(s(s(elem!1)), z)),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[4905, 9754])).
% 1.45/1.68 tff(9756,plain,
% 1.45/1.68 (~r(z, s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2057, 124, 9341, 9753])).
% 1.45/1.68 tff(9757,plain,
% 1.45/1.68 (b(z, s(s(elem!1)))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[2071, 9756])).
% 1.45/1.68 tff(9758,plain,
% 1.45/1.68 (~b(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[8131, 238, 9562, 9757, 9755])).
% 1.45/1.68 tff(9759,plain,
% 1.45/1.68 (r(z, s(s(s(elem!1))))),
% 1.45/1.68 inference(unit_resolution,[status(thm)],[3795, 51, 3785, 9758])).
% 1.45/1.68 tff(9760,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9761,plain,
% 1.45/1.68 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.68 inference(rewrite,[status(thm)],[])).
% 1.45/1.68 tff(9762,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.45/1.68 inference(monotonicity,[status(thm)],[9761])).
% 1.45/1.68 tff(9763,plain,
% 1.45/1.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.68 inference(transitivity,[status(thm)],[9762, 9760])).
% 1.45/1.68 tff(9764,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.68 inference(quant_inst,[status(thm)],[])).
% 1.45/1.68 tff(9765,plain,
% 1.45/1.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9764, 9763])).
% 1.45/1.69 tff(9766,plain,
% 1.45/1.69 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9765, 238, 3818, 5036, 8125])).
% 1.45/1.69 tff(9767,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9768,plain,
% 1.45/1.69 (((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9769,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9768])).
% 1.45/1.69 tff(9770,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9769, 9767])).
% 1.45/1.69 tff(9771,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9772,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9771, 9770])).
% 1.45/1.69 tff(9773,plain,
% 1.45/1.69 (~r(s(s(elem!1)), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9772, 124, 162, 2288])).
% 1.45/1.69 tff(9774,plain,
% 1.45/1.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9775,plain,
% 1.45/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9776,plain,
% 1.45/1.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9775, 9774])).
% 1.45/1.69 tff(9777,plain,
% 1.45/1.69 (s(s(elem!1)) = s(s(s(z)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9776, 51, 9773, 9766])).
% 1.45/1.69 tff(9778,plain,
% 1.45/1.69 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9777])).
% 1.45/1.69 tff(9779,plain,
% 1.45/1.69 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9778])).
% 1.45/1.69 tff(9780,plain,
% 1.45/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[546, 9779])).
% 1.45/1.69 tff(9781,plain,
% 1.45/1.69 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9777])).
% 1.45/1.69 tff(9782,plain,
% 1.45/1.69 (s(elem!1) = s(s(z))),
% 1.45/1.69 inference(transitivity,[status(thm)],[18, 9781, 138])).
% 1.45/1.69 tff(9783,plain,
% 1.45/1.69 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9782])).
% 1.45/1.69 tff(9784,plain,
% 1.45/1.69 (elem!1 = s(z)),
% 1.45/1.69 inference(transitivity,[status(thm)],[155, 9783, 12])).
% 1.45/1.69 tff(9785,plain,
% 1.45/1.69 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9784])).
% 1.45/1.69 tff(9786,plain,
% 1.45/1.69 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.45/1.69 inference(symmetry,[status(thm)],[9785])).
% 1.45/1.69 tff(9787,plain,
% 1.45/1.69 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9786])).
% 1.45/1.69 tff(9788,plain,
% 1.45/1.69 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[728, 9787])).
% 1.45/1.69 tff(9789,plain,
% 1.45/1.69 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9778])).
% 1.45/1.69 tff(9790,plain,
% 1.45/1.69 (r(z, s(s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5517, 9789])).
% 1.45/1.69 tff(9791,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 1.45/1.69 tff(9792,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9791])).
% 1.45/1.69 tff(9793,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.45/1.69 inference(symmetry,[status(thm)],[9792])).
% 1.45/1.69 tff(9794,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[3580, 124, 1711, 2288])).
% 1.45/1.69 tff(9795,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1101, 9794])).
% 1.45/1.69 tff(9796,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9795, 9793])).
% 1.45/1.69 tff(9797,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9798,plain,
% 1.45/1.69 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9799,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9798])).
% 1.45/1.69 tff(9800,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9799, 9797])).
% 1.45/1.69 tff(9801,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9802,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9801, 9800])).
% 1.45/1.69 tff(9803,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), z)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9802, 124, 1711, 3476, 1545])).
% 1.45/1.69 tff(9804,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), z)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 9803])).
% 1.45/1.69 tff(9805,plain,
% 1.45/1.69 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[7343, 9804, 4047, 2078])).
% 1.45/1.69 tff(9806,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9805, 9796])).
% 1.45/1.69 tff(9807,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(9808,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9807, 9777, 8125, 5036, 9790, 1545, 2288])).
% 1.45/1.69 tff(9809,plain,
% 1.45/1.69 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[276])).
% 1.45/1.69 tff(9810,plain,
% 1.45/1.69 (r(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5272, 9809])).
% 1.45/1.69 tff(9811,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1776, 9810])).
% 1.45/1.69 tff(9812,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(9813,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9812, 9808, 9784])).
% 1.45/1.69 tff(9814,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1064, 9813, 9788])).
% 1.45/1.69 tff(9815,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.45/1.69 inference(monotonicity,[status(thm)],[1358])).
% 1.45/1.69 tff(9816,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(symmetry,[status(thm)],[9815])).
% 1.45/1.69 tff(9817,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[5293, 9816])).
% 1.45/1.69 tff(9818,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9819,plain,
% 1.45/1.69 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9820,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9819])).
% 1.45/1.69 tff(9821,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9820, 9818])).
% 1.45/1.69 tff(9822,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9823,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9822, 9821])).
% 1.45/1.69 tff(9824,plain,
% 1.45/1.69 (~b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9823, 238, 1817, 2765, 1906])).
% 1.45/1.69 tff(9825,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9824, 9817])).
% 1.45/1.69 tff(9826,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(9827,plain,
% 1.45/1.69 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9826, 9814, 8300, 9784, 9780])).
% 1.45/1.69 tff(9828,plain,
% 1.45/1.69 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9782])).
% 1.45/1.69 tff(9829,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.45/1.69 inference(symmetry,[status(thm)],[9828])).
% 1.45/1.69 tff(9830,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9778])).
% 1.45/1.69 tff(9831,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.69 inference(symmetry,[status(thm)],[9830])).
% 1.45/1.69 tff(9832,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9831, 9829])).
% 1.45/1.69 tff(9833,plain,
% 1.45/1.69 (~r(s(s(s(s(z)))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[8420, 2288, 1545])).
% 1.45/1.69 tff(9834,plain,
% 1.45/1.69 (b(s(s(s(s(z)))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1624, 9833])).
% 1.45/1.69 tff(9835,plain,
% 1.45/1.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[3059, 238, 8300, 546, 9834])).
% 1.45/1.69 tff(9836,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1604, 9835])).
% 1.45/1.69 tff(9837,plain,
% 1.45/1.69 (r(s(elem!1), s(s(s(elem!1))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9836, 9832])).
% 1.45/1.69 tff(9838,plain,
% 1.45/1.69 (b(s(s(s(s(s(z))))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1781, 9808])).
% 1.45/1.69 tff(9839,plain,
% 1.45/1.69 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[4153, 9838, 546, 9834])).
% 1.45/1.69 tff(9840,plain,
% 1.45/1.69 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1904, 9839])).
% 1.45/1.69 tff(9841,plain,
% 1.45/1.69 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[8506, 9840, 9837, 9782])).
% 1.45/1.69 tff(9842,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1738, 9841, 9827])).
% 1.45/1.69 tff(9843,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(9844,plain,
% 1.45/1.69 (~r(s(s(s(z))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9843, 9753, 4225, 9759, 9341])).
% 1.45/1.69 tff(9845,plain,
% 1.45/1.69 (b(s(s(s(z))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5118, 9844])).
% 1.45/1.69 tff(9846,plain,
% 1.45/1.69 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[3059, 238, 8300, 546, 1784])).
% 1.45/1.69 tff(9847,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(s(z)))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1604, 9846])).
% 1.45/1.69 tff(9848,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9849,plain,
% 1.45/1.69 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9850,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9849])).
% 1.45/1.69 tff(9851,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9850, 9848])).
% 1.45/1.69 tff(9852,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9853,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9852, 9851])).
% 1.45/1.69 tff(9854,plain,
% 1.45/1.69 (~b(s(s(z)), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9853, 238, 8300, 546, 1456])).
% 1.45/1.69 tff(9855,plain,
% 1.45/1.69 (r(s(s(z)), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[4334, 9854])).
% 1.45/1.69 tff(9856,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9857,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9858,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9857, 9856])).
% 1.45/1.69 tff(9859,plain,
% 1.45/1.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9858, 238, 546, 1784, 1456])).
% 1.45/1.69 tff(9860,plain,
% 1.45/1.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[5176, 9859])).
% 1.45/1.69 tff(9861,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9862,plain,
% 1.45/1.69 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9863,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9862])).
% 1.45/1.69 tff(9864,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9863, 9861])).
% 1.45/1.69 tff(9865,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9866,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9865, 9864])).
% 1.45/1.69 tff(9867,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9866, 124, 9860, 9855, 9847])).
% 1.45/1.69 tff(9868,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.69 tff(9869,plain,
% 1.45/1.69 (~b(s(s(s(s(z)))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9868, 9845, 4225])).
% 1.45/1.69 tff(9870,plain,
% 1.45/1.69 (r(s(s(s(s(z)))), s(z))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[1624, 9869])).
% 1.45/1.69 tff(9871,plain,
% 1.45/1.69 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[8871, 9870, 9753, 9757, 9755, 9341])).
% 1.45/1.69 tff(9872,plain,
% 1.45/1.69 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9871])).
% 1.45/1.69 tff(9873,plain,
% 1.45/1.69 (s(s(s(z))) = s(elem!1)),
% 1.45/1.69 inference(transitivity,[status(thm)],[716, 9872, 17])).
% 1.45/1.69 tff(9874,plain,
% 1.45/1.69 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9873])).
% 1.45/1.69 tff(9875,plain,
% 1.45/1.69 (b(s(elem!1), s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9845, 9874])).
% 1.45/1.69 tff(9876,plain,
% 1.45/1.69 (r(s(s(s(z))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9873])).
% 1.45/1.69 tff(9877,plain,
% 1.45/1.69 (~b(s(s(s(z))), s(s(z)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[8428, 238, 8300, 4225, 9845])).
% 1.45/1.69 tff(9878,plain,
% 1.45/1.69 (r(s(s(s(z))), s(s(z)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2298, 51, 9877, 149])).
% 1.45/1.69 tff(9879,plain,
% 1.45/1.69 (r(s(elem!1), s(s(z)))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9878, 9876])).
% 1.45/1.69 tff(9880,plain,
% 1.45/1.69 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[2893, 9871])).
% 1.45/1.69 tff(9881,plain,
% 1.45/1.69 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9873])).
% 1.45/1.69 tff(9882,plain,
% 1.45/1.69 (s(s(z)) = elem!1),
% 1.45/1.69 inference(transitivity,[status(thm)],[144, 9881, 154])).
% 1.45/1.69 tff(9883,plain,
% 1.45/1.69 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9882])).
% 1.45/1.69 tff(9884,plain,
% 1.45/1.69 (b(elem!1, s(z))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[8300, 9883])).
% 1.45/1.69 tff(9885,plain,
% 1.45/1.69 (~b(elem!1, s(s(s(elem!1))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[554, 9884, 4225, 9562])).
% 1.45/1.69 tff(9886,plain,
% 1.45/1.69 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[4820, 9885, 9880])).
% 1.45/1.69 tff(9887,plain,
% 1.45/1.69 (b(s(elem!1), s(s(s(elem!1))))),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[8397, 9886, 150, 9879])).
% 1.45/1.69 tff(9888,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9889,plain,
% 1.45/1.69 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(rewrite,[status(thm)],[])).
% 1.45/1.69 tff(9890,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.45/1.69 inference(monotonicity,[status(thm)],[9889])).
% 1.45/1.69 tff(9891,plain,
% 1.45/1.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.45/1.69 inference(transitivity,[status(thm)],[9890, 9888])).
% 1.45/1.69 tff(9892,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))))),
% 1.45/1.69 inference(quant_inst,[status(thm)],[])).
% 1.45/1.69 tff(9893,plain,
% 1.45/1.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.45/1.69 inference(modus_ponens,[status(thm)],[9892, 9891])).
% 1.45/1.69 tff(9894,plain,
% 1.45/1.69 ($false),
% 1.45/1.69 inference(unit_resolution,[status(thm)],[9893, 238, 9887, 9562, 9875, 4225])).
% 1.45/1.69 tff(9895,plain,((elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.70 tff(9896,plain,
% 1.45/1.70 (elem!1 = s(s(elem!1))),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[9895, 1, 63])).
% 1.45/1.70 tff(9897,plain,
% 1.45/1.70 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[9896])).
% 1.45/1.70 tff(9898,plain,
% 1.45/1.70 ((~b(elem!1, s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[9897])).
% 1.45/1.70 tff(9899,plain,
% 1.45/1.70 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(elem!1)))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[9896])).
% 1.45/1.70 tff(9900,plain,
% 1.45/1.70 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.45/1.70 inference(symmetry,[status(thm)],[9899])).
% 1.45/1.70 tff(9901,plain,
% 1.45/1.70 (s(elem!1) = s(s(s(elem!1)))),
% 1.45/1.70 inference(unit_resolution,[status(thm)],[2097, 9896])).
% 1.45/1.70 tff(9902,plain,
% 1.45/1.70 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.45/1.70 inference(monotonicity,[status(thm)],[9901])).
% 1.45/1.70 tff(9903,plain,
% 1.45/1.70 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.55/1.70 inference(symmetry,[status(thm)],[9902])).
% 1.55/1.70 tff(9904,plain,
% 1.55/1.70 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 1.55/1.70 inference(transitivity,[status(thm)],[9903, 9900])).
% 1.55/1.70 tff(9905,plain,
% 1.55/1.70 (b(s(elem!1), elem!1)),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9562, 9904])).
% 1.55/1.70 tff(9906,plain,
% 1.55/1.70 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9901])).
% 1.55/1.70 tff(9907,plain,
% 1.55/1.70 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.55/1.70 inference(symmetry,[status(thm)],[9906])).
% 1.55/1.70 tff(9908,plain,
% 1.55/1.70 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9907])).
% 1.55/1.70 tff(9909,plain,
% 1.55/1.70 (~(s(elem!1) = s(s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[1291, 9908])).
% 1.55/1.70 tff(9910,plain,
% 1.55/1.70 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2879, 9901])).
% 1.55/1.70 tff(9911,plain,
% 1.55/1.70 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5222, 9901, 22])).
% 1.55/1.70 tff(9912,plain,
% 1.55/1.70 (~b(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8694, 1456, 546])).
% 1.55/1.70 tff(9913,plain,
% 1.55/1.70 (r(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1542, 9912])).
% 1.55/1.70 tff(9914,plain,
% 1.55/1.70 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9868, 1456, 546])).
% 1.55/1.70 tff(9915,plain,
% 1.55/1.70 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1624, 9914])).
% 1.55/1.70 tff(9916,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8247, 2971, 3797])).
% 1.55/1.70 tff(9917,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.55/1.70 tff(9918,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.55/1.70 tff(9919,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3805, 238, 226, 1041, 9918, 9917])).
% 1.55/1.70 tff(9920,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9921,plain,
% 1.55/1.70 (~b(z, s(s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9920, 9916, 226, 8411])).
% 1.55/1.70 tff(9922,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3795, 51, 3792, 3785, 9921])).
% 1.55/1.70 tff(9923,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9924,plain,
% 1.55/1.70 (~r(s(s(s(elem!1))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9923, 9913, 3797, 226, 9915])).
% 1.55/1.70 tff(9925,plain,
% 1.55/1.70 (b(s(s(s(elem!1))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[576, 51, 94, 9924])).
% 1.55/1.70 tff(9926,plain,
% 1.55/1.70 (~b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3895, 9925, 546, 226])).
% 1.55/1.70 tff(9927,plain,
% 1.55/1.70 (r(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[112, 9926])).
% 1.55/1.70 tff(9928,plain,
% 1.55/1.70 (b(z, s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2071, 2066])).
% 1.55/1.70 tff(9929,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8871, 8125, 9928, 5233, 1545, 1544, 162])).
% 1.55/1.70 tff(9930,plain,(r(z, s(s(elem!1))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9931,plain,
% 1.55/1.70 (r(z, s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9930, 9913, 5233, 9915, 9927])).
% 1.55/1.70 tff(9932,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2057, 124, 9927, 9931, 9913])).
% 1.55/1.70 tff(9933,plain,((~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9934,plain,
% 1.55/1.70 (~b(s(s(s(z))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9933, 9911, 4225, 9562, 9910])).
% 1.55/1.70 tff(9935,plain,
% 1.55/1.70 (r(s(s(s(z))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5118, 9934])).
% 1.55/1.70 tff(9936,plain,
% 1.55/1.70 (~b(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8674, 1784, 546])).
% 1.55/1.70 tff(9937,plain,
% 1.55/1.70 (r(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1542, 9936])).
% 1.55/1.70 tff(9938,plain,
% 1.55/1.70 (~b(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9522, 9937, 2073, 1784, 114, 546])).
% 1.55/1.70 tff(9939,plain,
% 1.55/1.70 (r(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[56, 9938])).
% 1.55/1.70 tff(9940,plain,
% 1.55/1.70 (~b(s(s(s(z))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9933, 6832, 546, 226, 2963])).
% 1.55/1.70 tff(9941,plain,
% 1.55/1.70 (r(s(s(s(z))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5118, 9940])).
% 1.55/1.70 tff(9942,plain,
% 1.55/1.70 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[2073])).
% 1.55/1.70 tff(9943,plain,
% 1.55/1.70 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9942])).
% 1.55/1.70 tff(9944,plain,
% 1.55/1.70 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9465, 9943])).
% 1.55/1.70 tff(9945,plain,
% 1.55/1.70 (~r(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9499, 9937, 9944, 9941])).
% 1.55/1.70 tff(9946,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[112, 9945])).
% 1.55/1.70 tff(9947,plain,
% 1.55/1.70 (~b(s(s(z)), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8310, 9946, 8300, 546])).
% 1.55/1.70 tff(9948,plain,
% 1.55/1.70 (r(s(s(z)), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[135, 9947, 114])).
% 1.55/1.70 tff(9949,plain,
% 1.55/1.70 (~r(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9625, 9948, 9939])).
% 1.55/1.70 tff(9950,plain,
% 1.55/1.70 (b(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4557, 51, 9949, 7947])).
% 1.55/1.70 tff(9951,plain,
% 1.55/1.70 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8247, 7406, 2963])).
% 1.55/1.70 tff(9952,plain,
% 1.55/1.70 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8666, 9950, 8300, 546])).
% 1.55/1.70 tff(9953,plain,
% 1.55/1.70 (r(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3233, 9952])).
% 1.55/1.70 tff(9954,plain,
% 1.55/1.70 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3010, 9953, 9951])).
% 1.55/1.70 tff(9955,plain,
% 1.55/1.70 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1564, 9954])).
% 1.55/1.70 tff(9956,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(9957,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(9958,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9957, 9956])).
% 1.55/1.70 tff(9959,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9958, 238, 8300, 9955, 9950, 1784])).
% 1.55/1.70 tff(9960,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9961,plain,
% 1.55/1.70 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9960, 22, 4225, 9896, 9562])).
% 1.55/1.70 tff(9962,plain,
% 1.55/1.70 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1624, 9961])).
% 1.55/1.70 tff(9963,plain,
% 1.55/1.70 (~r(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8420, 9962, 9935])).
% 1.55/1.70 tff(9964,plain,
% 1.55/1.70 (b(z, s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1542, 9963])).
% 1.55/1.70 tff(9965,plain,
% 1.55/1.70 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8848, 9964, 4225])).
% 1.55/1.70 tff(9966,plain,
% 1.55/1.70 (~r(s(elem!1), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3017, 9965, 9901])).
% 1.55/1.70 tff(9967,plain,
% 1.55/1.70 (b(s(elem!1), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[488, 9966, 9909])).
% 1.55/1.70 tff(9968,plain,
% 1.55/1.70 (~b(elem!1, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3027, 9967, 8300, 9905])).
% 1.55/1.70 tff(9969,plain,
% 1.55/1.70 (~b(s(s(elem!1)), s(s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9968, 9898])).
% 1.55/1.70 tff(9970,plain,
% 1.55/1.70 (r(s(s(elem!1)), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[5230, 51, 9969, 5385])).
% 1.55/1.70 tff(9971,plain,
% 1.55/1.70 (b(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3233, 9965])).
% 1.55/1.70 tff(9972,plain,
% 1.55/1.70 (~b(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[8666, 9971, 8300, 4225])).
% 1.55/1.70 tff(9973,plain,
% 1.55/1.70 (r(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4557, 51, 9972, 7947])).
% 1.55/1.70 tff(9974,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(9975,plain,
% 1.55/1.70 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(9976,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9975])).
% 1.55/1.70 tff(9977,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[9976, 9974])).
% 1.55/1.70 tff(9978,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(9979,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9978, 9977])).
% 1.55/1.70 tff(9980,plain,
% 1.55/1.70 (~r(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9979, 124, 9973, 9970])).
% 1.55/1.70 tff(9981,plain,
% 1.55/1.70 (b(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[56, 9980])).
% 1.55/1.70 tff(9982,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(9983,plain,
% 1.55/1.70 (((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(9984,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9983])).
% 1.55/1.70 tff(9985,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[9984, 9982])).
% 1.55/1.70 tff(9986,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(9987,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9986, 9985])).
% 1.55/1.70 tff(9988,plain,
% 1.55/1.70 (~r(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9987, 124, 9973, 9970])).
% 1.55/1.70 tff(9989,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[112, 9988])).
% 1.55/1.70 tff(9990,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[3192, 9989, 9981, 4225, 9562])).
% 1.55/1.70 tff(9991,plain,((s(elem!1) = s(z)) | r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(9992,plain,
% 1.55/1.70 (s(elem!1) = s(z)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9991, 63])).
% 1.55/1.70 tff(9993,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9992])).
% 1.55/1.70 tff(9994,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9077, 9992, 8300])).
% 1.55/1.70 tff(9995,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[9994, 9993])).
% 1.55/1.70 tff(9996,plain,
% 1.55/1.70 (s(s(z)) = s(s(elem!1))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[357, 9992])).
% 1.55/1.70 tff(9997,plain,
% 1.55/1.70 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9996])).
% 1.55/1.70 tff(9998,plain,
% 1.55/1.70 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.55/1.70 inference(transitivity,[status(thm)],[9997, 3730])).
% 1.55/1.70 tff(9999,plain,
% 1.55/1.70 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[9998])).
% 1.55/1.70 tff(10000,plain,
% 1.55/1.70 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4960, 9996])).
% 1.55/1.70 tff(10001,plain,
% 1.55/1.70 (~(s(s(z)) = elem!1)),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1385, 10000])).
% 1.55/1.70 tff(10002,plain,
% 1.55/1.70 (~(elem!1 = s(s(elem!1)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[10001, 9999])).
% 1.55/1.70 tff(10003,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9339, 10002, 9995, 8300, 63])).
% 1.55/1.70 tff(10004,plain,(r(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(10005,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10004, 62])).
% 1.55/1.70 tff(10006,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(10007,plain,
% 1.55/1.70 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10006, 24])).
% 1.55/1.70 tff(10008,plain,
% 1.55/1.70 (b(s(s(elem!1)), s(z))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[112, 107])).
% 1.55/1.70 tff(10009,plain,
% 1.55/1.70 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[208, 206])).
% 1.55/1.70 tff(10010,plain,
% 1.55/1.70 ((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (s(elem!1) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9617, 8300])).
% 1.55/1.70 tff(10011,plain,
% 1.55/1.70 (b(s(s(z)), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10010, 1137, 206, 114, 1457])).
% 1.55/1.70 tff(10012,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10013,plain,
% 1.55/1.70 (((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10014,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[10013])).
% 1.55/1.70 tff(10015,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[10014, 10012])).
% 1.55/1.70 tff(10016,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(10017,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[10016, 10015])).
% 1.55/1.70 tff(10018,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10017, 238, 8300, 1137, 10011, 23])).
% 1.55/1.70 tff(10019,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(elem!1))) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.70 tff(10020,plain,
% 1.55/1.70 (~b(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10019, 114, 206, 23, 1457])).
% 1.55/1.70 tff(10021,plain,
% 1.55/1.70 (r(s(z), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[56, 10020])).
% 1.55/1.70 tff(10022,plain,
% 1.55/1.70 ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[218, 10004])).
% 1.55/1.70 tff(10023,plain,
% 1.55/1.70 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10022, 10021])).
% 1.55/1.70 tff(10024,plain,
% 1.55/1.70 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[223, 10023, 10009])).
% 1.55/1.70 tff(10025,plain,
% 1.55/1.70 (~r(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9625, 192, 160])).
% 1.55/1.70 tff(10026,plain,
% 1.55/1.70 (b(s(z), s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[4557, 51, 10025, 7947])).
% 1.55/1.70 tff(10027,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10028,plain,
% 1.55/1.70 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10029,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[10028])).
% 1.55/1.70 tff(10030,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[10029, 10027])).
% 1.55/1.70 tff(10031,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(10032,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[10031, 10030])).
% 1.55/1.70 tff(10033,plain,
% 1.55/1.70 (~b(z, s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10032, 238, 10026, 23, 1457])).
% 1.55/1.70 tff(10034,plain,
% 1.55/1.70 (r(z, s(s(elem!1)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[2071, 10033])).
% 1.55/1.70 tff(10035,plain,
% 1.55/1.70 (~r(z, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[9101, 10034, 192])).
% 1.55/1.70 tff(10036,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10037,plain,
% 1.55/1.70 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(rewrite,[status(thm)],[])).
% 1.55/1.70 tff(10038,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 1.55/1.70 inference(monotonicity,[status(thm)],[10037])).
% 1.55/1.70 tff(10039,plain,
% 1.55/1.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.55/1.70 inference(transitivity,[status(thm)],[10038, 10036])).
% 1.55/1.70 tff(10040,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 1.55/1.70 inference(quant_inst,[status(thm)],[])).
% 1.55/1.70 tff(10041,plain,
% 1.55/1.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 1.55/1.70 inference(modus_ponens,[status(thm)],[10040, 10039])).
% 1.55/1.70 tff(10042,plain,
% 1.55/1.70 (~b(z, s(s(z)))),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[10041, 238, 8300, 10026, 1457])).
% 1.55/1.70 tff(10043,plain,
% 1.55/1.70 ($false),
% 1.55/1.70 inference(unit_resolution,[status(thm)],[1511, 51, 10042, 10035, 4848])).
% 1.55/1.71 tff(10044,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(10045,plain,
% 1.55/1.71 (~r(s(s(z)), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10044, 10021, 1457, 23])).
% 1.55/1.71 tff(10046,plain,
% 1.55/1.71 (b(s(s(z)), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[135, 10045, 114])).
% 1.55/1.71 tff(10047,plain,
% 1.55/1.71 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[6287, 238, 10046, 10024, 23])).
% 1.55/1.71 tff(10048,plain,
% 1.55/1.71 (r(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3233, 10047])).
% 1.55/1.71 tff(10049,plain,
% 1.55/1.71 ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4568, 10004])).
% 1.55/1.71 tff(10050,plain,
% 1.55/1.71 (~r(s(z), s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10049, 10048])).
% 1.55/1.71 tff(10051,plain,
% 1.55/1.71 (b(s(z), s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4557, 51, 10050, 7947])).
% 1.55/1.71 tff(10052,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(elem!1)))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10053,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(elem!1)))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(10054,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10053, 10052])).
% 1.55/1.71 tff(10055,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10054, 238, 8300, 10046, 10051, 23])).
% 1.55/1.71 tff(10056,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(10057,plain,
% 1.55/1.71 (s(s(z)) = s(s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10056, 159, 1457, 10008])).
% 1.55/1.71 tff(10058,plain,
% 1.55/1.71 (s(elem!1) = s(z)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[21, 10057])).
% 1.55/1.71 tff(10059,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.55/1.71 tff(10060,plain,
% 1.55/1.71 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[353])).
% 1.55/1.71 tff(10061,plain,
% 1.55/1.71 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10060])).
% 1.55/1.71 tff(10062,plain,
% 1.55/1.71 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10061])).
% 1.55/1.71 tff(10063,plain,
% 1.55/1.71 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[81, 10062])).
% 1.55/1.71 tff(10064,plain,
% 1.55/1.71 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[3927])).
% 1.55/1.71 tff(10065,plain,
% 1.55/1.71 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10064, 5534])).
% 1.55/1.71 tff(10066,plain,
% 1.55/1.71 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10065])).
% 1.55/1.71 tff(10067,plain,
% 1.55/1.71 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[94, 10066])).
% 1.55/1.71 tff(10068,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[539, 10067, 10063, 10059])).
% 1.55/1.71 tff(10069,plain,((~(s(elem!1) = s(z))) | r(s(elem!1), s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(10070,plain,
% 1.55/1.71 (r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10069, 10058, 81])).
% 1.55/1.71 tff(10071,plain,
% 1.55/1.71 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10058])).
% 1.55/1.71 tff(10072,plain,
% 1.55/1.71 (elem!1 = z),
% 1.55/1.71 inference(transitivity,[status(thm)],[155, 10071, 26])).
% 1.55/1.71 tff(10073,plain,
% 1.55/1.71 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10072])).
% 1.55/1.71 tff(10074,plain,
% 1.55/1.71 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.55/1.71 inference(transitivity,[status(thm)],[10073, 3716])).
% 1.55/1.71 tff(10075,plain,
% 1.55/1.71 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10074])).
% 1.55/1.71 tff(10076,plain,
% 1.55/1.71 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10075])).
% 1.55/1.71 tff(10077,plain,
% 1.55/1.71 (~(elem!1 = s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[821, 10076])).
% 1.55/1.71 tff(10078,plain,
% 1.55/1.71 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10057])).
% 1.55/1.71 tff(10079,plain,
% 1.55/1.71 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10078])).
% 1.55/1.71 tff(10080,plain,
% 1.55/1.71 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(z)), s(z)))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10079])).
% 1.55/1.71 tff(10081,plain,
% 1.55/1.71 (~r(s(s(z)), s(z))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[107, 10080])).
% 1.55/1.71 tff(10082,plain,
% 1.55/1.71 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4960, 10057])).
% 1.55/1.71 tff(10083,plain,
% 1.55/1.71 (~(s(s(z)) = elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1385, 10082])).
% 1.55/1.71 tff(10084,plain,
% 1.55/1.71 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10057])).
% 1.55/1.71 tff(10085,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10084])).
% 1.55/1.71 tff(10086,plain,
% 1.55/1.71 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10085])).
% 1.55/1.71 tff(10087,plain,
% 1.55/1.71 ((~![X: $i] : (~b(X, X))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(10088,plain,
% 1.55/1.71 (~b(s(s(elem!1)), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10087, 837])).
% 1.55/1.71 tff(10089,plain,
% 1.55/1.71 (~b(s(s(z)), s(s(elem!1)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10088, 10086])).
% 1.55/1.71 tff(10090,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 1.55/1.71 tff(10091,plain,
% 1.55/1.71 (b(s(s(z)), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[79, 10090])).
% 1.55/1.71 tff(10092,plain,
% 1.55/1.71 (~(elem!1 = s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[4995, 374])).
% 1.55/1.71 tff(10093,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10094,plain,
% 1.55/1.71 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10095,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10094])).
% 1.55/1.71 tff(10096,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10095, 10093])).
% 1.55/1.71 tff(10097,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(10098,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10097, 10096])).
% 1.55/1.71 tff(10099,plain,
% 1.55/1.71 (~b(s(s(z)), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10098, 238, 1817, 1137, 370])).
% 1.55/1.71 tff(10100,plain,
% 1.55/1.71 (r(s(s(z)), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1275, 10099, 374])).
% 1.55/1.71 tff(10101,plain,
% 1.55/1.71 (~(s(elem!1) = s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5709, 370, 5389])).
% 1.55/1.71 tff(10102,plain,
% 1.55/1.71 (~(s(s(z)) = s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[21, 10101])).
% 1.55/1.71 tff(10103,plain,
% 1.55/1.71 (r(s(s(z)), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[135, 10102, 2213])).
% 1.55/1.71 tff(10104,plain,
% 1.55/1.71 (r(s(elem!1), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[473, 10101, 1808])).
% 1.55/1.71 tff(10105,plain,
% 1.55/1.71 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[7043])).
% 1.55/1.71 tff(10106,plain,
% 1.55/1.71 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10105])).
% 1.55/1.71 tff(10107,plain,
% 1.55/1.71 (b(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[8582, 10106])).
% 1.55/1.71 tff(10108,plain,
% 1.55/1.71 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[2073])).
% 1.55/1.71 tff(10109,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[370, 10108])).
% 1.55/1.71 tff(10110,plain,
% 1.55/1.71 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[9492, 2073, 192, 9472, 1817, 1137, 10109])).
% 1.55/1.71 tff(10111,plain,
% 1.55/1.71 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1624, 10110])).
% 1.55/1.71 tff(10112,plain,
% 1.55/1.71 (~r(z, s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1571, 124, 10111, 1545])).
% 1.55/1.71 tff(10113,plain,
% 1.55/1.71 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1487, 51, 10112])).
% 1.55/1.71 tff(10114,plain,
% 1.55/1.71 (b(z, s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10113, 1454])).
% 1.55/1.71 tff(10115,plain,
% 1.55/1.71 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[2970, 124, 10111, 2599])).
% 1.55/1.71 tff(10116,plain,
% 1.55/1.71 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[2974, 51, 10115, 2963])).
% 1.55/1.71 tff(10117,plain,
% 1.55/1.71 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.55/1.71 inference(commutativity,[status(thm)],[])).
% 1.55/1.71 tff(10118,plain,
% 1.55/1.71 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10117])).
% 1.55/1.71 tff(10119,plain,
% 1.55/1.71 ((~(s(s(s(s(z)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10118])).
% 1.55/1.71 tff(10120,plain,
% 1.55/1.71 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[2963, 10119])).
% 1.55/1.71 tff(10121,plain,
% 1.55/1.71 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[9285, 124, 10111, 2599])).
% 1.55/1.71 tff(10122,plain,
% 1.55/1.71 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3051, 51, 10121])).
% 1.55/1.71 tff(10123,plain,
% 1.55/1.71 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10122, 10120])).
% 1.55/1.71 tff(10124,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10125,plain,
% 1.55/1.71 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10126,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10125])).
% 1.55/1.71 tff(10127,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10126, 10124])).
% 1.55/1.71 tff(10128,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(10129,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10128, 10127])).
% 1.55/1.71 tff(10130,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10129, 238, 10123, 10116, 10114, 10107])).
% 1.55/1.71 tff(10131,plain,((~(elem!1 = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(10132,plain,
% 1.55/1.71 (~(elem!1 = s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10131, 10103, 5390, 1817, 1137, 10104, 370, 10102])).
% 1.55/1.71 tff(10133,plain,
% 1.55/1.71 (~(s(s(elem!1)) = elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[166, 10132])).
% 1.55/1.71 tff(10134,plain,
% 1.55/1.71 (r(s(s(elem!1)), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[255, 10133, 249])).
% 1.55/1.71 tff(10135,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10136,plain,
% 1.55/1.71 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10137,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10136])).
% 1.55/1.71 tff(10138,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1)))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10137, 10135])).
% 1.55/1.71 tff(10139,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.55/1.71 inference(quant_inst,[status(thm)],[])).
% 1.55/1.71 tff(10140,plain,
% 1.55/1.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), elem!1))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10139, 10138])).
% 1.55/1.71 tff(10141,plain,
% 1.55/1.71 ($false),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10140, 124, 10134, 10103, 10100])).
% 1.55/1.71 tff(10142,plain,((~b(elem!1, s(z))) | b(s(s(elem!1)), elem!1) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | b(s(s(z)), s(s(elem!1))) | b(s(elem!1), s(z)) | b(z, s(z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.71 tff(10143,plain,
% 1.55/1.71 (~b(elem!1, s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[10142, 249, 1817, 57, 2213, 1808, 5389, 374])).
% 1.55/1.71 tff(10144,plain,
% 1.55/1.71 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[4043])).
% 1.55/1.71 tff(10145,plain,
% 1.55/1.71 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10144])).
% 1.55/1.71 tff(10146,plain,
% 1.55/1.71 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(z)), s(s(s(s(z))))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[7239])).
% 1.55/1.71 tff(10147,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[9077, 353, 1817])).
% 1.55/1.71 tff(10148,plain,
% 1.55/1.71 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[3762])).
% 1.55/1.71 tff(10149,plain,
% 1.55/1.71 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.55/1.71 inference(symmetry,[status(thm)],[10148])).
% 1.55/1.71 tff(10150,plain,
% 1.55/1.71 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10149, 9219])).
% 1.55/1.71 tff(10151,plain,
% 1.55/1.71 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10150])).
% 1.55/1.71 tff(10152,plain,
% 1.55/1.71 (~(elem!1 = s(s(s(z))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[1469, 10151])).
% 1.55/1.71 tff(10153,plain,
% 1.55/1.71 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[3762])).
% 1.55/1.71 tff(10154,plain,
% 1.55/1.71 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10153])).
% 1.55/1.71 tff(10155,plain,
% 1.55/1.71 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[805])).
% 1.55/1.71 tff(10156,plain,
% 1.55/1.71 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.55/1.71 inference(symmetry,[status(thm)],[10155])).
% 1.55/1.71 tff(10157,plain,
% 1.55/1.71 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.71 inference(transitivity,[status(thm)],[10156, 10154])).
% 1.55/1.71 tff(10158,plain,
% 1.55/1.71 ((~r(z, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10157])).
% 1.55/1.71 tff(10159,plain,
% 1.55/1.71 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[3762])).
% 1.55/1.71 tff(10160,plain,
% 1.55/1.71 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10159])).
% 1.55/1.71 tff(10161,plain,
% 1.55/1.71 (~(s(elem!1) = s(s(z)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[2858, 1808, 1817])).
% 1.55/1.71 tff(10162,plain,
% 1.55/1.71 (~(elem!1 = s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[280, 10161])).
% 1.55/1.71 tff(10163,plain,
% 1.55/1.71 (r(elem!1, s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[363, 1400, 10162])).
% 1.55/1.71 tff(10164,plain,
% 1.55/1.71 (~r(elem!1, s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1378, 10163, 102])).
% 1.55/1.71 tff(10165,plain,
% 1.55/1.71 (~r(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10164, 10160])).
% 1.55/1.71 tff(10166,plain,
% 1.55/1.71 (~r(elem!1, s(s(s(z))))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10165, 10158])).
% 1.55/1.71 tff(10167,plain,
% 1.55/1.71 (b(elem!1, s(s(s(z))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5079, 10166, 10152])).
% 1.55/1.71 tff(10168,plain,
% 1.55/1.71 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[5363, 57, 81])).
% 1.55/1.71 tff(10169,plain,
% 1.55/1.71 (~r(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[263, 301, 10163])).
% 1.55/1.71 tff(10170,plain,
% 1.55/1.71 (b(s(s(elem!1)), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[110, 51, 10169, 106])).
% 1.55/1.71 tff(10171,plain,
% 1.55/1.71 (b(z, s(s(s(elem!1))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3795, 51, 10165, 3785])).
% 1.55/1.71 tff(10172,plain,
% 1.55/1.71 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[815])).
% 1.55/1.71 tff(10173,plain,
% 1.55/1.71 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.55/1.71 inference(symmetry,[status(thm)],[10172])).
% 1.55/1.71 tff(10174,plain,
% 1.55/1.71 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.55/1.71 inference(monotonicity,[status(thm)],[806, 3762])).
% 1.55/1.71 tff(10175,plain,
% 1.55/1.71 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.71 inference(symmetry,[status(thm)],[10174])).
% 1.55/1.71 tff(10176,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.55/1.71 tff(10177,plain,
% 1.55/1.71 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3973, 1544, 1545, 353])).
% 1.55/1.71 tff(10178,plain,
% 1.55/1.71 (r(s(s(elem!1)), z)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[7149, 353, 301])).
% 1.55/1.71 tff(10179,plain,
% 1.55/1.71 (~r(s(s(s(elem!1))), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1182, 210, 301])).
% 1.55/1.71 tff(10180,plain,
% 1.55/1.71 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[647, 10179, 7122])).
% 1.55/1.71 tff(10181,plain,
% 1.55/1.71 (b(s(s(s(z))), z)),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10180, 10174])).
% 1.55/1.71 tff(10182,plain,
% 1.55/1.71 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3937, 210, 23, 289, 353, 7481, 1776, 5782])).
% 1.55/1.71 tff(10183,plain,
% 1.55/1.71 (r(s(s(s(z))), s(s(elem!1)))),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[210, 7220])).
% 1.55/1.71 tff(10184,plain,
% 1.55/1.71 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[3867, 10183, 10182])).
% 1.55/1.71 tff(10185,plain,
% 1.55/1.71 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1101, 10184])).
% 1.55/1.71 tff(10186,plain,
% 1.55/1.71 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[9245, 10185, 10176, 10181])).
% 1.55/1.71 tff(10187,plain,
% 1.55/1.71 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.71 inference(unit_resolution,[status(thm)],[1064, 10186, 7187])).
% 1.55/1.71 tff(10188,plain,
% 1.55/1.71 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.71 inference(modus_ponens,[status(thm)],[10187, 7183])).
% 1.55/1.71 tff(10189,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10190,plain,
% 1.55/1.71 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(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))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.55/1.71 inference(rewrite,[status(thm)],[])).
% 1.55/1.71 tff(10191,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z))))),
% 1.55/1.71 inference(monotonicity,[status(thm)],[10190])).
% 1.55/1.71 tff(10192,plain,
% 1.55/1.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10191, 10189])).
% 1.55/1.72 tff(10193,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10194,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(elem!1)), z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10193, 10192])).
% 1.55/1.72 tff(10195,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10194, 124, 10182, 10188, 10178])).
% 1.55/1.72 tff(10196,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | r(s(s(s(s(s(z))))), s(z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(10197,plain,
% 1.55/1.72 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10196, 10177, 10176, 23, 289, 353, 301])).
% 1.55/1.72 tff(10198,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[223, 10197, 545])).
% 1.55/1.72 tff(10199,plain,
% 1.55/1.72 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3909, 238, 1137, 10198, 23])).
% 1.55/1.72 tff(10200,plain,
% 1.55/1.72 (~b(s(s(s(z))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3886, 10199, 804])).
% 1.55/1.72 tff(10201,plain,
% 1.55/1.72 (r(s(s(s(z))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5118, 10200])).
% 1.55/1.72 tff(10202,plain,
% 1.55/1.72 (~r(s(s(s(z))), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2827, 10201, 1545])).
% 1.55/1.72 tff(10203,plain,
% 1.55/1.72 (b(s(s(s(z))), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1524, 10202])).
% 1.55/1.72 tff(10204,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10203, 10175])).
% 1.55/1.72 tff(10205,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10204, 10173])).
% 1.55/1.72 tff(10206,plain,
% 1.55/1.72 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[4158, 7100])).
% 1.55/1.72 tff(10207,plain,
% 1.55/1.72 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10201, 4068])).
% 1.55/1.72 tff(10208,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2970, 124, 1544, 10207])).
% 1.55/1.72 tff(10209,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2974, 51, 10208, 10206])).
% 1.55/1.72 tff(10210,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.55/1.72 inference(monotonicity,[status(thm)],[3762])).
% 1.55/1.72 tff(10211,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[4041, 10210])).
% 1.55/1.72 tff(10212,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10213,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10214,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10213, 10212])).
% 1.55/1.72 tff(10215,plain,
% 1.55/1.72 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10214, 238, 10211, 9918])).
% 1.55/1.72 tff(10216,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10215, 10209, 10205])).
% 1.55/1.72 tff(10217,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~(s(elem!1) = s(z))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(10218,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10217, 10171, 353, 1545, 57, 10170, 10168, 10167, 10147, 301])).
% 1.55/1.72 tff(10219,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1624, 10218])).
% 1.55/1.72 tff(10220,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10221,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10222,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10221, 10220])).
% 1.55/1.72 tff(10223,plain,
% 1.55/1.72 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10222, 238, 57, 10170, 10219])).
% 1.55/1.72 tff(10224,plain,
% 1.55/1.72 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10223, 10146])).
% 1.55/1.72 tff(10225,plain,
% 1.55/1.72 (r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1604, 10224])).
% 1.55/1.72 tff(10226,plain,
% 1.55/1.72 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10225, 10145])).
% 1.55/1.72 tff(10227,plain,
% 1.55/1.72 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[807])).
% 1.55/1.72 tff(10228,plain,
% 1.55/1.72 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10227])).
% 1.55/1.72 tff(10229,plain,
% 1.55/1.72 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2920, 10168])).
% 1.55/1.72 tff(10230,plain,
% 1.55/1.72 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[807])).
% 1.55/1.72 tff(10231,plain,
% 1.55/1.72 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(symmetry,[status(thm)],[10230])).
% 1.55/1.72 tff(10232,plain,
% 1.55/1.72 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10231])).
% 1.55/1.72 tff(10233,plain,
% 1.55/1.72 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[7881, 238, 57, 10170, 10219])).
% 1.55/1.72 tff(10234,plain,
% 1.55/1.72 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5236, 51, 8151, 10233])).
% 1.55/1.72 tff(10235,plain,
% 1.55/1.72 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[353])).
% 1.55/1.72 tff(10236,plain,
% 1.55/1.72 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.55/1.72 inference(symmetry,[status(thm)],[10235])).
% 1.55/1.72 tff(10237,plain,
% 1.55/1.72 (r(elem!1, s(elem!1))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10163, 10236])).
% 1.55/1.72 tff(10238,plain,
% 1.55/1.72 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[3927])).
% 1.55/1.72 tff(10239,plain,
% 1.55/1.72 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.55/1.72 inference(symmetry,[status(thm)],[10238])).
% 1.55/1.72 tff(10240,plain,
% 1.55/1.72 (r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10069, 353, 81])).
% 1.55/1.72 tff(10241,plain,
% 1.55/1.72 (~r(elem!1, s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1329, 10240, 590])).
% 1.55/1.72 tff(10242,plain,
% 1.55/1.72 (elem!1 = s(s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1319, 10241, 1314])).
% 1.55/1.72 tff(10243,plain,
% 1.55/1.72 (s(s(s(elem!1))) = elem!1),
% 1.55/1.72 inference(symmetry,[status(thm)],[10242])).
% 1.55/1.72 tff(10244,plain,
% 1.55/1.72 (s(s(s(elem!1))) = z),
% 1.55/1.72 inference(transitivity,[status(thm)],[10243, 155, 10239, 26])).
% 1.55/1.72 tff(10245,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[821, 10244])).
% 1.55/1.72 tff(10246,plain,((~(s(elem!1) = s(z))) | b(elem!1, s(s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(10247,plain,
% 1.55/1.72 (b(elem!1, s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10246, 10237, 353, 81])).
% 1.55/1.72 tff(10248,plain,
% 1.55/1.72 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3909, 238, 1137, 226, 23])).
% 1.55/1.72 tff(10249,plain,
% 1.55/1.72 (~b(s(s(s(z))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3886, 10248, 804])).
% 1.55/1.72 tff(10250,plain,
% 1.55/1.72 (r(s(s(s(z))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5118, 10249])).
% 1.55/1.72 tff(10251,plain,
% 1.55/1.72 (~r(s(s(s(z))), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2827, 10250, 1545])).
% 1.55/1.72 tff(10252,plain,
% 1.55/1.72 (b(s(s(s(z))), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1524, 10251])).
% 1.55/1.72 tff(10253,plain,
% 1.55/1.72 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.55/1.72 inference(monotonicity,[status(thm)],[815])).
% 1.55/1.72 tff(10254,plain,
% 1.55/1.72 ((~b(s(z), z)) <=> (~b(s(z), elem!1))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10253])).
% 1.55/1.72 tff(10255,plain,
% 1.55/1.72 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5236, 51, 8151, 7882])).
% 1.55/1.72 tff(10256,plain,
% 1.55/1.72 (~b(elem!1, s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3306, 226, 543, 289])).
% 1.55/1.72 tff(10257,plain,
% 1.55/1.72 (r(elem!1, s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[606, 10256, 150])).
% 1.55/1.72 tff(10258,plain,
% 1.55/1.72 (r(z, s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[7136, 10257, 353])).
% 1.55/1.72 tff(10259,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10260,plain,
% 1.55/1.72 (((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10261,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10260])).
% 1.55/1.72 tff(10262,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10261, 10259])).
% 1.55/1.72 tff(10263,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10264,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10263, 10262])).
% 1.55/1.72 tff(10265,plain,
% 1.55/1.72 (~r(z, s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10264, 124, 10258, 10255])).
% 1.55/1.72 tff(10266,plain,
% 1.55/1.72 (~r(elem!1, s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10265, 3765])).
% 1.55/1.72 tff(10267,plain,
% 1.55/1.72 (b(elem!1, s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[935, 10266, 3761])).
% 1.55/1.72 tff(10268,plain,
% 1.55/1.72 (b(z, s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10267, 3757])).
% 1.55/1.72 tff(10269,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10252, 10175])).
% 1.55/1.72 tff(10270,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10269, 10173])).
% 1.55/1.72 tff(10271,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10272,plain,
% 1.55/1.72 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10273,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10272])).
% 1.55/1.72 tff(10274,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10273, 10271])).
% 1.55/1.72 tff(10275,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10276,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10275, 10274])).
% 1.55/1.72 tff(10277,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10276, 124, 10258, 10255])).
% 1.55/1.72 tff(10278,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), elem!1)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10277, 4038])).
% 1.55/1.72 tff(10279,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2131, 10278, 4036])).
% 1.55/1.72 tff(10280,plain,
% 1.55/1.72 (b(s(s(s(s(z)))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10279, 10210])).
% 1.55/1.72 tff(10281,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10282,plain,
% 1.55/1.72 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10283,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10282])).
% 1.55/1.72 tff(10284,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10283, 10281])).
% 1.55/1.72 tff(10285,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10286,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10285, 10284])).
% 1.55/1.72 tff(10287,plain,
% 1.55/1.72 ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10286, 238, 10280, 10268])).
% 1.55/1.72 tff(10288,plain,
% 1.55/1.72 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10287, 10270])).
% 1.55/1.72 tff(10289,plain,
% 1.55/1.72 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2974, 51, 10288, 10206])).
% 1.55/1.72 tff(10290,plain,
% 1.55/1.72 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[8241, 124, 10289, 161])).
% 1.55/1.72 tff(10291,plain,
% 1.55/1.72 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[6600, 10290])).
% 1.55/1.72 tff(10292,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10293,plain,
% 1.55/1.72 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10294,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10293])).
% 1.55/1.72 tff(10295,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10294, 10292])).
% 1.55/1.72 tff(10296,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10297,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10296, 10295])).
% 1.55/1.72 tff(10298,plain,
% 1.55/1.72 (~b(s(z), z)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10297, 238, 10291, 1784, 10268])).
% 1.55/1.72 tff(10299,plain,
% 1.55/1.72 (~b(s(z), elem!1)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10298, 10254])).
% 1.55/1.72 tff(10300,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5589, 10299, 1808, 1400])).
% 1.55/1.72 tff(10301,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5751, 10300, 804])).
% 1.55/1.72 tff(10302,plain,
% 1.55/1.72 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[9245, 10301, 10176, 10252])).
% 1.55/1.72 tff(10303,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1064, 10302, 7187])).
% 1.55/1.72 tff(10304,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10303, 7183])).
% 1.55/1.72 tff(10305,plain,
% 1.55/1.72 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[7489, 10303, 301])).
% 1.55/1.72 tff(10306,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[7528, 10305, 10300, 7481, 226])).
% 1.55/1.72 tff(10307,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10194, 124, 10306, 10304, 10178])).
% 1.55/1.72 tff(10308,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(z))))) | b(s(elem!1), s(z)) | b(elem!1, s(z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.72 tff(10309,plain,
% 1.55/1.72 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10308, 353, 301, 10167, 1808, 1400, 10219, 102, 1545, 57, 10170, 150, 10247, 10147])).
% 1.55/1.72 tff(10310,plain,
% 1.55/1.72 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[223, 10309, 10168])).
% 1.55/1.72 tff(10311,plain,
% 1.55/1.72 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[6297, 124, 10310, 10234])).
% 1.55/1.72 tff(10312,plain,
% 1.55/1.72 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10311, 10232])).
% 1.55/1.72 tff(10313,plain,
% 1.55/1.72 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[921, 10312, 10229])).
% 1.55/1.72 tff(10314,plain,
% 1.55/1.72 (~r(s(s(s(elem!1))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1182, 10310, 301])).
% 1.55/1.72 tff(10315,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[647, 10314, 7122])).
% 1.55/1.72 tff(10316,plain,
% 1.55/1.72 (~r(s(elem!1), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3876, 353, 24])).
% 1.55/1.72 tff(10317,plain,
% 1.55/1.72 (b(s(elem!1), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[534, 10316, 159])).
% 1.55/1.72 tff(10318,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10196, 10310, 10167, 10170, 10147, 353, 301])).
% 1.55/1.72 tff(10319,plain,
% 1.55/1.72 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1826, 10318, 102])).
% 1.55/1.72 tff(10320,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1814, 10319, 5782])).
% 1.55/1.72 tff(10321,plain,
% 1.55/1.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[5751, 10320, 804])).
% 1.55/1.72 tff(10322,plain,
% 1.55/1.72 (b(s(s(s(z))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10315, 10174])).
% 1.55/1.72 tff(10323,plain,
% 1.55/1.72 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[9245, 10322, 10167, 10321])).
% 1.55/1.72 tff(10324,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[1064, 10323, 7187])).
% 1.55/1.72 tff(10325,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10324, 7183])).
% 1.55/1.72 tff(10326,plain,
% 1.55/1.72 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10194, 124, 10325, 10178])).
% 1.55/1.72 tff(10327,plain,
% 1.55/1.72 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[2695, 10326, 10147, 7481, 10317, 3926])).
% 1.55/1.72 tff(10328,plain,
% 1.55/1.72 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[3845, 10327, 10310, 5782, 7187, 10315, 10237, 10247])).
% 1.55/1.72 tff(10329,plain,
% 1.55/1.72 (b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[459, 10328, 421])).
% 1.55/1.72 tff(10330,plain,
% 1.55/1.72 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[929, 10329, 10247, 10313])).
% 1.55/1.72 tff(10331,plain,
% 1.55/1.72 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10330, 10228])).
% 1.55/1.72 tff(10332,plain,
% 1.55/1.72 (r(elem!1, s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[935, 10331, 3761])).
% 1.55/1.72 tff(10333,plain,
% 1.55/1.72 (r(z, s(s(s(s(z)))))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10332, 3763])).
% 1.55/1.72 tff(10334,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10335,plain,
% 1.55/1.72 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.72 inference(rewrite,[status(thm)],[])).
% 1.55/1.72 tff(10336,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))))),
% 1.55/1.72 inference(monotonicity,[status(thm)],[10335])).
% 1.55/1.72 tff(10337,plain,
% 1.55/1.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.72 inference(transitivity,[status(thm)],[10336, 10334])).
% 1.55/1.72 tff(10338,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.72 inference(quant_inst,[status(thm)],[])).
% 1.55/1.72 tff(10339,plain,
% 1.55/1.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))),
% 1.55/1.72 inference(modus_ponens,[status(thm)],[10338, 10337])).
% 1.55/1.72 tff(10340,plain,
% 1.55/1.72 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10339, 124, 10333, 10178])).
% 1.55/1.72 tff(10341,plain,
% 1.55/1.72 ($false),
% 1.55/1.72 inference(unit_resolution,[status(thm)],[10340, 10226])).
% 1.55/1.72 tff(10342,plain,((~(s(elem!1) = s(z))) | (~r(s(s(elem!1)), elem!1)) | b(s(elem!1), s(z)) | b(elem!1, s(z)) | (~r(z, s(z))) | (elem!1 = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10343,plain,
% 1.55/1.73 (~(s(elem!1) = s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10342, 8757, 1808, 1400, 1545, 150, 81, 1817, 24])).
% 1.55/1.73 tff(10344,plain,
% 1.55/1.73 (r(s(elem!1), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[473, 10343, 1808])).
% 1.55/1.73 tff(10345,plain,
% 1.55/1.73 (~r(z, s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3111, 124, 10344, 1545])).
% 1.55/1.73 tff(10346,plain,
% 1.55/1.73 ((z = s(elem!1)) | b(z, s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3115, 51, 10345])).
% 1.55/1.73 tff(10347,plain,
% 1.55/1.73 (b(z, s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10346, 3105])).
% 1.55/1.73 tff(10348,plain,
% 1.55/1.73 (~(elem!1 = z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4830, 10343])).
% 1.55/1.73 tff(10349,plain,
% 1.55/1.73 (~r(elem!1, z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4838, 124, 10163, 1545])).
% 1.55/1.73 tff(10350,plain,
% 1.55/1.73 ((elem!1 = z) | b(elem!1, z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4843, 51, 10349])).
% 1.55/1.73 tff(10351,plain,
% 1.55/1.73 (b(elem!1, z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10350, 10348])).
% 1.55/1.73 tff(10352,plain,
% 1.55/1.73 (~r(s(elem!1), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2626, 124, 10163, 10344])).
% 1.55/1.73 tff(10353,plain,
% 1.55/1.73 (b(s(elem!1), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[408, 10352, 394])).
% 1.55/1.73 tff(10354,plain,
% 1.55/1.73 (~r(elem!1, s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5000, 10344, 10163])).
% 1.55/1.73 tff(10355,plain,
% 1.55/1.73 (b(elem!1, s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[629, 10354, 387])).
% 1.55/1.73 tff(10356,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[8640, 238, 10355, 10353, 10351, 10347])).
% 1.55/1.73 tff(10357,plain,((elem!1 = s(s(elem!1))) | (~r(z, s(z))) | b(s(elem!1), s(z)) | b(elem!1, s(z)) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | r(s(z), s(s(elem!1))) | b(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10358,plain,
% 1.55/1.73 (elem!1 = s(s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10357, 10143, 1808, 5390, 81, 1817, 24, 249])).
% 1.55/1.73 tff(10359,plain,
% 1.55/1.73 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10358])).
% 1.55/1.73 tff(10360,plain,
% 1.55/1.73 ((~r(elem!1, z)) <=> (~r(s(s(elem!1)), z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10359])).
% 1.55/1.73 tff(10361,plain,
% 1.55/1.73 (r(elem!1, s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[363, 10143, 10162])).
% 1.55/1.73 tff(10362,plain,
% 1.55/1.73 (~r(elem!1, z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4838, 124, 10361, 5390])).
% 1.55/1.73 tff(10363,plain,
% 1.55/1.73 (~r(s(s(elem!1)), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10362, 10360])).
% 1.55/1.73 tff(10364,plain,
% 1.55/1.73 (b(s(s(elem!1)), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4030, 51, 92, 10363])).
% 1.55/1.73 tff(10365,plain,
% 1.55/1.73 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10358])).
% 1.55/1.73 tff(10366,plain,
% 1.55/1.73 ((~r(z, elem!1)) <=> (~r(z, s(s(elem!1))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10365])).
% 1.55/1.73 tff(10367,plain,
% 1.55/1.73 (~r(z, elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3130, 124, 10361, 5390])).
% 1.55/1.73 tff(10368,plain,
% 1.55/1.73 (~r(z, s(s(elem!1)))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10367, 10366])).
% 1.55/1.73 tff(10369,plain,
% 1.55/1.73 (b(z, s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2069, 51, 10368, 2064])).
% 1.55/1.73 tff(10370,plain,
% 1.55/1.73 (s(elem!1) = s(s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2097, 10358])).
% 1.55/1.73 tff(10371,plain,
% 1.55/1.73 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10370])).
% 1.55/1.73 tff(10372,plain,
% 1.55/1.73 ((s(elem!1) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10370])).
% 1.55/1.73 tff(10373,plain,
% 1.55/1.73 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10372])).
% 1.55/1.73 tff(10374,plain,
% 1.55/1.73 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10373])).
% 1.55/1.73 tff(10375,plain,
% 1.55/1.73 (~(s(elem!1) = s(z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[94, 10374])).
% 1.55/1.73 tff(10376,plain,
% 1.55/1.73 (r(s(elem!1), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[473, 10375, 1808])).
% 1.55/1.73 tff(10377,plain,
% 1.55/1.73 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10376, 10371])).
% 1.55/1.73 tff(10378,plain,
% 1.55/1.73 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10358])).
% 1.55/1.73 tff(10379,plain,
% 1.55/1.73 (r(s(s(elem!1)), s(z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10361, 10378])).
% 1.55/1.73 tff(10380,plain,
% 1.55/1.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[6918, 124, 10379, 10377])).
% 1.55/1.73 tff(10381,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[223, 10380, 10168])).
% 1.55/1.73 tff(10382,plain,
% 1.55/1.73 (~b(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[8131, 238, 10381, 10369, 10364])).
% 1.55/1.73 tff(10383,plain,
% 1.55/1.73 (~r(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3791, 124, 10377, 5390])).
% 1.55/1.73 tff(10384,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3795, 51, 10383, 3785, 10382])).
% 1.55/1.73 tff(10385,plain,(b(s(s(elem!1)), elem!1) | b(s(elem!1), s(z)) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(z)), s(z))) | r(s(z), s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | b(z, s(z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10386,plain,
% 1.55/1.73 (b(s(s(elem!1)), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10385, 1808, 81, 1817, 24, 2213, 5389, 374])).
% 1.55/1.73 tff(10387,plain,
% 1.55/1.73 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[2073])).
% 1.55/1.73 tff(10388,plain,
% 1.55/1.73 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(elem!1)), elem!1)),
% 1.55/1.73 inference(symmetry,[status(thm)],[10387])).
% 1.55/1.73 tff(10389,plain,
% 1.55/1.73 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10388])).
% 1.55/1.73 tff(10390,plain,
% 1.55/1.73 (~b(s(s(elem!1)), elem!1)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10088, 10389])).
% 1.55/1.73 tff(10391,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[228, 10390])).
% 1.55/1.73 tff(10392,plain,((~(elem!1 = s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10393,plain,
% 1.55/1.73 (~(elem!1 = s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10392, 228])).
% 1.55/1.73 tff(10394,plain,
% 1.55/1.73 (r(s(s(z)), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[135, 22, 2213])).
% 1.55/1.73 tff(10395,plain,
% 1.55/1.73 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4743, 5791, 161])).
% 1.55/1.73 tff(10396,plain,
% 1.55/1.73 (b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[539, 415, 10059])).
% 1.55/1.73 tff(10397,plain,
% 1.55/1.73 (~r(elem!1, s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[8593, 10396, 4840, 1545, 387, 306])).
% 1.55/1.73 tff(10398,plain,
% 1.55/1.73 (b(elem!1, s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[363, 10397, 330])).
% 1.55/1.73 tff(10399,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(10400,plain,
% 1.55/1.73 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(10401,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10400])).
% 1.55/1.73 tff(10402,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[10401, 10399])).
% 1.55/1.73 tff(10403,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(10404,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10403, 10402])).
% 1.55/1.73 tff(10405,plain,
% 1.55/1.73 (~b(elem!1, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10404, 238, 1817, 1137, 10398])).
% 1.55/1.73 tff(10406,plain,
% 1.55/1.73 (r(elem!1, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[763, 10405, 541])).
% 1.55/1.73 tff(10407,plain,
% 1.55/1.73 (~r(elem!1, s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4484, 10406, 192])).
% 1.55/1.73 tff(10408,plain,
% 1.55/1.73 (b(elem!1, s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[606, 10407, 150])).
% 1.55/1.73 tff(10409,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1147, 238, 10408, 228, 1137, 10398])).
% 1.55/1.73 tff(10410,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (elem!1 = s(s(z))) | (~b(s(s(z)), s(z))) | (elem!1 = s(z)) | (elem!1 = z) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | r(s(elem!1), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10411,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10410, 10395, 10394, 1137, 228, 541, 1817, 10162, 10393, 1545, 5791, 4831])).
% 1.55/1.73 tff(10412,plain,((s(elem!1) = s(z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = s(s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(s(elem!1))) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10413,plain,
% 1.55/1.73 (s(elem!1) = s(z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10412, 10386, 57, 10092, 1817, 5390, 102, 2213, 1808])).
% 1.55/1.73 tff(10414,plain,
% 1.55/1.73 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10413])).
% 1.55/1.73 tff(10415,plain,
% 1.55/1.73 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10414])).
% 1.55/1.73 tff(10416,plain,
% 1.55/1.73 (z = elem!1),
% 1.55/1.73 inference(transitivity,[status(thm)],[769, 10415, 154])).
% 1.55/1.73 tff(10417,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10416])).
% 1.55/1.73 tff(10418,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.55/1.73 inference(symmetry,[status(thm)],[10417])).
% 1.55/1.73 tff(10419,plain,
% 1.55/1.73 (elem!1 = z),
% 1.55/1.73 inference(transitivity,[status(thm)],[155, 10414, 26])).
% 1.55/1.73 tff(10420,plain,
% 1.55/1.73 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10419])).
% 1.55/1.73 tff(10421,plain,
% 1.55/1.73 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.55/1.73 inference(transitivity,[status(thm)],[10420, 3716])).
% 1.55/1.73 tff(10422,plain,
% 1.55/1.73 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10421])).
% 1.55/1.73 tff(10423,plain,
% 1.55/1.73 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.55/1.73 inference(transitivity,[status(thm)],[10422, 641])).
% 1.55/1.73 tff(10424,plain,
% 1.55/1.73 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10423])).
% 1.55/1.73 tff(10425,plain,
% 1.55/1.73 (~(s(s(s(elem!1))) = elem!1)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[821, 10424])).
% 1.55/1.73 tff(10426,plain,
% 1.55/1.73 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10413])).
% 1.55/1.73 tff(10427,plain,
% 1.55/1.73 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10426])).
% 1.55/1.73 tff(10428,plain,
% 1.55/1.73 (~b(elem!1, s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5709, 10413, 5389])).
% 1.55/1.73 tff(10429,plain,
% 1.55/1.73 (r(elem!1, s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[363, 10428, 10162])).
% 1.55/1.73 tff(10430,plain,
% 1.55/1.73 (r(elem!1, s(elem!1))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10429, 10427])).
% 1.55/1.73 tff(10431,plain,
% 1.55/1.73 (b(elem!1, s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10246, 10430, 10413, 81])).
% 1.55/1.73 tff(10432,plain,
% 1.55/1.73 (~(elem!1 = s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10392, 10386])).
% 1.55/1.73 tff(10433,plain,
% 1.55/1.73 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[9077, 10413, 1817])).
% 1.55/1.73 tff(10434,plain,
% 1.55/1.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[414, 10432])).
% 1.55/1.73 tff(10435,plain,
% 1.55/1.73 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[420, 10434])).
% 1.55/1.73 tff(10436,plain,
% 1.55/1.73 (~r(s(s(elem!1)), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10342, 10413, 1808, 10428, 5390, 10432, 81, 1817, 24])).
% 1.55/1.73 tff(10437,plain,
% 1.55/1.73 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10419])).
% 1.55/1.73 tff(10438,plain,
% 1.55/1.73 (b(s(s(elem!1)), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10386, 10437])).
% 1.55/1.73 tff(10439,plain,
% 1.55/1.73 (~(s(elem!1) = s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[158, 10432])).
% 1.55/1.73 tff(10440,plain,
% 1.55/1.73 (~r(s(elem!1), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3876, 10413, 24])).
% 1.55/1.73 tff(10441,plain,
% 1.55/1.73 (b(s(elem!1), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[534, 10440, 10439])).
% 1.55/1.73 tff(10442,plain,
% 1.55/1.73 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10419])).
% 1.55/1.73 tff(10443,plain,
% 1.55/1.73 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.55/1.73 inference(symmetry,[status(thm)],[10442])).
% 1.55/1.73 tff(10444,plain,
% 1.55/1.73 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[10443, 9219])).
% 1.55/1.73 tff(10445,plain,
% 1.55/1.73 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10444])).
% 1.55/1.73 tff(10446,plain,
% 1.55/1.73 (~(elem!1 = s(s(s(z))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[1469, 10445])).
% 1.55/1.73 tff(10447,plain,
% 1.55/1.73 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10419])).
% 1.55/1.73 tff(10448,plain,
% 1.55/1.73 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10447])).
% 1.55/1.73 tff(10449,plain,
% 1.55/1.73 (s(s(z)) = s(s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[357, 10413])).
% 1.55/1.73 tff(10450,plain,
% 1.55/1.73 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10449])).
% 1.55/1.73 tff(10451,plain,
% 1.55/1.73 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10450])).
% 1.55/1.73 tff(10452,plain,
% 1.55/1.73 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10451])).
% 1.55/1.73 tff(10453,plain,
% 1.55/1.73 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[10452, 10448])).
% 1.55/1.73 tff(10454,plain,
% 1.55/1.73 ((~r(z, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10453])).
% 1.55/1.73 tff(10455,plain,
% 1.55/1.73 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10419])).
% 1.55/1.73 tff(10456,plain,
% 1.55/1.73 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10455])).
% 1.55/1.73 tff(10457,plain,
% 1.55/1.73 (~r(elem!1, s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1378, 10429, 102])).
% 1.55/1.73 tff(10458,plain,
% 1.55/1.73 (~r(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10457, 10456])).
% 1.55/1.73 tff(10459,plain,
% 1.55/1.73 (~r(elem!1, s(s(s(z))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10458, 10454])).
% 1.55/1.73 tff(10460,plain,
% 1.55/1.73 (b(elem!1, s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5079, 10459, 10446])).
% 1.55/1.73 tff(10461,plain,
% 1.55/1.73 (b(z, s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3795, 51, 10458, 3785])).
% 1.55/1.73 tff(10462,plain,
% 1.55/1.73 (~(elem!1 = s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[386, 10439])).
% 1.55/1.73 tff(10463,plain,
% 1.55/1.73 (~(s(elem!1) = elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[393, 10462])).
% 1.55/1.73 tff(10464,plain,
% 1.55/1.73 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[805])).
% 1.55/1.73 tff(10465,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10464])).
% 1.55/1.73 tff(10466,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(transitivity,[status(thm)],[8157, 10465])).
% 1.55/1.73 tff(10467,plain,
% 1.55/1.73 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10466])).
% 1.55/1.73 tff(10468,plain,
% 1.55/1.73 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10227])).
% 1.55/1.73 tff(10469,plain,
% 1.55/1.73 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[3940, 10468])).
% 1.55/1.73 tff(10470,plain,
% 1.55/1.73 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(z))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[4044])).
% 1.55/1.73 tff(10471,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[4053, 238, 4047, 10211, 3941])).
% 1.55/1.73 tff(10472,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10471, 10470])).
% 1.55/1.73 tff(10473,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1564, 10472])).
% 1.55/1.73 tff(10474,plain,
% 1.55/1.73 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3010, 10473, 3002])).
% 1.55/1.73 tff(10475,plain,
% 1.55/1.73 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10474, 10232])).
% 1.55/1.73 tff(10476,plain,
% 1.55/1.73 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[921, 10475, 777])).
% 1.55/1.73 tff(10477,plain,
% 1.55/1.73 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[929, 10476, 543, 10469])).
% 1.55/1.73 tff(10478,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10477, 10467])).
% 1.55/1.73 tff(10479,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5118, 10478])).
% 1.55/1.73 tff(10480,plain,
% 1.55/1.73 (~r(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2827, 10479, 1545])).
% 1.55/1.73 tff(10481,plain,
% 1.55/1.73 (b(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1524, 10480])).
% 1.55/1.73 tff(10482,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10481, 10175])).
% 1.55/1.73 tff(10483,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10482, 10173])).
% 1.55/1.73 tff(10484,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2974, 51, 10474, 10206])).
% 1.55/1.73 tff(10485,plain,
% 1.55/1.73 (~b(s(s(s(elem!1))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10214, 238, 10484, 10211, 9918])).
% 1.55/1.73 tff(10486,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10485, 10483])).
% 1.55/1.73 tff(10487,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(elem!1) = s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.73 tff(10488,plain,
% 1.55/1.73 (~r(s(s(s(s(z)))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10487, 7244, 9918, 1545, 543, 777, 353, 4047])).
% 1.55/1.73 tff(10489,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1624, 10488])).
% 1.55/1.73 tff(10490,plain,
% 1.55/1.73 (b(s(s(elem!1)), s(z))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10147, 9072])).
% 1.55/1.73 tff(10491,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[7881, 238, 1137, 10490, 10489])).
% 1.55/1.73 tff(10492,plain,
% 1.55/1.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10491, 10470])).
% 1.55/1.73 tff(10493,plain,
% 1.55/1.73 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1564, 10492])).
% 1.55/1.73 tff(10494,plain,
% 1.55/1.73 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3010, 10493, 7244])).
% 1.55/1.73 tff(10495,plain,
% 1.55/1.73 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2974, 51, 10494, 10206])).
% 1.55/1.73 tff(10496,plain,
% 1.55/1.73 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5670, 10489, 1137, 10495])).
% 1.55/1.73 tff(10497,plain,
% 1.55/1.73 (~b(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3886, 10496, 804])).
% 1.55/1.73 tff(10498,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[5118, 10497])).
% 1.55/1.73 tff(10499,plain,
% 1.55/1.73 (~r(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2827, 10498, 1545])).
% 1.55/1.73 tff(10500,plain,
% 1.55/1.73 (b(s(s(s(z))), z)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1524, 10499])).
% 1.55/1.73 tff(10501,plain,
% 1.55/1.73 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[353])).
% 1.55/1.73 tff(10502,plain,
% 1.55/1.73 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10501])).
% 1.55/1.73 tff(10503,plain,
% 1.55/1.73 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.73 inference(transitivity,[status(thm)],[4068, 10502])).
% 1.55/1.73 tff(10504,plain,
% 1.55/1.73 (r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10498, 10503])).
% 1.55/1.73 tff(10505,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10500, 10175])).
% 1.55/1.73 tff(10506,plain,
% 1.55/1.73 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3845, 10505, 210, 5782, 7187, 10504, 590, 543])).
% 1.55/1.73 tff(10507,plain,
% 1.55/1.73 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[2695, 10506, 10147, 7481, 288, 3926])).
% 1.55/1.73 tff(10508,plain,
% 1.55/1.73 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3867, 10507, 10183])).
% 1.55/1.73 tff(10509,plain,
% 1.55/1.73 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1101, 10508])).
% 1.55/1.73 tff(10510,plain,
% 1.55/1.73 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[9245, 10509, 10176, 10500])).
% 1.55/1.73 tff(10511,plain,
% 1.55/1.73 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1064, 10510, 7187])).
% 1.55/1.73 tff(10512,plain,
% 1.55/1.73 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10511, 7183])).
% 1.55/1.73 tff(10513,plain,
% 1.55/1.73 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.55/1.73 inference(monotonicity,[status(thm)],[815])).
% 1.55/1.73 tff(10514,plain,
% 1.55/1.73 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.55/1.73 inference(symmetry,[status(thm)],[10513])).
% 1.55/1.73 tff(10515,plain,
% 1.55/1.73 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.55/1.73 inference(transitivity,[status(thm)],[7204, 10514])).
% 1.55/1.73 tff(10516,plain,
% 1.55/1.73 (b(s(elem!1), s(s(z))) <=> b(s(z), s(s(z)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[353])).
% 1.55/1.73 tff(10517,plain,
% 1.55/1.73 (b(s(z), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10516])).
% 1.55/1.73 tff(10518,plain,
% 1.55/1.73 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[804])).
% 1.55/1.73 tff(10519,plain,
% 1.55/1.73 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10518])).
% 1.55/1.73 tff(10520,plain,
% 1.55/1.73 (b(s(z), s(s(elem!1))) <=> b(s(elem!1), s(s(z)))),
% 1.55/1.73 inference(transitivity,[status(thm)],[10519, 10517])).
% 1.55/1.73 tff(10521,plain,
% 1.55/1.73 (b(s(elem!1), s(s(z)))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[1137, 10520])).
% 1.55/1.73 tff(10522,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[807])).
% 1.55/1.73 tff(10523,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(symmetry,[status(thm)],[10522])).
% 1.55/1.73 tff(10524,plain,
% 1.55/1.73 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10222, 238, 1137, 10490, 10489])).
% 1.55/1.73 tff(10525,plain,
% 1.55/1.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10524, 10146])).
% 1.55/1.73 tff(10526,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1604, 10525])).
% 1.55/1.73 tff(10527,plain,
% 1.55/1.73 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10526, 10523])).
% 1.55/1.73 tff(10528,plain,
% 1.55/1.73 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[3763, 7178])).
% 1.55/1.73 tff(10529,plain,
% 1.55/1.73 ((~b(z, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[3756])).
% 1.55/1.73 tff(10530,plain,
% 1.55/1.73 (b(s(s(s(elem!1))), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10505, 10173])).
% 1.55/1.73 tff(10531,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(10532,plain,
% 1.55/1.73 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.73 inference(rewrite,[status(thm)],[])).
% 1.55/1.73 tff(10533,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.55/1.73 inference(monotonicity,[status(thm)],[10532])).
% 1.55/1.73 tff(10534,plain,
% 1.55/1.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.73 inference(transitivity,[status(thm)],[10533, 10531])).
% 1.55/1.73 tff(10535,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.73 inference(quant_inst,[status(thm)],[])).
% 1.55/1.73 tff(10536,plain,
% 1.55/1.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10535, 10534])).
% 1.55/1.73 tff(10537,plain,
% 1.55/1.73 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10536, 238, 10495, 9918])).
% 1.55/1.73 tff(10538,plain,
% 1.55/1.73 (~b(z, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[10537, 10530])).
% 1.55/1.73 tff(10539,plain,
% 1.55/1.73 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10538, 10529])).
% 1.55/1.73 tff(10540,plain,
% 1.55/1.73 (r(elem!1, s(s(s(s(z)))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[935, 10539, 3761])).
% 1.55/1.73 tff(10541,plain,
% 1.55/1.73 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10540, 10528])).
% 1.55/1.73 tff(10542,plain,
% 1.55/1.73 (~r(elem!1, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[948, 10541, 10527])).
% 1.55/1.73 tff(10543,plain,
% 1.55/1.73 (b(elem!1, s(s(z)))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[763, 10542, 541])).
% 1.55/1.73 tff(10544,plain,
% 1.55/1.73 (~b(s(elem!1), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[3027, 10543, 1817, 10521])).
% 1.55/1.73 tff(10545,plain,
% 1.55/1.73 (r(s(elem!1), elem!1)),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[408, 10544, 632])).
% 1.55/1.73 tff(10546,plain,
% 1.55/1.73 (r(s(z), z)),
% 1.55/1.73 inference(modus_ponens,[status(thm)],[10545, 10515])).
% 1.55/1.73 tff(10547,plain,
% 1.55/1.73 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[9262, 124, 10546, 10512])).
% 1.55/1.73 tff(10548,plain,
% 1.55/1.73 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1781, 10547])).
% 1.55/1.73 tff(10549,plain,
% 1.55/1.73 (~r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[9254, 124, 10546, 10512])).
% 1.55/1.73 tff(10550,plain,
% 1.55/1.73 (b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1709, 10549])).
% 1.55/1.73 tff(10551,plain,
% 1.55/1.73 ($false),
% 1.55/1.73 inference(unit_resolution,[status(thm)],[1930, 10550, 10548, 1817, 10489])).
% 1.55/1.73 tff(10552,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~(s(elem!1) = s(z))) | (s(elem!1) = elem!1) | (elem!1 = s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10553,plain,
% 1.55/1.74 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10552, 10413, 1817, 10463, 10092, 10461, 10460, 10441, 10430, 10431, 5390, 57, 10229, 10438])).
% 1.55/1.74 tff(10554,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[223, 10553, 10168])).
% 1.55/1.74 tff(10555,plain,
% 1.55/1.74 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[815])).
% 1.55/1.74 tff(10556,plain,
% 1.55/1.74 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10555])).
% 1.55/1.74 tff(10557,plain,
% 1.55/1.74 (r(z, s(z))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[1370, 10556])).
% 1.55/1.74 tff(10558,plain,
% 1.55/1.74 (r(elem!1, s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[615, 226, 150, 250, 543])).
% 1.55/1.74 tff(10559,plain,
% 1.55/1.74 (r(z, s(s(elem!1)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10558, 7133])).
% 1.55/1.74 tff(10560,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[3927])).
% 1.55/1.74 tff(10561,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10560])).
% 1.55/1.74 tff(10562,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[3927])).
% 1.55/1.74 tff(10563,plain,
% 1.55/1.74 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10562])).
% 1.55/1.74 tff(10564,plain,
% 1.55/1.74 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[3927])).
% 1.55/1.74 tff(10565,plain,
% 1.55/1.74 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10564])).
% 1.55/1.74 tff(10566,plain,
% 1.55/1.74 (b(s(s(elem!1)), s(z))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[289, 10565])).
% 1.55/1.74 tff(10567,plain,
% 1.55/1.74 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[3909, 238, 1137, 226])).
% 1.55/1.74 tff(10568,plain,
% 1.55/1.74 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10567, 10566])).
% 1.55/1.74 tff(10569,plain,
% 1.55/1.74 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10568, 10563])).
% 1.55/1.74 tff(10570,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[459, 10569, 453])).
% 1.55/1.74 tff(10571,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10570, 10561])).
% 1.55/1.74 tff(10572,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10573,plain,
% 1.55/1.74 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10574,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10573])).
% 1.55/1.74 tff(10575,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[10574, 10572])).
% 1.55/1.74 tff(10576,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10577,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10576, 10575])).
% 1.55/1.74 tff(10578,plain,
% 1.55/1.74 ((~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10577, 124, 10571])).
% 1.55/1.74 tff(10579,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10578, 10559, 10557, 4263])).
% 1.55/1.74 tff(10580,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | r(s(s(elem!1)), elem!1) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10581,plain,
% 1.55/1.74 (~r(s(s(s(elem!1))), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10580, 10554, 10413, 10436, 10435, 10433, 10429, 10432, 10431, 57])).
% 1.55/1.74 tff(10582,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[647, 10581, 10425])).
% 1.55/1.74 tff(10583,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), z)),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10582, 10418])).
% 1.55/1.74 tff(10584,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10585,plain,
% 1.55/1.74 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10586,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10585])).
% 1.55/1.74 tff(10587,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[10586, 10584])).
% 1.55/1.74 tff(10588,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10589,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1)))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10588, 10587])).
% 1.55/1.74 tff(10590,plain,
% 1.55/1.74 (~b(s(s(s(elem!1))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10589, 238, 10554, 10438, 10461])).
% 1.55/1.74 tff(10591,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10590, 10583])).
% 1.55/1.74 tff(10592,plain,(b(s(elem!1), s(z)) | (~b(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(elem!1))) | b(z, s(z)) | b(s(s(z)), s(s(elem!1))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10593,plain,
% 1.55/1.74 (b(s(elem!1), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10592, 5389, 81, 24, 1817, 2213, 374])).
% 1.55/1.74 tff(10594,plain,
% 1.55/1.74 (~r(s(s(z)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[9609, 159, 1137, 1152, 192])).
% 1.55/1.74 tff(10595,plain,
% 1.55/1.74 (~b(s(s(z)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[9588, 238, 1817, 1137, 1152])).
% 1.55/1.74 tff(10596,plain,
% 1.55/1.74 ((s(s(z)) = s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1260, 51, 10595])).
% 1.55/1.74 tff(10597,plain,
% 1.55/1.74 (s(s(z)) = s(elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10596, 10594])).
% 1.55/1.74 tff(10598,plain,
% 1.55/1.74 (s(s(s(z))) = s(s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10597])).
% 1.55/1.74 tff(10599,plain,
% 1.55/1.74 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10597, 10598])).
% 1.55/1.74 tff(10600,plain,
% 1.55/1.74 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10599])).
% 1.55/1.74 tff(10601,plain,
% 1.55/1.74 (r(s(s(z)), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10597])).
% 1.55/1.74 tff(10602,plain,
% 1.55/1.74 (r(s(elem!1), s(s(elem!1)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[192, 10601])).
% 1.55/1.74 tff(10603,plain,
% 1.55/1.74 (r(s(s(z)), s(s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10602, 10600])).
% 1.55/1.74 tff(10604,plain,
% 1.55/1.74 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10598])).
% 1.55/1.74 tff(10605,plain,
% 1.55/1.74 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10604])).
% 1.55/1.74 tff(10606,plain,
% 1.55/1.74 (b(s(z), s(s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[1137, 10605])).
% 1.55/1.74 tff(10607,plain,
% 1.55/1.74 (s(elem!1) = s(s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1249, 10597])).
% 1.55/1.74 tff(10608,plain,
% 1.55/1.74 (elem!1 = s(z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[379, 10607])).
% 1.55/1.74 tff(10609,plain,
% 1.55/1.74 (r(elem!1, s(s(s(elem!1))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1368, 10608, 81])).
% 1.55/1.74 tff(10610,plain,
% 1.55/1.74 (~r(elem!1, s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1378, 10609, 102])).
% 1.55/1.74 tff(10611,plain,
% 1.55/1.74 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1149, 370, 1137, 590, 150])).
% 1.55/1.74 tff(10612,plain,
% 1.55/1.74 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[323, 10611, 272])).
% 1.55/1.74 tff(10613,plain,
% 1.55/1.74 (~b(s(s(z)), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[8902, 10612, 1137, 1817])).
% 1.55/1.74 tff(10614,plain,
% 1.55/1.74 (r(s(s(z)), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[135, 10613, 114])).
% 1.55/1.74 tff(10615,plain,
% 1.55/1.74 (~b(elem!1, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10404, 238, 1817, 1137, 370])).
% 1.55/1.74 tff(10616,plain,
% 1.55/1.74 (r(elem!1, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[763, 10615, 3255])).
% 1.55/1.74 tff(10617,plain,
% 1.55/1.74 (~r(elem!1, s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[4484, 10616, 10614])).
% 1.55/1.74 tff(10618,plain,
% 1.55/1.74 (b(elem!1, s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[606, 10617, 150])).
% 1.55/1.74 tff(10619,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[4464, 238, 10618, 10612, 1137, 370])).
% 1.55/1.74 tff(10620,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10621,plain,
% 1.55/1.74 (~b(elem!1, s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10620, 590, 150, 1817, 374, 114, 1137])).
% 1.55/1.74 tff(10622,plain,
% 1.55/1.74 (elem!1 = s(z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[363, 10621, 359])).
% 1.55/1.74 tff(10623,plain,
% 1.55/1.74 (s(elem!1) = s(s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[280, 10622])).
% 1.55/1.74 tff(10624,plain,
% 1.55/1.74 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10623])).
% 1.55/1.74 tff(10625,plain,
% 1.55/1.74 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10622])).
% 1.55/1.74 tff(10626,plain,
% 1.55/1.74 (r(s(z), s(elem!1))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[590, 10625])).
% 1.55/1.74 tff(10627,plain,
% 1.55/1.74 (r(s(z), s(s(z)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10626, 10624])).
% 1.55/1.74 tff(10628,plain,
% 1.55/1.74 (s(s(elem!1)) = s(s(s(z)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10623])).
% 1.55/1.74 tff(10629,plain,
% 1.55/1.74 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10628])).
% 1.55/1.74 tff(10630,plain,
% 1.55/1.74 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10629])).
% 1.55/1.74 tff(10631,plain,
% 1.55/1.74 (r(s(z), s(s(s(s(z)))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[102, 10630])).
% 1.55/1.74 tff(10632,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10633,plain,
% 1.55/1.74 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10634,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10633])).
% 1.55/1.74 tff(10635,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[10634, 10632])).
% 1.55/1.74 tff(10636,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10637,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10636, 10635])).
% 1.55/1.74 tff(10638,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10637, 124, 1650, 4560, 1545, 1575])).
% 1.55/1.74 tff(10639,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10640,plain,
% 1.55/1.74 (~r(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10639, 10631, 10627, 1545])).
% 1.55/1.74 tff(10641,plain,
% 1.55/1.74 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1511, 51, 10640])).
% 1.55/1.74 tff(10642,plain,
% 1.55/1.74 (b(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10641, 1450])).
% 1.55/1.74 tff(10643,plain,
% 1.55/1.74 (r(elem!1, s(s(s(elem!1))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1368, 10622, 81])).
% 1.55/1.74 tff(10644,plain,
% 1.55/1.74 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[3753, 10643, 590])).
% 1.55/1.74 tff(10645,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[459, 10644, 421])).
% 1.55/1.74 tff(10646,plain,
% 1.55/1.74 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1632, 10645, 10623])).
% 1.55/1.74 tff(10647,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10648,plain,
% 1.55/1.74 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10649,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10648])).
% 1.55/1.74 tff(10650,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[10649, 10647])).
% 1.55/1.74 tff(10651,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10652,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 1.55/1.74 tff(10653,plain,
% 1.55/1.74 (~b(z, s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10652, 238, 1817, 10646, 10642])).
% 1.55/1.74 tff(10654,plain,
% 1.55/1.74 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1487, 51, 10653])).
% 1.55/1.74 tff(10655,plain,
% 1.55/1.74 (r(z, s(s(s(s(z)))))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10654, 1454])).
% 1.55/1.74 tff(10656,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10657,plain,
% 1.55/1.74 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10658,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10657])).
% 1.55/1.74 tff(10659,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[10658, 10656])).
% 1.55/1.74 tff(10660,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10661,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10660, 10659])).
% 1.55/1.74 tff(10662,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10661, 124, 10631, 10655, 1545])).
% 1.55/1.74 tff(10663,plain,((~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | r(elem!1, s(z)) | (elem!1 = s(s(elem!1))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10664,plain,
% 1.55/1.74 (~r(elem!1, s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10663, 10610, 1817, 81, 1137, 1545, 374, 150, 114])).
% 1.55/1.74 tff(10665,plain,
% 1.55/1.74 (b(elem!1, s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[629, 10664, 387])).
% 1.55/1.74 tff(10666,plain,
% 1.55/1.74 (~b(elem!1, s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1160, 10665, 1137, 1152])).
% 1.55/1.74 tff(10667,plain,
% 1.55/1.74 (elem!1 = s(z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[363, 359, 1400])).
% 1.55/1.74 tff(10668,plain,
% 1.55/1.74 (s(elem!1) = s(s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[280, 10667])).
% 1.55/1.74 tff(10669,plain,
% 1.55/1.74 (s(s(elem!1)) = s(s(s(z)))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10668])).
% 1.55/1.74 tff(10670,plain,
% 1.55/1.74 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10669])).
% 1.55/1.74 tff(10671,plain,
% 1.55/1.74 (b(s(z), s(s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[1137, 10670])).
% 1.55/1.74 tff(10672,plain,
% 1.55/1.74 (~r(elem!1, s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10663, 359, 1817, 81, 1137, 1545, 374, 150, 114])).
% 1.55/1.74 tff(10673,plain,
% 1.55/1.74 (b(elem!1, s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[629, 10672, 387])).
% 1.55/1.74 tff(10674,plain,
% 1.55/1.74 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[276])).
% 1.55/1.74 tff(10675,plain,
% 1.55/1.74 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.74 inference(symmetry,[status(thm)],[10674])).
% 1.55/1.74 tff(10676,plain,
% 1.55/1.74 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[10675])).
% 1.55/1.74 tff(10677,plain,
% 1.55/1.74 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[728, 10676])).
% 1.55/1.74 tff(10678,plain,
% 1.55/1.74 (s(s(z)) = s(elem!1)),
% 1.55/1.74 inference(symmetry,[status(thm)],[281])).
% 1.55/1.74 tff(10679,plain,
% 1.55/1.74 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[2701, 10678])).
% 1.55/1.74 tff(10680,plain,
% 1.55/1.74 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10679])).
% 1.55/1.74 tff(10681,plain,
% 1.55/1.74 (b(s(elem!1), s(z))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[2858, 281, 1817])).
% 1.55/1.74 tff(10682,plain,
% 1.55/1.74 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[276])).
% 1.55/1.74 tff(10683,plain,
% 1.55/1.74 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 1.55/1.74 inference(symmetry,[status(thm)],[10682])).
% 1.55/1.74 tff(10684,plain,
% 1.55/1.74 (b(s(elem!1), elem!1)),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[1152, 10683])).
% 1.55/1.74 tff(10685,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.55/1.74 tff(10686,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10685, 10684])).
% 1.55/1.74 tff(10687,plain,((~(elem!1 = s(z))) | b(s(elem!1), elem!1) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10688,plain,
% 1.55/1.74 (b(s(elem!1), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10687, 10681, 276])).
% 1.55/1.74 tff(10689,plain,
% 1.55/1.74 (~r(s(z), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[218, 210, 161])).
% 1.55/1.74 tff(10690,plain,
% 1.55/1.74 (b(s(z), s(s(elem!1)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[56, 10689])).
% 1.55/1.74 tff(10691,plain,
% 1.55/1.74 (b(elem!1, s(s(elem!1)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10690, 3290])).
% 1.55/1.74 tff(10692,plain,
% 1.55/1.74 (~b(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[5551, 10691, 631, 10688])).
% 1.55/1.74 tff(10693,plain,
% 1.55/1.74 (r(s(s(elem!1)), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[323, 10692, 272])).
% 1.55/1.74 tff(10694,plain,
% 1.55/1.74 (r(s(s(s(z))), s(s(z)))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10693, 10680])).
% 1.55/1.74 tff(10695,plain,
% 1.55/1.74 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1397, 10693, 210])).
% 1.55/1.74 tff(10696,plain,
% 1.55/1.74 (b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[459, 10695, 421])).
% 1.55/1.74 tff(10697,plain,
% 1.55/1.74 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1632, 10696, 281])).
% 1.55/1.74 tff(10698,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.55/1.74 inference(transitivity,[status(thm)],[3399, 3401])).
% 1.55/1.74 tff(10699,plain,
% 1.55/1.74 (~b(s(s(s(elem!1))), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[786, 10696, 631, 10688])).
% 1.55/1.74 tff(10700,plain,
% 1.55/1.74 (r(s(s(s(elem!1))), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[647, 10699, 2706])).
% 1.55/1.74 tff(10701,plain,
% 1.55/1.74 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10700, 10698])).
% 1.55/1.74 tff(10702,plain,
% 1.55/1.74 (~r(s(s(s(s(z)))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1938, 124, 10701, 1545])).
% 1.55/1.74 tff(10703,plain,
% 1.55/1.74 (b(s(s(s(s(z)))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1499, 51, 726, 10702])).
% 1.55/1.74 tff(10704,plain,
% 1.55/1.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.74 inference(rewrite,[status(thm)],[])).
% 1.55/1.74 tff(10705,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.74 inference(quant_inst,[status(thm)],[])).
% 1.55/1.74 tff(10706,plain,
% 1.55/1.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10705, 10704])).
% 1.55/1.74 tff(10707,plain,
% 1.55/1.74 ($false),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10706, 238, 1817, 1587, 4200, 7558])).
% 1.55/1.74 tff(10708,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.74 tff(10709,plain,
% 1.55/1.74 (~b(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10708, 10703, 10697, 1817])).
% 1.55/1.74 tff(10710,plain,
% 1.55/1.74 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1511, 51, 10709])).
% 1.55/1.74 tff(10711,plain,
% 1.55/1.74 (r(z, s(s(z)))),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[10710, 1450])).
% 1.55/1.74 tff(10712,plain,
% 1.55/1.74 (~r(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1531, 124, 10711, 10694])).
% 1.55/1.74 tff(10713,plain,
% 1.55/1.74 (b(s(s(s(z))), z)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1524, 10712])).
% 1.55/1.74 tff(10714,plain,
% 1.55/1.74 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.55/1.74 inference(monotonicity,[status(thm)],[276])).
% 1.55/1.74 tff(10715,plain,
% 1.55/1.74 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.55/1.74 inference(symmetry,[status(thm)],[10714])).
% 1.55/1.74 tff(10716,plain,
% 1.55/1.74 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.55/1.74 inference(transitivity,[status(thm)],[3287, 10715])).
% 1.55/1.74 tff(10717,plain,
% 1.55/1.74 (b(elem!1, s(s(s(z))))),
% 1.55/1.74 inference(modus_ponens,[status(thm)],[10690, 10716])).
% 1.55/1.74 tff(10718,plain,
% 1.55/1.74 (~r(s(s(elem!1)), elem!1)),
% 1.55/1.74 inference(unit_resolution,[status(thm)],[1182, 10700, 210])).
% 1.55/1.75 tff(10719,plain,
% 1.55/1.75 (b(s(s(elem!1)), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[255, 10718, 167])).
% 1.55/1.75 tff(10720,plain,
% 1.55/1.75 (~b(s(s(z)), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3161, 10719, 10690, 1817])).
% 1.55/1.75 tff(10721,plain,
% 1.55/1.75 (r(s(s(z)), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[135, 10720, 114])).
% 1.55/1.75 tff(10722,plain,
% 1.55/1.75 (r(s(s(z)), s(s(s(z))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10721, 3616])).
% 1.55/1.75 tff(10723,plain,
% 1.55/1.75 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1203, 10696, 210, 150, 631, 2706])).
% 1.55/1.75 tff(10724,plain,
% 1.55/1.75 (b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[539, 10723, 415])).
% 1.55/1.75 tff(10725,plain,
% 1.55/1.75 (b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10724, 3332])).
% 1.55/1.75 tff(10726,plain,
% 1.55/1.75 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[1648, 375])).
% 1.55/1.75 tff(10727,plain,
% 1.55/1.75 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10726])).
% 1.55/1.75 tff(10728,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[4437, 1906, 1587, 1501])).
% 1.55/1.75 tff(10729,plain,
% 1.55/1.75 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1904, 10728])).
% 1.55/1.75 tff(10730,plain,
% 1.55/1.75 (~r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1660, 10729, 1650])).
% 1.55/1.75 tff(10731,plain,
% 1.55/1.75 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3552, 10730, 375, 3543])).
% 1.55/1.75 tff(10732,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10733,plain,
% 1.55/1.75 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10734,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10733])).
% 1.55/1.75 tff(10735,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10734, 10732])).
% 1.55/1.75 tff(10736,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(10737,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10736, 10735])).
% 1.55/1.75 tff(10738,plain,
% 1.55/1.75 ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10737, 238])).
% 1.55/1.75 tff(10739,plain,
% 1.55/1.75 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10738, 10731, 507, 631])).
% 1.55/1.75 tff(10740,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10739, 10727])).
% 1.55/1.75 tff(10741,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1906, 10740])).
% 1.55/1.75 tff(10742,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~(s(elem!1) = s(s(z)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(10743,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10742, 281, 10688, 631, 3390, 4421, 10697, 10725])).
% 1.55/1.75 tff(10744,plain,
% 1.55/1.75 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1738, 10743])).
% 1.55/1.75 tff(10745,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[4329, 10744, 10722])).
% 1.55/1.75 tff(10746,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1101, 10745])).
% 1.55/1.75 tff(10747,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[9245, 10746, 10717, 10713])).
% 1.55/1.75 tff(10748,plain,
% 1.55/1.75 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1064, 10747, 10677])).
% 1.55/1.75 tff(10749,plain,
% 1.55/1.75 (r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[9812, 10748, 276])).
% 1.55/1.75 tff(10750,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3947, 124, 10749, 1545])).
% 1.55/1.75 tff(10751,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 10750])).
% 1.55/1.75 tff(10752,plain,
% 1.55/1.75 (~r(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1571, 124, 10701, 1545])).
% 1.55/1.75 tff(10753,plain,
% 1.55/1.75 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1487, 51, 10752])).
% 1.55/1.75 tff(10754,plain,
% 1.55/1.75 (b(z, s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10753, 1454])).
% 1.55/1.75 tff(10755,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3963, 124, 10749, 10701])).
% 1.55/1.75 tff(10756,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1904, 10755])).
% 1.55/1.75 tff(10757,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10758,plain,
% 1.55/1.75 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10759,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10758])).
% 1.55/1.75 tff(10760,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10759, 10757])).
% 1.55/1.75 tff(10761,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(10762,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10761, 10760])).
% 1.55/1.75 tff(10763,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10762, 238, 10697, 10756, 10754, 10751])).
% 1.55/1.75 tff(10764,plain,((~(elem!1 = s(z))) | (~r(z, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(10765,plain,
% 1.55/1.75 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10764, 10673, 1817, 1545, 114, 10667, 150, 102])).
% 1.55/1.75 tff(10766,plain,
% 1.55/1.75 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[223, 10765, 7709])).
% 1.55/1.75 tff(10767,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[2405, 10766, 10668])).
% 1.55/1.75 tff(10768,plain,
% 1.55/1.75 (~b(s(s(s(z))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[7971, 10667, 249])).
% 1.55/1.75 tff(10769,plain,
% 1.55/1.75 (r(s(s(s(z))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[5118, 10768])).
% 1.55/1.75 tff(10770,plain,
% 1.55/1.75 (~r(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[2827, 10769, 1545])).
% 1.55/1.75 tff(10771,plain,
% 1.55/1.75 (b(s(s(s(z))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1524, 10770])).
% 1.55/1.75 tff(10772,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10773,plain,
% 1.55/1.75 (((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10774,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10773])).
% 1.55/1.75 tff(10775,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10774, 10772])).
% 1.55/1.75 tff(10776,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(10777,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10776, 10775])).
% 1.55/1.75 tff(10778,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10777, 238, 10771, 10767, 10671])).
% 1.55/1.75 tff(10779,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1624, 10778])).
% 1.55/1.75 tff(10780,plain,
% 1.55/1.75 (~r(s(s(s(s(z)))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1938, 124, 10779, 1545])).
% 1.55/1.75 tff(10781,plain,
% 1.55/1.75 (~r(z, s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[2816, 124, 10769, 1545])).
% 1.55/1.75 tff(10782,plain,
% 1.55/1.75 (b(z, s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1475, 10781])).
% 1.55/1.75 tff(10783,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10784,plain,
% 1.55/1.75 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10785,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10784])).
% 1.55/1.75 tff(10786,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10785, 10783])).
% 1.55/1.75 tff(10787,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(10788,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10787, 10786])).
% 1.55/1.75 tff(10789,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10788, 238, 10771, 10767, 10782])).
% 1.55/1.75 tff(10790,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1499, 51, 726, 10789, 10780])).
% 1.55/1.75 tff(10791,plain,(r(elem!1, s(z)) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(10792,plain,
% 1.55/1.75 (b(s(s(elem!1)), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10791, 10666, 1137, 1817, 114, 150, 10610, 81, 374, 1545])).
% 1.55/1.75 tff(10793,plain,
% 1.55/1.75 (b(s(s(s(z))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1428, 10792, 10608])).
% 1.55/1.75 tff(10794,plain,
% 1.55/1.75 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10598])).
% 1.55/1.75 tff(10795,plain,
% 1.55/1.75 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.55/1.75 inference(symmetry,[status(thm)],[10794])).
% 1.55/1.75 tff(10796,plain,
% 1.55/1.75 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10795])).
% 1.55/1.75 tff(10797,plain,
% 1.55/1.75 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10796, 1008])).
% 1.55/1.75 tff(10798,plain,
% 1.55/1.75 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.75 inference(symmetry,[status(thm)],[10797])).
% 1.55/1.75 tff(10799,plain,
% 1.55/1.75 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10798])).
% 1.55/1.75 tff(10800,plain,
% 1.55/1.75 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[2782, 10799])).
% 1.55/1.75 tff(10801,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10794])).
% 1.55/1.75 tff(10802,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10608])).
% 1.55/1.75 tff(10803,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10802, 10801])).
% 1.55/1.75 tff(10804,plain,
% 1.55/1.75 ((elem!1 = s(s(s(s(z))))) <=> (s(z) = s(s(s(s(z)))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10608])).
% 1.55/1.75 tff(10805,plain,
% 1.55/1.75 ((s(z) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.55/1.75 inference(symmetry,[status(thm)],[10804])).
% 1.55/1.75 tff(10806,plain,
% 1.55/1.75 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.55/1.75 inference(transitivity,[status(thm)],[10805, 789])).
% 1.55/1.75 tff(10807,plain,
% 1.55/1.75 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10806])).
% 1.55/1.75 tff(10808,plain,
% 1.55/1.75 (~(s(s(s(s(z)))) = elem!1)),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[3140, 10807])).
% 1.55/1.75 tff(10809,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10608])).
% 1.55/1.75 tff(10810,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.55/1.75 inference(symmetry,[status(thm)],[10809])).
% 1.55/1.75 tff(10811,plain,
% 1.55/1.75 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10794])).
% 1.55/1.75 tff(10812,plain,
% 1.55/1.75 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.55/1.75 inference(symmetry,[status(thm)],[10811])).
% 1.55/1.75 tff(10813,plain,
% 1.55/1.75 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.55/1.75 inference(transitivity,[status(thm)],[10812, 10810])).
% 1.55/1.75 tff(10814,plain,
% 1.55/1.75 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10813])).
% 1.55/1.75 tff(10815,plain,
% 1.55/1.75 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10608])).
% 1.55/1.75 tff(10816,plain,
% 1.55/1.75 (b(s(s(elem!1)), s(z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10792, 10815])).
% 1.55/1.75 tff(10817,plain,
% 1.55/1.75 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10764, 10665, 1817, 1545, 114, 10608, 150, 102])).
% 1.55/1.75 tff(10818,plain,
% 1.55/1.75 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[223, 10817, 7709])).
% 1.55/1.75 tff(10819,plain,
% 1.55/1.75 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3909, 238, 1137, 10818, 10816])).
% 1.55/1.75 tff(10820,plain,
% 1.55/1.75 (~b(s(s(s(s(z)))), elem!1)),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10819, 10814])).
% 1.55/1.75 tff(10821,plain,
% 1.55/1.75 (r(s(s(s(s(z)))), elem!1)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[2131, 10820, 10808])).
% 1.55/1.75 tff(10822,plain,
% 1.55/1.75 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10821, 10803])).
% 1.55/1.75 tff(10823,plain,
% 1.55/1.75 (~r(z, s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3791, 124, 10822, 1545])).
% 1.55/1.75 tff(10824,plain,
% 1.55/1.75 (b(z, s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[3795, 51, 10823, 3785])).
% 1.55/1.75 tff(10825,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1826, 1711, 161])).
% 1.55/1.75 tff(10826,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1814, 10825, 1380])).
% 1.55/1.75 tff(10827,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10828,plain,
% 1.55/1.75 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(rewrite,[status(thm)],[])).
% 1.55/1.75 tff(10829,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[10828])).
% 1.55/1.75 tff(10830,plain,
% 1.55/1.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(transitivity,[status(thm)],[10829, 10827])).
% 1.55/1.75 tff(10831,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.55/1.75 inference(quant_inst,[status(thm)],[])).
% 1.55/1.75 tff(10832,plain,
% 1.55/1.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.55/1.75 inference(modus_ponens,[status(thm)],[10831, 10830])).
% 1.55/1.75 tff(10833,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), z)),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10832, 238, 226, 10826, 9918])).
% 1.55/1.75 tff(10834,plain,
% 1.55/1.75 ($false),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 3948, 10833])).
% 1.55/1.75 tff(10835,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.75 tff(10836,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[10835, 10818, 1545, 10824, 10800, 102])).
% 1.55/1.75 tff(10837,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1781, 10836])).
% 1.55/1.75 tff(10838,plain,
% 1.55/1.75 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[5745, 10837, 10793, 10606])).
% 1.55/1.75 tff(10839,plain,
% 1.55/1.75 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1101, 10838])).
% 1.55/1.75 tff(10840,plain,
% 1.55/1.75 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[4329, 10839, 10603])).
% 1.55/1.75 tff(10841,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.75 inference(unit_resolution,[status(thm)],[1738, 10840])).
% 1.55/1.75 tff(10842,plain,
% 1.55/1.75 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.55/1.75 inference(monotonicity,[status(thm)],[1246])).
% 1.55/1.76 tff(10843,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.76 inference(symmetry,[status(thm)],[10842])).
% 1.55/1.76 tff(10844,plain,
% 1.55/1.76 ((~b(s(s(s(s(s(z))))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10843])).
% 1.55/1.76 tff(10845,plain,
% 1.55/1.76 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[4349, 10844])).
% 1.55/1.76 tff(10846,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1906, 10845])).
% 1.55/1.76 tff(10847,plain,(b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~(s(s(z)) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(10848,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10847, 10841, 10597])).
% 1.55/1.76 tff(10849,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10850,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(10851,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10850, 10849])).
% 1.55/1.76 tff(10852,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10851, 238, 1137, 1152, 10837, 10848])).
% 1.55/1.76 tff(10853,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(10854,plain,
% 1.55/1.76 (elem!1 = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10853, 8907, 1152, 1545, 1137, 1817, 114, 81, 374])).
% 1.55/1.76 tff(10855,plain,
% 1.55/1.76 (s(elem!1) = s(s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2097, 10854])).
% 1.55/1.76 tff(10856,plain,
% 1.55/1.76 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10855])).
% 1.55/1.76 tff(10857,plain,
% 1.55/1.76 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.55/1.76 inference(symmetry,[status(thm)],[10856])).
% 1.55/1.76 tff(10858,plain,
% 1.55/1.76 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10857])).
% 1.55/1.76 tff(10859,plain,
% 1.55/1.76 (~(s(elem!1) = s(s(elem!1)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[7709, 10858])).
% 1.55/1.76 tff(10860,plain,
% 1.55/1.76 (b(s(z), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3083, 10854, 1137])).
% 1.55/1.76 tff(10861,plain,
% 1.55/1.76 (~(elem!1 = s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1802, 10860])).
% 1.55/1.76 tff(10862,plain,
% 1.55/1.76 (~(s(elem!1) = s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[379, 10861])).
% 1.55/1.76 tff(10863,plain,
% 1.55/1.76 (~(s(s(z)) = s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1249, 10862])).
% 1.55/1.76 tff(10864,plain,
% 1.55/1.76 (r(s(s(z)), s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10596, 10863])).
% 1.55/1.76 tff(10865,plain,
% 1.55/1.76 (s(elem!1) = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9609, 10864, 1137, 1152, 8907])).
% 1.55/1.76 tff(10866,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10865, 10859])).
% 1.55/1.76 tff(10867,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(10868,plain,
% 1.55/1.76 (s(s(z)) = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10867, 10593, 57, 5390, 1817, 81, 374, 2213])).
% 1.55/1.76 tff(10869,plain,
% 1.55/1.76 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10868])).
% 1.55/1.76 tff(10870,plain,
% 1.55/1.76 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.55/1.76 inference(symmetry,[status(thm)],[10869])).
% 1.55/1.76 tff(10871,plain,
% 1.55/1.76 (s(elem!1) = s(z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[21, 10868])).
% 1.55/1.76 tff(10872,plain,
% 1.55/1.76 (~r(s(elem!1), s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[3876, 10871, 24])).
% 1.55/1.76 tff(10873,plain,
% 1.55/1.76 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9077, 10871, 1817])).
% 1.55/1.76 tff(10874,plain,
% 1.55/1.76 (~b(s(elem!1), s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[4533, 10873, 57, 10593])).
% 1.55/1.76 tff(10875,plain,
% 1.55/1.76 (s(elem!1) = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[534, 10874, 10872])).
% 1.55/1.76 tff(10876,plain,
% 1.55/1.76 (elem!1 = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[158, 10875])).
% 1.55/1.76 tff(10877,plain,
% 1.55/1.76 (s(elem!1) = s(s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2097, 10876])).
% 1.55/1.76 tff(10878,plain,
% 1.55/1.76 (s(s(s(elem!1))) = s(elem!1)),
% 1.55/1.76 inference(symmetry,[status(thm)],[10877])).
% 1.55/1.76 tff(10879,plain,
% 1.55/1.76 (s(s(s(elem!1))) = s(z)),
% 1.55/1.76 inference(transitivity,[status(thm)],[10878, 18, 10870, 12])).
% 1.55/1.76 tff(10880,plain,
% 1.55/1.76 ($false),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[94, 10879])).
% 1.55/1.76 tff(10881,plain,(b(z, s(z)) | (~b(s(s(z)), s(z))) | r(s(z), s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.76 tff(10882,plain,
% 1.55/1.76 (b(z, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10881, 24, 10091, 81, 374, 2213])).
% 1.55/1.76 tff(10883,plain,
% 1.55/1.76 (~b(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9571, 238, 10091, 57, 10882])).
% 1.55/1.76 tff(10884,plain,
% 1.55/1.76 ((z = s(s(z))) | r(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1511, 51, 10883])).
% 1.55/1.76 tff(10885,plain,
% 1.55/1.76 (r(z, s(s(z)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10884, 1450])).
% 1.55/1.76 tff(10886,plain,
% 1.55/1.76 (~(s(elem!1) = s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5343, 10168])).
% 1.55/1.76 tff(10887,plain,
% 1.55/1.76 (s(s(z)) = s(s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9617, 10886, 10882, 10091, 57, 2213])).
% 1.55/1.76 tff(10888,plain,
% 1.55/1.76 (s(elem!1) = s(z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[21, 10887])).
% 1.55/1.76 tff(10889,plain,
% 1.55/1.76 (r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10069, 10888, 81])).
% 1.55/1.76 tff(10890,plain,
% 1.55/1.76 (~(elem!1 = s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[386, 10886])).
% 1.55/1.76 tff(10891,plain,
% 1.55/1.76 (~(s(elem!1) = elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[393, 10890])).
% 1.55/1.76 tff(10892,plain,
% 1.55/1.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2595, 10168])).
% 1.55/1.76 tff(10893,plain,
% 1.55/1.76 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10887])).
% 1.55/1.76 tff(10894,plain,
% 1.55/1.76 (b(s(s(elem!1)), s(z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10091, 10893])).
% 1.55/1.76 tff(10895,plain,
% 1.55/1.76 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10887])).
% 1.55/1.76 tff(10896,plain,
% 1.55/1.76 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10895, 3730])).
% 1.55/1.76 tff(10897,plain,
% 1.55/1.76 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10896])).
% 1.55/1.76 tff(10898,plain,
% 1.55/1.76 (~(elem!1 = s(s(elem!1)))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[374, 10897])).
% 1.55/1.76 tff(10899,plain,
% 1.55/1.76 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9077, 10888, 10091])).
% 1.55/1.76 tff(10900,plain,
% 1.55/1.76 (~b(z, s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[4881, 10899, 57, 10882])).
% 1.55/1.76 tff(10901,plain,
% 1.55/1.76 (r(z, s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2071, 10900])).
% 1.55/1.76 tff(10902,plain,
% 1.55/1.76 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10888])).
% 1.55/1.76 tff(10903,plain,
% 1.55/1.76 (elem!1 = z),
% 1.55/1.76 inference(transitivity,[status(thm)],[155, 10902, 26])).
% 1.55/1.76 tff(10904,plain,
% 1.55/1.76 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10903])).
% 1.55/1.76 tff(10905,plain,
% 1.55/1.76 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.55/1.76 inference(symmetry,[status(thm)],[10904])).
% 1.55/1.76 tff(10906,plain,
% 1.55/1.76 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10905])).
% 1.55/1.76 tff(10907,plain,
% 1.55/1.76 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10887])).
% 1.55/1.76 tff(10908,plain,
% 1.55/1.76 ((~b(s(s(z)), z)) <=> (~b(s(s(elem!1)), z))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10907])).
% 1.55/1.76 tff(10909,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10910,plain,
% 1.55/1.76 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10911,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10910])).
% 1.55/1.76 tff(10912,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10911, 10909])).
% 1.55/1.76 tff(10913,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(10914,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10913, 10912])).
% 1.55/1.76 tff(10915,plain,
% 1.55/1.76 (~b(s(s(z)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10914, 238, 10091, 57, 10882])).
% 1.55/1.76 tff(10916,plain,
% 1.55/1.76 (~b(s(s(elem!1)), z)),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10915, 10908])).
% 1.55/1.76 tff(10917,plain,
% 1.55/1.76 (~b(s(s(elem!1)), elem!1)),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10916, 10906])).
% 1.55/1.76 tff(10918,plain,
% 1.55/1.76 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.55/1.76 inference(transitivity,[status(thm)],[10896, 4108])).
% 1.55/1.76 tff(10919,plain,
% 1.55/1.76 ((~(s(s(z)) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10918])).
% 1.55/1.76 tff(10920,plain,
% 1.55/1.76 (~(s(s(elem!1)) = elem!1)),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[374, 10919])).
% 1.55/1.76 tff(10921,plain,
% 1.55/1.76 (r(s(s(elem!1)), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[255, 10920, 10917])).
% 1.55/1.76 tff(10922,plain,
% 1.55/1.76 (r(s(s(elem!1)), z)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[4030, 51, 92, 10916])).
% 1.55/1.76 tff(10923,plain,
% 1.55/1.76 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10888])).
% 1.55/1.76 tff(10924,plain,
% 1.55/1.76 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.55/1.76 inference(symmetry,[status(thm)],[10923])).
% 1.55/1.76 tff(10925,plain,
% 1.55/1.76 (b(elem!1, s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[6376, 10888, 10882])).
% 1.55/1.76 tff(10926,plain,
% 1.55/1.76 (b(elem!1, s(elem!1))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10925, 10924])).
% 1.55/1.76 tff(10927,plain,
% 1.55/1.76 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3719])).
% 1.55/1.76 tff(10928,plain,
% 1.55/1.76 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3815])).
% 1.55/1.76 tff(10929,plain,
% 1.55/1.76 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10928, 767])).
% 1.55/1.76 tff(10930,plain,
% 1.55/1.76 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10929])).
% 1.55/1.76 tff(10931,plain,
% 1.55/1.76 (~(elem!1 = s(s(s(s(z)))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[726, 10930])).
% 1.55/1.76 tff(10932,plain,
% 1.55/1.76 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3701])).
% 1.55/1.76 tff(10933,plain,
% 1.55/1.76 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10932])).
% 1.55/1.76 tff(10934,plain,
% 1.55/1.76 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3717])).
% 1.55/1.76 tff(10935,plain,
% 1.55/1.76 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.55/1.76 inference(symmetry,[status(thm)],[10934])).
% 1.55/1.76 tff(10936,plain,
% 1.55/1.76 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3815])).
% 1.55/1.76 tff(10937,plain,
% 1.55/1.76 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.55/1.76 inference(transitivity,[status(thm)],[10936, 10935])).
% 1.55/1.76 tff(10938,plain,
% 1.55/1.76 ((~r(s(z), z)) <=> (~r(s(elem!1), elem!1))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10937])).
% 1.55/1.76 tff(10939,plain,
% 1.55/1.76 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.76 inference(commutativity,[status(thm)],[])).
% 1.55/1.76 tff(10940,plain,
% 1.55/1.76 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.55/1.76 inference(symmetry,[status(thm)],[10939])).
% 1.55/1.76 tff(10941,plain,
% 1.55/1.76 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10940])).
% 1.55/1.76 tff(10942,plain,
% 1.55/1.76 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[7253, 10941])).
% 1.55/1.76 tff(10943,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.55/1.76 inference(symmetry,[status(thm)],[3882])).
% 1.55/1.76 tff(10944,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[3717])).
% 1.55/1.76 tff(10945,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10944, 10943])).
% 1.55/1.76 tff(10946,plain,
% 1.55/1.76 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(z))), s(z)))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10945])).
% 1.55/1.76 tff(10947,plain,
% 1.55/1.76 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1203, 210, 150, 4230, 542, 631])).
% 1.55/1.76 tff(10948,plain,
% 1.55/1.76 (~b(s(s(s(z))), s(z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10947, 10946])).
% 1.55/1.76 tff(10949,plain,
% 1.55/1.76 (r(s(s(s(z))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5118, 10948])).
% 1.55/1.76 tff(10950,plain,
% 1.55/1.76 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10949, 3740])).
% 1.55/1.76 tff(10951,plain,
% 1.55/1.76 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.76 inference(symmetry,[status(thm)],[9228])).
% 1.55/1.76 tff(10952,plain,
% 1.55/1.76 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.55/1.76 inference(symmetry,[status(thm)],[9227])).
% 1.55/1.76 tff(10953,plain,
% 1.55/1.76 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10952, 10951])).
% 1.55/1.76 tff(10954,plain,
% 1.55/1.76 ((~r(z, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10953])).
% 1.55/1.76 tff(10955,plain,
% 1.55/1.76 (~r(elem!1, s(s(s(z))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[5526, 10954])).
% 1.55/1.76 tff(10956,plain,
% 1.55/1.76 (b(elem!1, s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5079, 10955, 9225])).
% 1.55/1.76 tff(10957,plain,
% 1.55/1.76 (r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10196, 10956, 289, 23, 301, 3717, 210])).
% 1.55/1.76 tff(10958,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10959,plain,
% 1.55/1.76 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10960,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10959])).
% 1.55/1.76 tff(10961,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10960, 10958])).
% 1.55/1.76 tff(10962,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(10963,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10962, 10961])).
% 1.55/1.76 tff(10964,plain,
% 1.55/1.76 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10963, 124, 10957, 10950])).
% 1.55/1.76 tff(10965,plain,
% 1.55/1.76 (((~![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)))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10966,plain,
% 1.55/1.76 ((~![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)))))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(10967,plain,
% 1.55/1.76 ((~![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))))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10966, 10965])).
% 1.55/1.76 tff(10968,plain,
% 1.55/1.76 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10967, 51, 10964])).
% 1.55/1.76 tff(10969,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10968, 10942])).
% 1.55/1.76 tff(10970,plain,
% 1.55/1.76 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1826, 10957, 161])).
% 1.55/1.76 tff(10971,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1814, 10970, 7253])).
% 1.55/1.76 tff(10972,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10973,plain,
% 1.55/1.76 (((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.76 inference(rewrite,[status(thm)],[])).
% 1.55/1.76 tff(10974,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1)))))))),
% 1.55/1.76 inference(monotonicity,[status(thm)],[10973])).
% 1.55/1.76 tff(10975,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1))))))),
% 1.55/1.76 inference(transitivity,[status(thm)],[10974, 10972])).
% 1.55/1.76 tff(10976,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.55/1.76 inference(quant_inst,[status(thm)],[])).
% 1.55/1.76 tff(10977,plain,
% 1.55/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(elem!1)))))),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10976, 10975])).
% 1.55/1.76 tff(10978,plain,
% 1.55/1.76 (~b(z, s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10977, 238, 10971, 10969, 5527])).
% 1.55/1.76 tff(10979,plain,
% 1.55/1.76 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1749, 51, 10978])).
% 1.55/1.76 tff(10980,plain,
% 1.55/1.76 (r(z, s(s(s(s(s(z))))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10979, 1715])).
% 1.55/1.76 tff(10981,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 1.55/1.76 inference(symmetry,[status(thm)],[3816])).
% 1.55/1.76 tff(10982,plain,
% 1.55/1.76 (b(s(s(s(elem!1))), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[647, 10179, 4230])).
% 1.55/1.76 tff(10983,plain,
% 1.55/1.76 (b(s(s(s(z))), z)),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10982, 10981])).
% 1.55/1.76 tff(10984,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[5751, 10971, 13])).
% 1.55/1.76 tff(10985,plain,
% 1.55/1.76 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[9245, 10984, 10956, 10983])).
% 1.55/1.76 tff(10986,plain,
% 1.55/1.76 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[1064, 10985, 3823])).
% 1.55/1.76 tff(10987,plain,
% 1.55/1.76 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.76 inference(modus_ponens,[status(thm)],[10986, 9238])).
% 1.55/1.76 tff(10988,plain,
% 1.55/1.76 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[10194, 124, 10987, 6338])).
% 1.55/1.76 tff(10989,plain,
% 1.55/1.76 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.76 inference(unit_resolution,[status(thm)],[2420, 51, 10988, 3851])).
% 1.55/1.76 tff(10990,plain,
% 1.55/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(10991,plain,
% 1.55/1.77 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(10992,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10991])).
% 1.55/1.77 tff(10993,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[10992, 10990])).
% 1.55/1.77 tff(10994,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(10995,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[10994, 10993])).
% 1.55/1.77 tff(10996,plain,
% 1.55/1.77 (~b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[10995, 238, 1137, 23, 10989])).
% 1.55/1.77 tff(10997,plain,
% 1.55/1.77 (r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1709, 10996])).
% 1.55/1.77 tff(10998,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(10999,plain,
% 1.55/1.77 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11000,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10999])).
% 1.55/1.77 tff(11001,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[11000, 10998])).
% 1.55/1.77 tff(11002,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(11003,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11002, 11001])).
% 1.55/1.77 tff(11004,plain,
% 1.55/1.77 (~r(s(z), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11003, 124, 10997, 10980])).
% 1.55/1.77 tff(11005,plain,
% 1.55/1.77 (~r(s(elem!1), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11004, 10938])).
% 1.55/1.77 tff(11006,plain,
% 1.55/1.77 (b(s(elem!1), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[408, 11005, 394])).
% 1.55/1.77 tff(11007,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.55/1.77 tff(11008,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[9274, 124, 210, 1544, 2964])).
% 1.55/1.77 tff(11009,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2974, 51, 11008, 3797])).
% 1.55/1.77 tff(11010,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11011,plain,
% 1.55/1.77 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11012,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11011])).
% 1.55/1.77 tff(11013,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.55/1.77 inference(transitivity,[status(thm)],[11012, 11010])).
% 1.55/1.77 tff(11014,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(11015,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11014, 11013])).
% 1.55/1.77 tff(11016,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11015, 238, 3965, 3957, 11009, 11007])).
% 1.55/1.77 tff(11017,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11018,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11017, 10969, 3713, 210, 10950, 10957])).
% 1.55/1.77 tff(11019,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1624, 11018])).
% 1.55/1.77 tff(11020,plain,
% 1.55/1.77 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11019, 4235])).
% 1.55/1.77 tff(11021,plain,
% 1.55/1.77 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[10738, 11020, 631, 11006])).
% 1.55/1.77 tff(11022,plain,
% 1.55/1.77 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11021, 10933])).
% 1.55/1.77 tff(11023,plain,
% 1.55/1.77 (r(elem!1, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[935, 11022, 10931])).
% 1.55/1.77 tff(11024,plain,
% 1.55/1.77 (r(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11023, 10927])).
% 1.55/1.77 tff(11025,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[7881, 238, 1137, 23, 11019])).
% 1.55/1.77 tff(11026,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11025, 3916])).
% 1.55/1.77 tff(11027,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1564, 11026])).
% 1.55/1.77 tff(11028,plain,
% 1.55/1.77 (~r(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3484, 11027, 1575])).
% 1.55/1.77 tff(11029,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11028, 11024])).
% 1.55/1.77 tff(11030,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11031,plain,
% 1.55/1.77 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11030, 10926, 10885, 10887, 57, 10894, 10922, 102, 10899, 10921, 10901, 10898, 10889])).
% 1.55/1.77 tff(11032,plain,
% 1.55/1.77 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[223, 11031, 10168])).
% 1.55/1.77 tff(11033,plain,
% 1.55/1.77 (~b(s(s(s(elem!1))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3909, 238, 57, 11032, 10894])).
% 1.55/1.77 tff(11034,plain,
% 1.55/1.77 (~b(s(s(s(z))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3886, 11033, 10887])).
% 1.55/1.77 tff(11035,plain,
% 1.55/1.77 (r(s(s(s(z))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[5118, 11034])).
% 1.55/1.77 tff(11036,plain,
% 1.55/1.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10887])).
% 1.55/1.77 tff(11037,plain,
% 1.55/1.77 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.55/1.77 inference(symmetry,[status(thm)],[11036])).
% 1.55/1.77 tff(11038,plain,
% 1.55/1.77 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11037])).
% 1.55/1.77 tff(11039,plain,
% 1.55/1.77 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(z))), z))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11038])).
% 1.55/1.77 tff(11040,plain,
% 1.55/1.77 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = z)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10903])).
% 1.55/1.77 tff(11041,plain,
% 1.55/1.77 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.77 inference(symmetry,[status(thm)],[11040])).
% 1.55/1.77 tff(11042,plain,
% 1.55/1.77 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11041])).
% 1.55/1.77 tff(11043,plain,
% 1.55/1.77 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[1006, 11042])).
% 1.55/1.77 tff(11044,plain,
% 1.55/1.77 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10887])).
% 1.55/1.77 tff(11045,plain,
% 1.55/1.77 ((~r(s(s(z)), s(z))) <=> (~r(s(s(elem!1)), s(z)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11044])).
% 1.55/1.77 tff(11046,plain,
% 1.55/1.77 (~r(s(s(elem!1)), s(z))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[10090, 11045])).
% 1.55/1.77 tff(11047,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[13])).
% 1.55/1.77 tff(11048,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.77 inference(symmetry,[status(thm)],[11047])).
% 1.55/1.77 tff(11049,plain,
% 1.55/1.77 ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11048])).
% 1.55/1.77 tff(11050,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[5272, 9238])).
% 1.55/1.77 tff(11051,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[10194, 124, 11050, 6338])).
% 1.55/1.77 tff(11052,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11051, 11049])).
% 1.55/1.77 tff(11053,plain,
% 1.55/1.77 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[7528, 11051, 226, 3851, 7490])).
% 1.55/1.77 tff(11054,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1814, 11053, 7253])).
% 1.55/1.77 tff(11055,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1824, 124, 161, 1818])).
% 1.55/1.77 tff(11056,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1779, 51, 11055, 728])).
% 1.55/1.77 tff(11057,plain,
% 1.55/1.77 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.55/1.77 inference(symmetry,[status(thm)],[2369])).
% 1.55/1.77 tff(11058,plain,
% 1.55/1.77 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11057])).
% 1.55/1.77 tff(11059,plain,
% 1.55/1.77 (~(s(s(elem!1)) = s(z))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[41, 11058])).
% 1.55/1.77 tff(11060,plain,
% 1.55/1.77 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[110, 51, 107])).
% 1.55/1.77 tff(11061,plain,
% 1.55/1.77 (b(s(s(elem!1)), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11060, 11059])).
% 1.55/1.77 tff(11062,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[5652, 238, 1137, 11061, 11056, 4122])).
% 1.55/1.77 tff(11063,plain,(r(s(s(elem!1)), s(z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11064,plain,
% 1.55/1.77 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11063, 11054, 1137, 107, 161])).
% 1.55/1.77 tff(11065,plain,
% 1.55/1.77 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[4318, 11064, 13])).
% 1.55/1.77 tff(11066,plain,
% 1.55/1.77 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1738, 11065])).
% 1.55/1.77 tff(11067,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11066, 11052])).
% 1.55/1.77 tff(11068,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | r(s(s(elem!1)), s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11069,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11068, 11032, 57, 10887, 102, 11046, 10922, 10921])).
% 1.55/1.77 tff(11070,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1064, 11069, 11043])).
% 1.55/1.77 tff(11071,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1826, 1818, 161])).
% 1.55/1.77 tff(11072,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1781, 11071])).
% 1.55/1.77 tff(11073,plain,
% 1.55/1.77 (~b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1872, 11072, 1817, 1457])).
% 1.55/1.77 tff(11074,plain,
% 1.55/1.77 (r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1709, 11073])).
% 1.55/1.77 tff(11075,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1834, 124, 11074, 161, 1818])).
% 1.55/1.77 tff(11076,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11077,plain,
% 1.55/1.77 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11076, 10882, 10091, 102])).
% 1.55/1.77 tff(11078,plain,
% 1.55/1.77 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[4960, 10887])).
% 1.55/1.77 tff(11079,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1814, 11078, 11077])).
% 1.55/1.77 tff(11080,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11081,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(11082,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11081, 11080])).
% 1.55/1.77 tff(11083,plain,
% 1.55/1.77 ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11082, 238, 1457, 1040])).
% 1.55/1.77 tff(11084,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11083, 7557, 6923])).
% 1.55/1.77 tff(11085,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11086,plain,
% 1.55/1.77 (~b(s(s(s(elem!1))), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11085, 10882, 11079, 11070, 10888])).
% 1.55/1.77 tff(11087,plain,
% 1.55/1.77 (~b(s(s(s(z))), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11086, 11039])).
% 1.55/1.77 tff(11088,plain,
% 1.55/1.77 (r(s(s(s(z))), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1524, 11087])).
% 1.55/1.77 tff(11089,plain,
% 1.55/1.77 (~r(z, s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2827, 11088, 11035])).
% 1.55/1.77 tff(11090,plain,
% 1.55/1.77 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11037])).
% 1.55/1.77 tff(11091,plain,
% 1.55/1.77 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[11090])).
% 1.55/1.77 tff(11092,plain,
% 1.55/1.77 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11091])).
% 1.55/1.77 tff(11093,plain,
% 1.55/1.77 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3711, 10887])).
% 1.55/1.77 tff(11094,plain,
% 1.55/1.77 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11093, 11092])).
% 1.55/1.77 tff(11095,plain,
% 1.55/1.77 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11036])).
% 1.55/1.77 tff(11096,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), s(z))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11035, 11095])).
% 1.55/1.77 tff(11097,plain,
% 1.55/1.77 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[3815])).
% 1.55/1.77 tff(11098,plain,
% 1.55/1.77 ((~b(z, s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11097])).
% 1.55/1.77 tff(11099,plain,
% 1.55/1.77 (~b(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[8258, 238, 1137, 1457, 1784])).
% 1.55/1.77 tff(11100,plain,
% 1.55/1.77 (~b(elem!1, s(s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11099, 11098])).
% 1.55/1.77 tff(11101,plain,
% 1.55/1.77 (r(elem!1, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[935, 11100, 10931])).
% 1.55/1.77 tff(11102,plain,
% 1.55/1.77 (r(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11101, 10927])).
% 1.55/1.77 tff(11103,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[7882, 3916])).
% 1.55/1.77 tff(11104,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1564, 11103])).
% 1.55/1.77 tff(11105,plain,
% 1.55/1.77 (~r(z, s(s(s(s(z)))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[3484, 11104, 1575])).
% 1.55/1.77 tff(11106,plain,
% 1.55/1.77 ($false),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11105, 11102])).
% 1.55/1.77 tff(11107,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.77 tff(11108,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11107, 10894, 10885, 57, 10882, 10887])).
% 1.55/1.77 tff(11109,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1624, 11108])).
% 1.55/1.77 tff(11110,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2970, 124, 11109, 11096])).
% 1.55/1.77 tff(11111,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2974, 51, 11110, 11094])).
% 1.55/1.77 tff(11112,plain,
% 1.55/1.77 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.55/1.77 inference(symmetry,[status(thm)],[10902])).
% 1.55/1.77 tff(11113,plain,
% 1.55/1.77 (z = elem!1),
% 1.55/1.77 inference(transitivity,[status(thm)],[769, 11112, 154])).
% 1.55/1.77 tff(11114,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11113])).
% 1.55/1.77 tff(11115,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.55/1.77 inference(symmetry,[status(thm)],[11114])).
% 1.55/1.77 tff(11116,plain,
% 1.55/1.77 (b(s(s(s(s(s(z))))), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11070, 11115])).
% 1.55/1.77 tff(11117,plain,
% 1.55/1.77 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11113])).
% 1.55/1.77 tff(11118,plain,
% 1.55/1.77 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.55/1.77 inference(symmetry,[status(thm)],[11117])).
% 1.55/1.77 tff(11119,plain,
% 1.55/1.77 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10888])).
% 1.55/1.77 tff(11120,plain,
% 1.55/1.77 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[10903])).
% 1.55/1.77 tff(11121,plain,
% 1.55/1.77 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.55/1.77 inference(transitivity,[status(thm)],[11120, 3716])).
% 1.55/1.77 tff(11122,plain,
% 1.55/1.77 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.55/1.77 inference(symmetry,[status(thm)],[11121])).
% 1.55/1.77 tff(11123,plain,
% 1.55/1.77 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.55/1.77 inference(transitivity,[status(thm)],[11122, 641])).
% 1.55/1.77 tff(11124,plain,
% 1.55/1.77 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11123])).
% 1.55/1.77 tff(11125,plain,
% 1.55/1.77 (~(s(s(s(elem!1))) = elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[821, 11124])).
% 1.55/1.77 tff(11126,plain,
% 1.55/1.77 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11036, 11113])).
% 1.55/1.77 tff(11127,plain,
% 1.55/1.77 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.55/1.77 inference(transitivity,[status(thm)],[11038, 11126])).
% 1.55/1.77 tff(11128,plain,
% 1.55/1.77 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11127])).
% 1.55/1.77 tff(11129,plain,
% 1.55/1.77 (~b(s(s(s(elem!1))), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11086, 11128])).
% 1.55/1.77 tff(11130,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[647, 11129, 11125])).
% 1.55/1.77 tff(11131,plain,
% 1.55/1.77 (~r(s(elem!1), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[657, 11130, 10889])).
% 1.55/1.77 tff(11132,plain,
% 1.55/1.77 (b(s(elem!1), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[408, 11131, 10891])).
% 1.55/1.77 tff(11133,plain,
% 1.55/1.77 (b(s(z), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11132, 11119])).
% 1.55/1.77 tff(11134,plain,
% 1.55/1.77 (b(s(z), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11133, 11118])).
% 1.55/1.77 tff(11135,plain,
% 1.55/1.77 ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[7574, 238, 10882])).
% 1.55/1.77 tff(11136,plain,
% 1.55/1.77 (~b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11135, 11134, 11116])).
% 1.55/1.77 tff(11137,plain,
% 1.55/1.77 (r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[1709, 11136])).
% 1.55/1.77 tff(11138,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[3719])).
% 1.55/1.77 tff(11139,plain,
% 1.55/1.77 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.55/1.77 inference(transitivity,[status(thm)],[10929, 789])).
% 1.55/1.77 tff(11140,plain,
% 1.55/1.77 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11139])).
% 1.55/1.77 tff(11141,plain,
% 1.55/1.77 (~(s(s(s(s(z)))) = elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[726, 11140])).
% 1.55/1.77 tff(11142,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(monotonicity,[status(thm)],[3815])).
% 1.55/1.77 tff(11143,plain,
% 1.55/1.77 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11142])).
% 1.55/1.77 tff(11144,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.55/1.77 tff(11145,plain,
% 1.55/1.77 (r(s(s(s(elem!1))), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[2819, 4226])).
% 1.55/1.77 tff(11146,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11147,plain,
% 1.55/1.77 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.77 inference(rewrite,[status(thm)],[])).
% 1.55/1.77 tff(11148,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))))),
% 1.55/1.77 inference(monotonicity,[status(thm)],[11147])).
% 1.55/1.77 tff(11149,plain,
% 1.55/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 1.55/1.77 inference(transitivity,[status(thm)],[11148, 11146])).
% 1.55/1.77 tff(11150,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.55/1.77 inference(quant_inst,[status(thm)],[])).
% 1.55/1.77 tff(11151,plain,
% 1.55/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11150, 11149])).
% 1.55/1.77 tff(11152,plain,
% 1.55/1.77 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[11151, 124, 11145, 6338])).
% 1.55/1.77 tff(11153,plain,
% 1.55/1.77 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2549, 51, 11152, 11144])).
% 1.55/1.77 tff(11154,plain,
% 1.55/1.77 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2978, 238, 226, 11153, 1041])).
% 1.55/1.77 tff(11155,plain,
% 1.55/1.77 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[5236, 51, 7254, 11154])).
% 1.55/1.77 tff(11156,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), z)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[10276, 124, 2026, 11155])).
% 1.55/1.77 tff(11157,plain,
% 1.55/1.77 (~r(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11156, 11143])).
% 1.55/1.77 tff(11158,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), elem!1)),
% 1.55/1.77 inference(unit_resolution,[status(thm)],[2131, 11157, 11141])).
% 1.55/1.77 tff(11159,plain,
% 1.55/1.77 (b(s(s(s(s(z)))), z)),
% 1.55/1.77 inference(modus_ponens,[status(thm)],[11158, 11138])).
% 1.55/1.77 tff(11160,plain,
% 1.55/1.77 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3815])).
% 1.55/1.78 tff(11161,plain,
% 1.55/1.78 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.55/1.78 inference(symmetry,[status(thm)],[11160])).
% 1.55/1.78 tff(11162,plain,
% 1.55/1.78 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3717])).
% 1.55/1.78 tff(11163,plain,
% 1.55/1.78 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3719])).
% 1.55/1.78 tff(11164,plain,
% 1.55/1.78 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[11163])).
% 1.55/1.78 tff(11165,plain,
% 1.55/1.78 (r(s(s(s(z))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.55/1.78 inference(transitivity,[status(thm)],[4226, 11164])).
% 1.55/1.78 tff(11166,plain,
% 1.55/1.78 (r(s(s(s(elem!1))), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[2819, 11165])).
% 1.55/1.78 tff(11167,plain,
% 1.55/1.78 (~r(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[657, 11166, 542])).
% 1.55/1.78 tff(11168,plain,
% 1.55/1.78 (b(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[408, 11167, 632])).
% 1.55/1.78 tff(11169,plain,
% 1.55/1.78 (b(s(z), elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11168, 11162])).
% 1.55/1.78 tff(11170,plain,
% 1.55/1.78 (b(s(z), z)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11169, 11161])).
% 1.55/1.78 tff(11171,plain,
% 1.55/1.78 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(symmetry,[status(thm)],[11097])).
% 1.55/1.78 tff(11172,plain,
% 1.55/1.78 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.55/1.78 inference(symmetry,[status(thm)],[10927])).
% 1.55/1.78 tff(11173,plain,
% 1.55/1.78 ((~r(z, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11172])).
% 1.55/1.78 tff(11174,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.55/1.78 tff(11175,plain,
% 1.55/1.78 (~r(elem!1, s(s(s(s(z)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11174, 11173])).
% 1.55/1.78 tff(11176,plain,
% 1.55/1.78 (b(elem!1, s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[935, 11175, 10931])).
% 1.55/1.78 tff(11177,plain,
% 1.55/1.78 (b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11176, 11171])).
% 1.55/1.78 tff(11178,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11179,plain,
% 1.55/1.78 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11180,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11179])).
% 1.55/1.78 tff(11181,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[11180, 11178])).
% 1.55/1.78 tff(11182,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11183,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11182, 11181])).
% 1.55/1.78 tff(11184,plain,
% 1.55/1.78 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11183, 238, 11159, 11177])).
% 1.55/1.78 tff(11185,plain,
% 1.55/1.78 (~b(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11184, 11170])).
% 1.55/1.78 tff(11186,plain,
% 1.55/1.78 (r(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6600, 11185])).
% 1.55/1.78 tff(11187,plain,
% 1.55/1.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1660, 11186, 1651])).
% 1.55/1.78 tff(11188,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1904, 11187])).
% 1.55/1.78 tff(11189,plain,
% 1.55/1.78 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[7564, 11188, 3717, 1457, 11159])).
% 1.55/1.78 tff(11190,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1064, 11189, 3823])).
% 1.55/1.78 tff(11191,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), z)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11190, 9238])).
% 1.55/1.78 tff(11192,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3847])).
% 1.55/1.78 tff(11193,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(symmetry,[status(thm)],[11192])).
% 1.55/1.78 tff(11194,plain,
% 1.55/1.78 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2050, 11056, 2040, 2026, 1836])).
% 1.55/1.78 tff(11195,plain,
% 1.55/1.78 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11194, 11049])).
% 1.55/1.78 tff(11196,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1737, 11195, 1729])).
% 1.55/1.78 tff(11197,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11196, 11193])).
% 1.55/1.78 tff(11198,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11199,plain,
% 1.55/1.78 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11200,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11199])).
% 1.55/1.78 tff(11201,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[11200, 11198])).
% 1.55/1.78 tff(11202,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11203,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11202, 11201])).
% 1.55/1.78 tff(11204,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11203, 238, 1137, 744, 11056, 11197])).
% 1.55/1.78 tff(11205,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | r(z, s(z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11206,plain,
% 1.55/1.78 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11205, 11153, 2040, 161, 13, 2026, 1137])).
% 1.55/1.78 tff(11207,plain,
% 1.55/1.78 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1814, 11206, 7253])).
% 1.55/1.78 tff(11208,plain,
% 1.55/1.78 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[7489, 11190, 301])).
% 1.55/1.78 tff(11209,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[7528, 11208, 226, 3851, 11207])).
% 1.55/1.78 tff(11210,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10194, 124, 11209, 11191, 6338])).
% 1.55/1.78 tff(11211,plain,((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | r(z, s(s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | r(z, s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(elem!1) = elem!1) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11212,plain,
% 1.55/1.78 (r(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11211, 11137, 11032, 10921, 10882, 11088, 10922, 10901, 11111, 11089, 102, 10887, 57, 10892, 10891, 10889])).
% 1.55/1.78 tff(11213,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.55/1.78 tff(11214,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11215,plain,
% 1.55/1.78 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11216,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11215])).
% 1.55/1.78 tff(11217,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[11216, 11214])).
% 1.55/1.78 tff(11218,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11219,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11218, 11217])).
% 1.55/1.78 tff(11220,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11219, 124, 3476, 11213, 1575])).
% 1.55/1.78 tff(11221,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11222,plain,
% 1.55/1.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11221, 11212, 10885])).
% 1.55/1.78 tff(11223,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11224,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11225,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11224, 11223])).
% 1.55/1.78 tff(11226,plain,
% 1.55/1.78 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11225, 238, 11032, 11079, 11111])).
% 1.55/1.78 tff(11227,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1904, 11226])).
% 1.55/1.78 tff(11228,plain,
% 1.55/1.78 (~r(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1660, 11137, 11227])).
% 1.55/1.78 tff(11229,plain,
% 1.55/1.78 (b(s(z), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6600, 11228])).
% 1.55/1.78 tff(11230,plain,
% 1.55/1.78 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3847])).
% 1.55/1.78 tff(11231,plain,
% 1.55/1.78 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.78 inference(symmetry,[status(thm)],[11230])).
% 1.55/1.78 tff(11232,plain,
% 1.55/1.78 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[1501, 11231])).
% 1.55/1.78 tff(11233,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11234,plain,
% 1.55/1.78 (((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11235,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11234])).
% 1.55/1.78 tff(11236,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.55/1.78 inference(transitivity,[status(thm)],[11235, 11233])).
% 1.55/1.78 tff(11237,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11238,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11237, 11236])).
% 1.55/1.78 tff(11239,plain,
% 1.55/1.78 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11238, 238, 2765, 23, 1041])).
% 1.55/1.78 tff(11240,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11239, 11232])).
% 1.55/1.78 tff(11241,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11242,plain,
% 1.55/1.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11241, 11229, 10887, 10894, 11111])).
% 1.55/1.78 tff(11243,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1604, 11242, 11222])).
% 1.55/1.78 tff(11244,plain,(r(s(z), s(s(elem!1))) | (s(s(z)) = elem!1) | r(s(s(z)), s(z)) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11245,plain,
% 1.55/1.78 (r(s(z), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11244, 10089, 81, 10083, 10081])).
% 1.55/1.78 tff(11246,plain,
% 1.55/1.78 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10022, 11245])).
% 1.55/1.78 tff(11247,plain,
% 1.55/1.78 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[223, 11246, 209])).
% 1.55/1.78 tff(11248,plain,
% 1.55/1.78 ((~(s(elem!1) = s(z))) | b(s(s(elem!1)), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[9077, 8300])).
% 1.55/1.78 tff(11249,plain,
% 1.55/1.78 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11248, 10058])).
% 1.55/1.78 tff(11250,plain,
% 1.55/1.78 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[10058])).
% 1.55/1.78 tff(11251,plain,
% 1.55/1.78 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.55/1.78 inference(symmetry,[status(thm)],[11250])).
% 1.55/1.78 tff(11252,plain,
% 1.55/1.78 (b(elem!1, s(z))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6376, 10058, 1457])).
% 1.55/1.78 tff(11253,plain,
% 1.55/1.78 (b(elem!1, s(elem!1))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11252, 11251])).
% 1.55/1.78 tff(11254,plain,
% 1.55/1.78 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3719])).
% 1.55/1.78 tff(11255,plain,
% 1.55/1.78 (r(s(elem!1), elem!1) <=> r(s(z), z)),
% 1.55/1.78 inference(transitivity,[status(thm)],[10934, 11254])).
% 1.55/1.78 tff(11256,plain,
% 1.55/1.78 (b(s(z), elem!1) <=> b(s(z), z)),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3719])).
% 1.55/1.78 tff(11257,plain,
% 1.55/1.78 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.55/1.78 inference(transitivity,[status(thm)],[11162, 11256])).
% 1.55/1.78 tff(11258,plain,
% 1.55/1.78 (b(s(z), z)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[507, 11257])).
% 1.55/1.78 tff(11259,plain,
% 1.55/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.78 inference(rewrite,[status(thm)],[])).
% 1.55/1.78 tff(11260,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.55/1.78 inference(quant_inst,[status(thm)],[])).
% 1.55/1.78 tff(11261,plain,
% 1.55/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11260, 11259])).
% 1.55/1.78 tff(11262,plain,
% 1.55/1.78 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11261, 238, 23, 1784, 11258])).
% 1.55/1.78 tff(11263,plain,
% 1.55/1.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11262, 9197])).
% 1.55/1.78 tff(11264,plain,
% 1.55/1.78 (r(z, s(s(z))) <=> r(z, s(s(elem!1)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[13])).
% 1.55/1.78 tff(11265,plain,
% 1.55/1.78 (r(z, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.55/1.78 inference(symmetry,[status(thm)],[11264])).
% 1.55/1.78 tff(11266,plain,
% 1.55/1.78 (r(z, s(s(z)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[2026, 11265])).
% 1.55/1.78 tff(11267,plain,
% 1.55/1.78 (b(elem!1, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[3719, 3701])).
% 1.55/1.78 tff(11268,plain,
% 1.55/1.78 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(z, s(s(s(s(z))))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11267])).
% 1.55/1.78 tff(11269,plain,
% 1.55/1.78 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10738, 507, 4236, 631])).
% 1.55/1.78 tff(11270,plain,
% 1.55/1.78 (~b(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11269, 11268])).
% 1.55/1.78 tff(11271,plain,
% 1.55/1.78 (r(z, s(s(s(s(z)))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1487, 51, 11270, 7182])).
% 1.55/1.78 tff(11272,plain,
% 1.55/1.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[3484, 11271, 11266])).
% 1.55/1.78 tff(11273,plain,
% 1.55/1.78 (b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1564, 11272])).
% 1.55/1.78 tff(11274,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11273, 11263])).
% 1.55/1.78 tff(11275,plain,((~b(s(elem!1), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11276,plain,
% 1.55/1.78 (~b(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11275, 2026, 23, 1784, 13, 631])).
% 1.55/1.78 tff(11277,plain,
% 1.55/1.78 (r(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[408, 11276, 632])).
% 1.55/1.78 tff(11278,plain,
% 1.55/1.78 (r(s(z), z)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11277, 11255])).
% 1.55/1.78 tff(11279,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6136, 124, 160, 2026, 11278])).
% 1.55/1.78 tff(11280,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = elem!1) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11281,plain,
% 1.55/1.78 (~r(z, s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11280, 11245, 394, 10008, 1784, 10057, 11253])).
% 1.55/1.78 tff(11282,plain,
% 1.55/1.78 (~r(elem!1, s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[7136, 11281, 10058])).
% 1.55/1.78 tff(11283,plain,
% 1.55/1.78 (b(elem!1, s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[606, 11282, 150])).
% 1.55/1.78 tff(11284,plain,
% 1.55/1.78 (~b(elem!1, s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[3306, 11283, 11249, 11247])).
% 1.55/1.78 tff(11285,plain,
% 1.55/1.78 (r(elem!1, s(s(s(elem!1))))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[1319, 11284, 10077])).
% 1.55/1.78 tff(11286,plain,
% 1.55/1.78 (~b(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5551, 11283, 11249, 11253])).
% 1.55/1.78 tff(11287,plain,
% 1.55/1.78 (r(s(elem!1), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[408, 11286, 394])).
% 1.55/1.78 tff(11288,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[3315, 11287, 11285, 10070])).
% 1.55/1.78 tff(11289,plain,((elem!1 = s(s(elem!1))) | (~b(s(s(s(s(z)))), s(z))) | b(s(z), s(s(s(elem!1)))) | r(s(s(elem!1)), s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11290,plain,
% 1.55/1.78 (elem!1 = s(s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11289, 107, 81, 1784, 1457])).
% 1.55/1.78 tff(11291,plain,
% 1.55/1.78 (s(elem!1) = s(s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2097, 11290])).
% 1.55/1.78 tff(11292,plain,
% 1.55/1.78 (s(s(s(elem!1))) = s(elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[11291])).
% 1.55/1.78 tff(11293,plain,
% 1.55/1.78 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11292])).
% 1.55/1.78 tff(11294,plain,
% 1.55/1.78 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11293])).
% 1.55/1.78 tff(11295,plain,
% 1.55/1.78 ((~(s(s(z)) = s(s(s(s(elem!1)))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11294])).
% 1.55/1.78 tff(11296,plain,
% 1.55/1.78 (~(s(s(z)) = s(s(elem!1)))),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[8493, 11295])).
% 1.55/1.78 tff(11297,plain,
% 1.55/1.78 ((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), elem!1)) | (~b(z, s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[6413, 8300])).
% 1.55/1.78 tff(11298,plain,
% 1.55/1.78 (~b(s(z), elem!1)),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11297, 11296, 10008, 1457])).
% 1.55/1.78 tff(11299,plain,
% 1.55/1.78 (~b(s(z), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[3083, 11298, 11290])).
% 1.55/1.78 tff(11300,plain,
% 1.55/1.78 (r(s(z), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[56, 11299])).
% 1.55/1.78 tff(11301,plain,
% 1.55/1.78 (~r(s(s(z)), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10044, 11300, 1457, 10008])).
% 1.55/1.78 tff(11302,plain,
% 1.55/1.78 (b(s(s(z)), s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[135, 11301, 11296])).
% 1.55/1.78 tff(11303,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10054, 238, 8300, 227, 2258, 23])).
% 1.55/1.78 tff(11304,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11305,plain,
% 1.55/1.78 (~b(s(z), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11304, 11302, 10008])).
% 1.55/1.78 tff(11306,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 1.55/1.78 tff(11307,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.55/1.78 tff(11308,plain,
% 1.55/1.78 ($false),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[4557, 51, 11307, 11306, 7947])).
% 1.55/1.78 tff(11309,plain,(b(s(z), s(s(z))) | r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.78 tff(11310,plain,
% 1.55/1.78 (r(s(z), s(s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11309, 11305])).
% 1.55/1.78 tff(11311,plain,
% 1.55/1.78 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11290])).
% 1.55/1.78 tff(11312,plain,
% 1.55/1.78 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[11311])).
% 1.55/1.78 tff(11313,plain,
% 1.55/1.78 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11312])).
% 1.55/1.78 tff(11314,plain,
% 1.55/1.78 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[2106, 11291])).
% 1.55/1.78 tff(11315,plain,
% 1.55/1.78 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.55/1.78 inference(modus_ponens,[status(thm)],[11314, 11313])).
% 1.55/1.78 tff(11316,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11290])).
% 1.55/1.78 tff(11317,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.78 inference(symmetry,[status(thm)],[11316])).
% 1.55/1.78 tff(11318,plain,
% 1.55/1.78 (s(elem!1) = s(s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[10056, 11296, 1457, 10008])).
% 1.55/1.78 tff(11319,plain,
% 1.55/1.78 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[5343, 11318])).
% 1.55/1.78 tff(11320,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11319])).
% 1.55/1.78 tff(11321,plain,
% 1.55/1.78 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.78 inference(transitivity,[status(thm)],[11320, 11317])).
% 1.55/1.78 tff(11322,plain,
% 1.55/1.78 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.55/1.78 inference(monotonicity,[status(thm)],[11321])).
% 1.55/1.78 tff(11323,plain,
% 1.55/1.78 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 1.55/1.78 inference(unit_resolution,[status(thm)],[11076, 8300, 10004])).
% 1.55/1.79 tff(11324,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11323, 1457])).
% 1.55/1.79 tff(11325,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11324, 11322])).
% 1.55/1.79 tff(11326,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), elem!1)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1064, 11325, 11315])).
% 1.55/1.79 tff(11327,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[5296, 11326, 11290])).
% 1.55/1.79 tff(11328,plain,
% 1.55/1.79 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[7807, 11327, 10008, 11302])).
% 1.55/1.79 tff(11329,plain,
% 1.55/1.79 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1738, 11328])).
% 1.55/1.79 tff(11330,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11331,plain,
% 1.55/1.79 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11332,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11331])).
% 1.55/1.79 tff(11333,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11332, 11330])).
% 1.55/1.79 tff(11334,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11335,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11334, 11333])).
% 1.55/1.79 tff(11336,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11335, 124, 11329, 11310])).
% 1.55/1.79 tff(11337,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1781, 11336])).
% 1.55/1.79 tff(11338,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11339,plain,
% 1.55/1.79 (((~r(s(s(s(s(s(z))))), 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(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11340,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11339])).
% 1.55/1.79 tff(11341,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11340, 11338])).
% 1.55/1.79 tff(11342,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(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))))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11343,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11342, 11341])).
% 1.55/1.79 tff(11344,plain,
% 1.55/1.79 (~r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11343, 124, 11329, 11310])).
% 1.55/1.79 tff(11345,plain,
% 1.55/1.79 (b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1709, 11344])).
% 1.55/1.79 tff(11346,plain,
% 1.55/1.79 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1930, 8300])).
% 1.55/1.79 tff(11347,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11346, 11345, 11337, 1784])).
% 1.55/1.79 tff(11348,plain,(r(s(s(elem!1)), s(z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11349,plain,
% 1.55/1.79 (r(s(s(elem!1)), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11348, 1784, 1457, 81])).
% 1.55/1.79 tff(11350,plain,
% 1.55/1.79 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[9958, 238, 8300, 2258, 1784])).
% 1.55/1.79 tff(11351,plain,
% 1.55/1.79 (r(s(s(s(s(z)))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1564, 11350])).
% 1.55/1.79 tff(11352,plain,
% 1.55/1.79 (~b(z, s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[10041, 238, 8300, 2258, 1457])).
% 1.55/1.79 tff(11353,plain,
% 1.55/1.79 (r(z, s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1511, 51, 11352, 4848])).
% 1.55/1.79 tff(11354,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11355,plain,
% 1.55/1.79 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11356,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11355])).
% 1.55/1.79 tff(11357,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11356, 11354])).
% 1.55/1.79 tff(11358,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11359,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11358, 11357])).
% 1.55/1.79 tff(11360,plain,
% 1.55/1.79 (~b(z, s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11359, 238, 2258, 1457, 1784])).
% 1.55/1.79 tff(11361,plain,
% 1.55/1.79 (r(z, s(s(s(s(z)))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1487, 51, 11360, 7182])).
% 1.55/1.79 tff(11362,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3484, 11361, 11353, 11351])).
% 1.55/1.79 tff(11363,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11364,plain,
% 1.55/1.79 (~b(s(z), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11363, 1784, 1457])).
% 1.55/1.79 tff(11365,plain,
% 1.55/1.79 (r(s(z), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11309, 11364])).
% 1.55/1.79 tff(11366,plain,
% 1.55/1.79 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[10049, 11365])).
% 1.55/1.79 tff(11367,plain,
% 1.55/1.79 (b(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3233, 11366])).
% 1.55/1.79 tff(11368,plain,
% 1.55/1.79 (~r(s(z), s(s(s(s(s(z))))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11343, 124, 1717, 4560])).
% 1.55/1.79 tff(11369,plain,
% 1.55/1.79 (b(s(z), s(s(s(s(s(z))))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1709, 11368])).
% 1.55/1.79 tff(11370,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11371,plain,
% 1.55/1.79 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11372,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11371])).
% 1.55/1.79 tff(11373,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11372, 11370])).
% 1.55/1.79 tff(11374,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11375,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11374, 11373])).
% 1.55/1.79 tff(11376,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11375, 124, 160, 1717, 4560])).
% 1.55/1.79 tff(11377,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1781, 11376])).
% 1.55/1.79 tff(11378,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11346, 11377, 11369, 1784])).
% 1.55/1.79 tff(11379,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11380,plain,
% 1.55/1.79 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11379, 160, 1784, 11365])).
% 1.55/1.79 tff(11381,plain,
% 1.55/1.79 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1738, 11380])).
% 1.55/1.79 tff(11382,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(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(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(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(s(elem!1))))))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11383,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(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(s(elem!1))))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11384,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11383, 11382])).
% 1.55/1.79 tff(11385,plain,
% 1.55/1.79 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11384, 238, 8300, 1906, 1235])).
% 1.55/1.79 tff(11386,plain,
% 1.55/1.79 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1814, 11385, 1809])).
% 1.55/1.79 tff(11387,plain,
% 1.55/1.79 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11386])).
% 1.55/1.79 tff(11388,plain,
% 1.55/1.79 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.55/1.79 inference(transitivity,[status(thm)],[723, 11387, 88])).
% 1.55/1.79 tff(11389,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[5233, 11388])).
% 1.55/1.79 tff(11390,plain,((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11391,plain,
% 1.55/1.79 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11390, 11381, 11324, 11367])).
% 1.55/1.79 tff(11392,plain,
% 1.55/1.79 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[2893, 11391])).
% 1.55/1.79 tff(11393,plain,
% 1.55/1.79 (~(s(s(z)) = s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[4960, 11392])).
% 1.55/1.79 tff(11394,plain,
% 1.55/1.79 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[5222, 11393, 11391])).
% 1.55/1.79 tff(11395,plain,
% 1.55/1.79 (~(s(elem!1) = s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[357, 11393])).
% 1.55/1.79 tff(11396,plain,
% 1.55/1.79 (~r(s(s(z)), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[9625, 160, 11365])).
% 1.55/1.79 tff(11397,plain,
% 1.55/1.79 (b(s(s(z)), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[135, 11393, 11396])).
% 1.55/1.79 tff(11398,plain,
% 1.55/1.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[10022, 160])).
% 1.55/1.79 tff(11399,plain,
% 1.55/1.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[223, 209, 11398])).
% 1.55/1.79 tff(11400,plain,
% 1.55/1.79 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[10049, 4560])).
% 1.55/1.79 tff(11401,plain,
% 1.55/1.79 (b(s(s(s(elem!1))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[3233, 11400])).
% 1.55/1.79 tff(11402,plain,
% 1.55/1.79 (~b(s(s(elem!1)), elem!1)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[9632, 11399, 227, 11401])).
% 1.55/1.79 tff(11403,plain,
% 1.55/1.79 (r(s(s(elem!1)), elem!1)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[255, 11402, 167])).
% 1.55/1.79 tff(11404,plain,
% 1.55/1.79 (~r(elem!1, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[263, 11403, 162])).
% 1.55/1.79 tff(11405,plain,
% 1.55/1.79 (~r(s(z), elem!1)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[342, 11403, 160])).
% 1.55/1.79 tff(11406,plain,
% 1.55/1.79 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[223, 219, 10009])).
% 1.55/1.79 tff(11407,plain,
% 1.55/1.79 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[4743, 306, 161])).
% 1.55/1.79 tff(11408,plain,
% 1.55/1.79 (b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[539, 11407, 418])).
% 1.55/1.79 tff(11409,plain,
% 1.55/1.79 (b(s(elem!1), s(s(elem!1)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[534, 5966, 206])).
% 1.55/1.79 tff(11410,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[298, 11409, 11408, 11406, 7960])).
% 1.55/1.79 tff(11411,plain,((~r(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11412,plain,
% 1.55/1.79 ((~r(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11411, 10004])).
% 1.55/1.79 tff(11413,plain,
% 1.55/1.79 (~r(s(elem!1), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11412, 415, 162, 160, 159])).
% 1.55/1.79 tff(11414,plain,
% 1.55/1.79 (b(s(elem!1), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[473, 11413, 1])).
% 1.55/1.79 tff(11415,plain,
% 1.55/1.79 (b(s(z), elem!1)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[351, 2617, 346])).
% 1.55/1.79 tff(11416,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11417,plain,
% 1.55/1.79 (((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11418,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11417])).
% 1.55/1.79 tff(11419,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11418, 11416])).
% 1.55/1.79 tff(11420,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11421,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), elem!1))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11420, 11419])).
% 1.55/1.79 tff(11422,plain,
% 1.55/1.79 (~b(s(elem!1), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11421, 238, 8300, 1152, 11415])).
% 1.55/1.79 tff(11423,plain,
% 1.55/1.79 (b(elem!1, s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[363, 330, 359])).
% 1.55/1.79 tff(11424,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11425,plain,
% 1.55/1.79 (((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(rewrite,[status(thm)],[])).
% 1.55/1.79 tff(11426,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1))))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11425])).
% 1.55/1.79 tff(11427,plain,
% 1.55/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)))),
% 1.55/1.79 inference(transitivity,[status(thm)],[11426, 11424])).
% 1.55/1.79 tff(11428,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.55/1.79 inference(quant_inst,[status(thm)],[])).
% 1.55/1.79 tff(11429,plain,
% 1.55/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[11428, 11427])).
% 1.55/1.79 tff(11430,plain,
% 1.55/1.79 (~b(elem!1, s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11429, 238, 8300, 11423, 11415])).
% 1.55/1.79 tff(11431,plain,
% 1.55/1.79 (~r(s(elem!1), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[9713, 11430, 1457, 1152, 11415, 11423, 391])).
% 1.55/1.79 tff(11432,plain,
% 1.55/1.79 ($false),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[488, 11431, 11422, 3258])).
% 1.55/1.79 tff(11433,plain,((elem!1 = s(z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (elem!1 = s(elem!1)) | r(s(z), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.79 tff(11434,plain,
% 1.55/1.79 (elem!1 = s(z)),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[11433, 11414, 1457, 387, 11405, 11404])).
% 1.55/1.79 tff(11435,plain,
% 1.55/1.79 (s(elem!1) = s(s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[280, 11434])).
% 1.55/1.79 tff(11436,plain,
% 1.55/1.79 (~b(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[7971, 11434, 11402])).
% 1.55/1.79 tff(11437,plain,
% 1.55/1.79 (r(s(s(s(z))), s(z))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[5118, 11436])).
% 1.55/1.79 tff(11438,plain,
% 1.55/1.79 (~r(s(s(s(z))), s(s(z)))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[9648, 11437, 160, 4560])).
% 1.55/1.79 tff(11439,plain,
% 1.55/1.79 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[1442, 11438, 11435])).
% 1.55/1.79 tff(11440,plain,
% 1.55/1.79 (b(s(s(elem!1)), s(elem!1))),
% 1.55/1.79 inference(unit_resolution,[status(thm)],[323, 11439, 272])).
% 1.55/1.79 tff(11441,plain,
% 1.55/1.79 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.55/1.79 inference(monotonicity,[status(thm)],[11435])).
% 1.55/1.79 tff(11442,plain,
% 1.55/1.79 (b(s(s(z)), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.55/1.79 inference(symmetry,[status(thm)],[11441])).
% 1.55/1.79 tff(11443,plain,
% 1.55/1.79 (b(s(elem!1), s(s(elem!1)))),
% 1.55/1.79 inference(modus_ponens,[status(thm)],[227, 11442])).
% 1.55/1.80 tff(11444,plain,
% 1.55/1.80 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[298, 11443, 11440, 11399])).
% 1.55/1.80 tff(11445,plain,
% 1.55/1.80 (r(elem!1, s(s(s(elem!1))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[1368, 11434, 81])).
% 1.55/1.80 tff(11446,plain,
% 1.55/1.80 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 1.55/1.80 inference(monotonicity,[status(thm)],[11434])).
% 1.55/1.80 tff(11447,plain,
% 1.55/1.80 (r(s(z), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.55/1.80 inference(symmetry,[status(thm)],[11446])).
% 1.55/1.80 tff(11448,plain,
% 1.55/1.80 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 1.55/1.80 inference(monotonicity,[status(thm)],[11435])).
% 1.55/1.80 tff(11449,plain,
% 1.55/1.80 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 1.55/1.80 inference(symmetry,[status(thm)],[11448])).
% 1.55/1.80 tff(11450,plain,
% 1.55/1.80 (r(s(z), s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.55/1.80 inference(transitivity,[status(thm)],[11449, 11447])).
% 1.55/1.80 tff(11451,plain,
% 1.55/1.80 (r(elem!1, s(elem!1))),
% 1.55/1.80 inference(modus_ponens,[status(thm)],[4560, 11450])).
% 1.55/1.80 tff(11452,plain,
% 1.55/1.80 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[1329, 11451, 11445])).
% 1.55/1.80 tff(11453,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[539, 11452, 11444, 415])).
% 1.55/1.80 tff(11454,plain,((elem!1 = s(s(elem!1))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(11455,plain,
% 1.55/1.80 (elem!1 = s(s(elem!1))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11454, 11397, 11365, 160, 81, 1457, 11349, 11395])).
% 1.55/1.80 tff(11456,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[2097, 11455, 11394])).
% 1.55/1.80 tff(11457,plain,((~r(s(z), s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(11458,plain,
% 1.55/1.80 (~r(s(z), s(s(elem!1)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11457, 1784, 1457, 81])).
% 1.55/1.80 tff(11459,plain,
% 1.55/1.80 (b(s(z), s(s(elem!1)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[56, 11458])).
% 1.55/1.80 tff(11460,plain,
% 1.55/1.80 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[5363, 11459, 81])).
% 1.55/1.80 tff(11461,plain,
% 1.55/1.80 (~(s(elem!1) = s(s(elem!1)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[5343, 11460])).
% 1.55/1.80 tff(11462,plain,
% 1.55/1.80 (~r(s(s(elem!1)), s(elem!1))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[7927, 1137, 162, 358, 1457, 3294])).
% 1.55/1.80 tff(11463,plain,
% 1.55/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[10010, 1137, 114, 206, 1457])).
% 1.55/1.80 tff(11464,plain,
% 1.55/1.80 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(elem!1))))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[8902, 8300])).
% 1.55/1.80 tff(11465,plain,
% 1.55/1.80 (~b(s(s(elem!1)), s(elem!1))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11464, 11463, 1137])).
% 1.55/1.80 tff(11466,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[323, 11465, 11462, 3294])).
% 1.55/1.80 tff(11467,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(11468,plain,
% 1.55/1.80 (s(s(z)) = s(s(elem!1))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11467, 11461, 1457, 11459, 11349])).
% 1.55/1.80 tff(11469,plain,
% 1.55/1.80 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.55/1.80 inference(monotonicity,[status(thm)],[11468])).
% 1.55/1.80 tff(11470,plain,
% 1.55/1.80 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.55/1.80 inference(symmetry,[status(thm)],[11469])).
% 1.55/1.80 tff(11471,plain,
% 1.55/1.80 (b(s(z), s(s(z)))),
% 1.55/1.80 inference(modus_ponens,[status(thm)],[11459, 11470])).
% 1.55/1.80 tff(11472,plain,
% 1.55/1.80 ($false),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11364, 11471])).
% 1.55/1.80 tff(11473,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.80 tff(11474,plain,
% 1.55/1.80 (~b(s(s(s(s(z)))), s(z))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[11473, 1457, 81])).
% 1.55/1.80 tff(11475,plain,
% 1.55/1.80 (r(s(s(s(s(z)))), s(z))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[1624, 11474])).
% 1.55/1.80 tff(11476,plain,
% 1.55/1.80 (s(s(z)) = s(s(elem!1))),
% 1.55/1.80 inference(unit_resolution,[status(thm)],[10056, 10008, 1457, 10886])).
% 1.65/1.80 tff(11477,plain,
% 1.65/1.80 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11476])).
% 1.65/1.80 tff(11478,plain,
% 1.65/1.80 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11477])).
% 1.65/1.80 tff(11479,plain,
% 1.65/1.80 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(z)), s(z)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11478])).
% 1.65/1.80 tff(11480,plain,
% 1.65/1.80 (~r(s(s(z)), s(z))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[107, 11479])).
% 1.65/1.80 tff(11481,plain,
% 1.65/1.80 (s(elem!1) = s(z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[21, 11476])).
% 1.65/1.80 tff(11482,plain,
% 1.65/1.80 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11248, 11481])).
% 1.65/1.80 tff(11483,plain,
% 1.65/1.80 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11464, 11482, 57])).
% 1.65/1.80 tff(11484,plain,
% 1.65/1.80 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[4960, 11476])).
% 1.65/1.80 tff(11485,plain,
% 1.65/1.80 (~(s(s(z)) = elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1385, 11484])).
% 1.65/1.80 tff(11486,plain,
% 1.65/1.80 (r(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11244, 11485, 81, 24, 11483])).
% 1.65/1.80 tff(11487,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11486, 11480])).
% 1.65/1.80 tff(11488,plain,(r(s(s(elem!1)), s(z)) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11489,plain,
% 1.65/1.80 (r(s(s(elem!1)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11488, 24, 81, 1457])).
% 1.65/1.80 tff(11490,plain,
% 1.65/1.80 (s(s(z)) = s(s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11467, 11489, 1457, 57, 10886])).
% 1.65/1.80 tff(11491,plain,
% 1.65/1.80 (s(elem!1) = s(z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[21, 11490])).
% 1.65/1.80 tff(11492,plain,
% 1.65/1.80 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11248, 11491])).
% 1.65/1.80 tff(11493,plain,
% 1.65/1.80 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11464, 11492, 57])).
% 1.65/1.80 tff(11494,plain,
% 1.65/1.80 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[4960, 11490])).
% 1.65/1.80 tff(11495,plain,
% 1.65/1.80 (~(s(s(z)) = elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1385, 11494])).
% 1.65/1.80 tff(11496,plain,
% 1.65/1.80 (r(s(s(z)), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11244, 11495, 81, 24, 11493])).
% 1.65/1.80 tff(11497,plain,
% 1.65/1.80 (~r(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5185, 11496, 11475])).
% 1.65/1.80 tff(11498,plain,
% 1.65/1.80 (b(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5118, 11497])).
% 1.65/1.80 tff(11499,plain,
% 1.65/1.80 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11490])).
% 1.65/1.80 tff(11500,plain,
% 1.65/1.80 (b(s(s(elem!1)), s(z))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[8300, 11499])).
% 1.65/1.80 tff(11501,plain,
% 1.65/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11490])).
% 1.65/1.80 tff(11502,plain,
% 1.65/1.80 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.80 inference(transitivity,[status(thm)],[11501, 5720])).
% 1.65/1.80 tff(11503,plain,
% 1.65/1.80 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11502])).
% 1.65/1.80 tff(11504,plain,
% 1.65/1.80 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[147, 11503])).
% 1.65/1.80 tff(11505,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[7781, 11504, 11500, 1457, 57, 11498])).
% 1.65/1.80 tff(11506,plain,(r(s(z), s(s(elem!1))) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11507,plain,
% 1.65/1.80 (r(s(z), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11506, 1457, 81])).
% 1.65/1.80 tff(11508,plain,
% 1.65/1.80 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[10044, 23, 1457, 160])).
% 1.65/1.80 tff(11509,plain,
% 1.65/1.80 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[135, 114, 11508])).
% 1.65/1.80 tff(11510,plain,
% 1.65/1.80 (~b(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11304, 11509, 23])).
% 1.65/1.80 tff(11511,plain,
% 1.65/1.80 (r(s(z), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11309, 11510])).
% 1.65/1.80 tff(11512,plain,
% 1.65/1.80 (s(elem!1) = s(s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[10056, 114, 1457, 23])).
% 1.65/1.80 tff(11513,plain,
% 1.65/1.80 (elem!1 = s(s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[158, 11512])).
% 1.65/1.80 tff(11514,plain,
% 1.65/1.80 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2097, 11513])).
% 1.65/1.80 tff(11515,plain,
% 1.65/1.80 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5222, 11514, 114])).
% 1.65/1.80 tff(11516,plain,
% 1.65/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[10049, 11511])).
% 1.65/1.80 tff(11517,plain,
% 1.65/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3233, 11516])).
% 1.65/1.80 tff(11518,plain,
% 1.65/1.80 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11390, 11517, 11324, 11515])).
% 1.65/1.80 tff(11519,plain,
% 1.65/1.80 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1738, 11518])).
% 1.65/1.80 tff(11520,plain,
% 1.65/1.80 (~r(s(z), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11343, 124, 11519, 11511])).
% 1.65/1.80 tff(11521,plain,
% 1.65/1.80 (b(s(z), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1709, 11520])).
% 1.65/1.80 tff(11522,plain,
% 1.65/1.80 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11375, 124, 160, 11519, 11511])).
% 1.65/1.80 tff(11523,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1781, 11522])).
% 1.65/1.80 tff(11524,plain,
% 1.65/1.80 ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1872, 8300])).
% 1.65/1.80 tff(11525,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11524, 11523, 11521, 1457])).
% 1.65/1.80 tff(11526,plain,((s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11527,plain,
% 1.65/1.80 (s(s(z)) = s(s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11526, 23, 11507, 1457])).
% 1.65/1.80 tff(11528,plain,
% 1.65/1.80 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[4960, 11527])).
% 1.65/1.80 tff(11529,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1814, 11528, 11324])).
% 1.65/1.80 tff(11530,plain,
% 1.65/1.80 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3850, 11527])).
% 1.65/1.80 tff(11531,plain,
% 1.65/1.80 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[10022, 11507])).
% 1.65/1.80 tff(11532,plain,
% 1.65/1.80 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11527])).
% 1.65/1.80 tff(11533,plain,
% 1.65/1.80 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11532])).
% 1.65/1.80 tff(11534,plain,
% 1.65/1.80 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[1291, 11533])).
% 1.65/1.80 tff(11535,plain,
% 1.65/1.80 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[223, 11534, 11531])).
% 1.65/1.80 tff(11536,plain,
% 1.65/1.80 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11527])).
% 1.65/1.80 tff(11537,plain,
% 1.65/1.80 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.65/1.80 inference(transitivity,[status(thm)],[11536, 3730])).
% 1.65/1.80 tff(11538,plain,
% 1.65/1.80 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.80 inference(transitivity,[status(thm)],[11537, 4108])).
% 1.65/1.80 tff(11539,plain,
% 1.65/1.80 ((~(s(s(z)) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11538])).
% 1.65/1.80 tff(11540,plain,
% 1.65/1.80 (~(s(s(z)) = elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1385, 11528])).
% 1.65/1.80 tff(11541,plain,
% 1.65/1.80 (~(s(s(elem!1)) = elem!1)),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11540, 11539])).
% 1.65/1.80 tff(11542,plain,
% 1.65/1.80 (s(elem!1) = s(z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[21, 11527])).
% 1.65/1.80 tff(11543,plain,
% 1.65/1.80 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11537])).
% 1.65/1.80 tff(11544,plain,
% 1.65/1.80 (~(elem!1 = s(s(elem!1)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11540, 11543])).
% 1.65/1.80 tff(11545,plain,
% 1.65/1.80 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11248, 11542])).
% 1.65/1.80 tff(11546,plain,
% 1.65/1.80 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11542])).
% 1.65/1.80 tff(11547,plain,
% 1.65/1.80 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11546])).
% 1.65/1.80 tff(11548,plain,
% 1.65/1.80 (b(elem!1, s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6376, 11542, 1457])).
% 1.65/1.80 tff(11549,plain,
% 1.65/1.80 (b(elem!1, s(elem!1))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11548, 11547])).
% 1.65/1.80 tff(11550,plain,
% 1.65/1.80 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11542])).
% 1.65/1.80 tff(11551,plain,
% 1.65/1.80 (elem!1 = z),
% 1.65/1.80 inference(transitivity,[status(thm)],[155, 11550, 26])).
% 1.65/1.80 tff(11552,plain,
% 1.65/1.80 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11551])).
% 1.65/1.80 tff(11553,plain,
% 1.65/1.80 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.65/1.80 inference(transitivity,[status(thm)],[11552, 3716])).
% 1.65/1.80 tff(11554,plain,
% 1.65/1.80 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11553])).
% 1.65/1.80 tff(11555,plain,
% 1.65/1.80 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11554])).
% 1.65/1.80 tff(11556,plain,
% 1.65/1.80 (~(elem!1 = s(s(s(elem!1))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[821, 11555])).
% 1.65/1.80 tff(11557,plain,
% 1.65/1.80 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11542])).
% 1.65/1.80 tff(11558,plain,
% 1.65/1.80 ((elem!1 = s(z)) <=> (elem!1 = s(elem!1))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11557])).
% 1.65/1.80 tff(11559,plain,
% 1.65/1.80 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11551])).
% 1.65/1.80 tff(11560,plain,
% 1.65/1.80 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.65/1.80 inference(transitivity,[status(thm)],[11559, 2036])).
% 1.65/1.80 tff(11561,plain,
% 1.65/1.80 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11560])).
% 1.65/1.80 tff(11562,plain,
% 1.65/1.80 ((s(z) = z) <=> (s(elem!1) = elem!1)),
% 1.65/1.80 inference(transitivity,[status(thm)],[11561, 11558, 2902])).
% 1.65/1.80 tff(11563,plain,
% 1.65/1.80 ((~(s(z) = z)) <=> (~(s(elem!1) = elem!1))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11562])).
% 1.65/1.80 tff(11564,plain,
% 1.65/1.80 (~(s(elem!1) = elem!1)),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[72, 11563])).
% 1.65/1.80 tff(11565,plain,
% 1.65/1.80 (r(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[10069, 11542, 81])).
% 1.65/1.80 tff(11566,plain,
% 1.65/1.80 (~b(elem!1, s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3306, 1185, 289, 226])).
% 1.65/1.80 tff(11567,plain,
% 1.65/1.80 (r(elem!1, s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1319, 11566, 514])).
% 1.65/1.80 tff(11568,plain,
% 1.65/1.80 (~b(s(elem!1), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5551, 1185, 631, 289])).
% 1.65/1.80 tff(11569,plain,
% 1.65/1.80 (r(s(elem!1), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[408, 11568, 632])).
% 1.65/1.80 tff(11570,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3315, 11569, 11567, 542])).
% 1.65/1.80 tff(11571,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(elem!1) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11572,plain,
% 1.65/1.80 (~b(elem!1, s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11571, 11565, 11564, 11556, 11549, 11545, 11535])).
% 1.65/1.80 tff(11573,plain,
% 1.65/1.80 (r(elem!1, s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[606, 11572, 11544])).
% 1.65/1.80 tff(11574,plain,
% 1.65/1.80 (r(z, s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[7136, 11573, 11542])).
% 1.65/1.80 tff(11575,plain,
% 1.65/1.80 (~r(s(z), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[6136, 124, 11507, 11574])).
% 1.65/1.80 tff(11576,plain,
% 1.65/1.80 (b(s(z), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5701, 11575])).
% 1.65/1.80 tff(11577,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(11578,plain,
% 1.65/1.80 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(11579,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11578])).
% 1.65/1.80 tff(11580,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.65/1.80 inference(transitivity,[status(thm)],[11579, 11577])).
% 1.65/1.80 tff(11581,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(11582,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11581, 11580])).
% 1.65/1.80 tff(11583,plain,
% 1.65/1.80 (~b(s(s(elem!1)), z)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11582, 238, 23, 1457, 11576])).
% 1.65/1.80 tff(11584,plain,
% 1.65/1.80 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 1.65/1.80 inference(monotonicity,[status(thm)],[3762])).
% 1.65/1.80 tff(11585,plain,
% 1.65/1.80 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.65/1.80 inference(symmetry,[status(thm)],[11584])).
% 1.65/1.80 tff(11586,plain,
% 1.65/1.80 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11585])).
% 1.65/1.80 tff(11587,plain,
% 1.65/1.80 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[4903, 11586])).
% 1.65/1.80 tff(11588,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[228, 11587])).
% 1.65/1.80 tff(11589,plain,((~b(s(s(elem!1)), elem!1)) | b(s(s(elem!1)), z) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11590,plain,
% 1.65/1.80 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11589, 11583, 11542])).
% 1.65/1.80 tff(11591,plain,
% 1.65/1.80 (r(s(s(elem!1)), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[255, 11590, 11541])).
% 1.65/1.80 tff(11592,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 1.65/1.80 inference(monotonicity,[status(thm)],[3762])).
% 1.65/1.80 tff(11593,plain,
% 1.65/1.80 (~b(s(z), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11524, 1783, 1457])).
% 1.65/1.80 tff(11594,plain,
% 1.65/1.80 (r(s(z), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1709, 11593])).
% 1.65/1.80 tff(11595,plain,
% 1.65/1.80 (~r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2016, 11594, 160])).
% 1.65/1.80 tff(11596,plain,
% 1.65/1.80 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[7528, 11595, 226, 2417, 1040])).
% 1.65/1.80 tff(11597,plain,
% 1.65/1.80 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[7489, 11596, 301])).
% 1.65/1.80 tff(11598,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1064, 11597, 7187])).
% 1.65/1.80 tff(11599,plain,
% 1.65/1.80 (b(s(s(s(s(s(z))))), z)),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11598, 11592])).
% 1.65/1.80 tff(11600,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(11601,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(11602,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11601, 11600])).
% 1.65/1.80 tff(11603,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11602, 238, 1457, 1783, 6925, 11599])).
% 1.65/1.80 tff(11604,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~(s(elem!1) = s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11605,plain,
% 1.65/1.80 (~b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11604, 11576, 1457, 11542, 11591, 11535, 11530, 11529, 11507])).
% 1.65/1.80 tff(11606,plain,
% 1.65/1.80 (r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1781, 11605])).
% 1.65/1.80 tff(11607,plain,
% 1.65/1.80 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3955, 124, 11606, 11475])).
% 1.65/1.80 tff(11608,plain,
% 1.65/1.80 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2893, 11528])).
% 1.65/1.80 tff(11609,plain,
% 1.65/1.80 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11527])).
% 1.65/1.80 tff(11610,plain,
% 1.65/1.80 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11609])).
% 1.65/1.80 tff(11611,plain,
% 1.65/1.80 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(z))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11610])).
% 1.65/1.80 tff(11612,plain,
% 1.65/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11531, 11611])).
% 1.65/1.80 tff(11613,plain,
% 1.65/1.80 (b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3233, 11612])).
% 1.65/1.80 tff(11614,plain,
% 1.65/1.80 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11390, 11613, 11324, 11608])).
% 1.65/1.80 tff(11615,plain,
% 1.65/1.80 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1738, 11614])).
% 1.65/1.80 tff(11616,plain,
% 1.65/1.80 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11527])).
% 1.65/1.80 tff(11617,plain,
% 1.65/1.80 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11616, 11527])).
% 1.65/1.80 tff(11618,plain,
% 1.65/1.80 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11617])).
% 1.65/1.80 tff(11619,plain,
% 1.65/1.80 (b(s(s(s(z))), s(s(z)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11535, 11618])).
% 1.65/1.80 tff(11620,plain,
% 1.65/1.80 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11616])).
% 1.65/1.80 tff(11621,plain,
% 1.65/1.80 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11620])).
% 1.65/1.80 tff(11622,plain,
% 1.65/1.80 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11621])).
% 1.65/1.80 tff(11623,plain,
% 1.65/1.80 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11616])).
% 1.65/1.80 tff(11624,plain,
% 1.65/1.80 ((s(elem!1) = s(s(elem!1))) <=> (s(z) = s(s(elem!1)))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11542])).
% 1.65/1.80 tff(11625,plain,
% 1.65/1.80 ((s(z) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11624])).
% 1.65/1.80 tff(11626,plain,
% 1.65/1.80 ((~(s(z) = s(s(elem!1)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11625])).
% 1.65/1.80 tff(11627,plain,
% 1.65/1.80 (~(s(elem!1) = s(s(elem!1)))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[41, 11626])).
% 1.65/1.80 tff(11628,plain,
% 1.65/1.80 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.65/1.80 inference(transitivity,[status(thm)],[8092, 8094])).
% 1.65/1.80 tff(11629,plain,
% 1.65/1.80 (b(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[564, 8158])).
% 1.65/1.80 tff(11630,plain,
% 1.65/1.80 (~b(s(s(s(elem!1))), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1222, 11629, 248, 631, 206, 226])).
% 1.65/1.80 tff(11631,plain,
% 1.65/1.80 (r(s(s(s(elem!1))), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[647, 11630, 7122])).
% 1.65/1.80 tff(11632,plain,
% 1.65/1.80 (~r(s(elem!1), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[657, 11631, 542])).
% 1.65/1.80 tff(11633,plain,
% 1.65/1.80 (b(s(elem!1), elem!1)),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[408, 11632, 1213])).
% 1.65/1.80 tff(11634,plain,
% 1.65/1.80 (b(s(z), z)),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11633, 11628])).
% 1.65/1.80 tff(11635,plain,
% 1.65/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.80 inference(rewrite,[status(thm)],[])).
% 1.65/1.80 tff(11636,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.80 inference(quant_inst,[status(thm)],[])).
% 1.65/1.80 tff(11637,plain,
% 1.65/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11636, 11635])).
% 1.65/1.80 tff(11638,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11637, 238, 226, 564, 23, 11634])).
% 1.65/1.80 tff(11639,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(elem!1), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(elem!1))) | (s(elem!1) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.80 tff(11640,plain,
% 1.65/1.80 (~b(s(s(s(elem!1))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[11639, 11535, 23, 11542, 11565, 11541, 11549, 11627])).
% 1.65/1.80 tff(11641,plain,
% 1.65/1.80 (~b(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[3886, 11640, 11527])).
% 1.65/1.80 tff(11642,plain,
% 1.65/1.80 (r(s(s(s(z))), s(z))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5118, 11641])).
% 1.65/1.80 tff(11643,plain,
% 1.65/1.80 (r(s(s(s(elem!1))), s(z))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11642, 11623])).
% 1.65/1.80 tff(11644,plain,
% 1.65/1.80 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[2970, 124, 11475, 11643])).
% 1.65/1.80 tff(11645,plain,
% 1.65/1.80 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11644, 11622])).
% 1.65/1.80 tff(11646,plain,
% 1.65/1.80 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5176, 11645])).
% 1.65/1.80 tff(11647,plain,
% 1.65/1.80 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.65/1.80 inference(symmetry,[status(thm)],[11616])).
% 1.65/1.80 tff(11648,plain,
% 1.65/1.80 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11647])).
% 1.65/1.80 tff(11649,plain,
% 1.65/1.80 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.65/1.80 inference(monotonicity,[status(thm)],[11648])).
% 1.65/1.80 tff(11650,plain,
% 1.65/1.80 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[9285, 124, 11475, 11643])).
% 1.65/1.80 tff(11651,plain,
% 1.65/1.80 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.80 inference(modus_ponens,[status(thm)],[11650, 11649])).
% 1.65/1.80 tff(11652,plain,
% 1.65/1.80 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[5167, 11651])).
% 1.65/1.80 tff(11653,plain,
% 1.65/1.80 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[9652, 11652, 11646, 11619])).
% 1.65/1.80 tff(11654,plain,
% 1.65/1.80 (r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[1604, 11653])).
% 1.65/1.80 tff(11655,plain,
% 1.65/1.80 ($false),
% 1.65/1.80 inference(unit_resolution,[status(thm)],[8503, 124, 1717, 1652, 11213])).
% 1.65/1.81 tff(11656,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(11657,plain,
% 1.65/1.81 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11656, 11654, 11615])).
% 1.65/1.81 tff(11658,plain,
% 1.65/1.81 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5751, 11529, 11527])).
% 1.65/1.81 tff(11659,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11616])).
% 1.65/1.81 tff(11660,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11652, 11659])).
% 1.65/1.81 tff(11661,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.81 tff(11662,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.65/1.81 tff(11663,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.81 tff(11664,plain,
% 1.65/1.81 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1902, 51, 1668, 11663])).
% 1.65/1.81 tff(11665,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11666,plain,
% 1.65/1.81 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11667,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11666])).
% 1.65/1.81 tff(11668,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[11667, 11665])).
% 1.65/1.81 tff(11669,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(11670,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11669, 11668])).
% 1.65/1.81 tff(11671,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11670, 238, 11664, 11662, 11661, 1080])).
% 1.65/1.81 tff(11672,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(11673,plain,
% 1.65/1.81 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(s(z)) = s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11672, 1898])).
% 1.65/1.81 tff(11674,plain,
% 1.65/1.81 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11673, 11660, 11527, 11658, 11657])).
% 1.65/1.81 tff(11675,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1051, 51, 11674, 11607, 2782])).
% 1.65/1.81 tff(11676,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(11677,plain,
% 1.65/1.81 (~b(s(s(elem!1)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11676, 1457, 81])).
% 1.65/1.81 tff(11678,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[112, 11677])).
% 1.65/1.81 tff(11679,plain,
% 1.65/1.81 (r(s(s(z)), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[135, 2213, 22])).
% 1.65/1.81 tff(11680,plain,
% 1.65/1.81 (~r(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[9625, 11679, 11507])).
% 1.65/1.81 tff(11681,plain,
% 1.65/1.81 (b(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11309, 11680])).
% 1.65/1.81 tff(11682,plain,
% 1.65/1.81 (~b(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[10041, 238, 8300, 11681, 1457])).
% 1.65/1.81 tff(11683,plain,
% 1.65/1.81 (r(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1511, 51, 11682, 4848])).
% 1.65/1.81 tff(11684,plain,
% 1.65/1.81 (~r(z, s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[9101, 11683, 11679])).
% 1.65/1.81 tff(11685,plain,
% 1.65/1.81 (b(z, s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2071, 11684])).
% 1.65/1.81 tff(11686,plain,
% 1.65/1.81 (~r(s(elem!1), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11412, 415, 11678, 11507, 206])).
% 1.65/1.81 tff(11687,plain,
% 1.65/1.81 (b(s(elem!1), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[473, 11686, 1])).
% 1.65/1.81 tff(11688,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11689,plain,
% 1.65/1.81 (((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11690,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11689])).
% 1.65/1.81 tff(11691,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[11690, 11688])).
% 1.65/1.81 tff(11692,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(11693,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11692, 11691])).
% 1.65/1.81 tff(11694,plain,
% 1.65/1.81 (~b(s(elem!1), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11693, 238, 8300, 11687, 11681])).
% 1.65/1.81 tff(11695,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11696,plain,
% 1.65/1.81 (((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11697,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11696])).
% 1.65/1.81 tff(11698,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[11697, 11695])).
% 1.65/1.81 tff(11699,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(elem!1))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(11700,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(elem!1)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11699, 11698])).
% 1.65/1.81 tff(11701,plain,
% 1.65/1.81 (~b(z, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11700, 238, 11687, 11681, 1457])).
% 1.65/1.81 tff(11702,plain,
% 1.65/1.81 (r(z, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3115, 51, 4923, 11701])).
% 1.65/1.81 tff(11703,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11704,plain,
% 1.65/1.81 (((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11705,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11704])).
% 1.65/1.81 tff(11706,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[11705, 11703])).
% 1.65/1.81 tff(11707,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(elem!1))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(11708,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11707, 11706])).
% 1.65/1.81 tff(11709,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11708, 124, 475, 1575, 4938])).
% 1.65/1.81 tff(11710,plain,((~r(s(elem!1), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(11711,plain,
% 1.65/1.81 (~r(s(elem!1), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11710, 11702, 11683])).
% 1.65/1.81 tff(11712,plain,
% 1.65/1.81 (s(elem!1) = s(s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[488, 11711, 11694])).
% 1.65/1.81 tff(11713,plain,
% 1.65/1.81 (s(s(elem!1)) = s(s(s(z)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11712])).
% 1.65/1.81 tff(11714,plain,
% 1.65/1.81 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11713])).
% 1.65/1.81 tff(11715,plain,
% 1.65/1.81 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11714])).
% 1.65/1.81 tff(11716,plain,
% 1.65/1.81 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11715])).
% 1.65/1.81 tff(11717,plain,
% 1.65/1.81 (~r(s(s(z)), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[200, 11679, 11507])).
% 1.65/1.81 tff(11718,plain,
% 1.65/1.81 (s(s(z)) = elem!1),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11244, 24, 10090, 81, 2213])).
% 1.65/1.81 tff(11719,plain,
% 1.65/1.81 (elem!1 = s(s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1231, 11718])).
% 1.65/1.81 tff(11720,plain,
% 1.65/1.81 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(z)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11719])).
% 1.65/1.81 tff(11721,plain,
% 1.65/1.81 (b(s(elem!1), s(s(z))) <=> b(s(elem!1), elem!1)),
% 1.65/1.81 inference(symmetry,[status(thm)],[11720])).
% 1.65/1.81 tff(11722,plain,
% 1.65/1.81 (s(elem!1) = s(s(s(z)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11719])).
% 1.65/1.81 tff(11723,plain,
% 1.65/1.81 (b(s(elem!1), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11722])).
% 1.65/1.81 tff(11724,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11723])).
% 1.65/1.81 tff(11725,plain,
% 1.65/1.81 (b(s(s(s(z))), s(s(z))) <=> b(s(elem!1), elem!1)),
% 1.65/1.81 inference(transitivity,[status(thm)],[11724, 11721])).
% 1.65/1.81 tff(11726,plain,
% 1.65/1.81 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(elem!1), elem!1))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11725])).
% 1.65/1.81 tff(11727,plain,
% 1.65/1.81 (~b(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[9617, 57, 1817, 159, 114, 2213])).
% 1.65/1.81 tff(11728,plain,
% 1.65/1.81 (r(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1542, 11727])).
% 1.65/1.81 tff(11729,plain,
% 1.65/1.81 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11722])).
% 1.65/1.81 tff(11730,plain,
% 1.65/1.81 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11729])).
% 1.65/1.81 tff(11731,plain,
% 1.65/1.81 (r(z, s(s(s(s(z))))) <=> r(z, s(s(elem!1)))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11730])).
% 1.65/1.81 tff(11732,plain,
% 1.65/1.81 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(s(elem!1))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11731])).
% 1.65/1.81 tff(11733,plain,
% 1.65/1.81 (~r(z, s(s(s(s(z)))))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1571, 124, 1544, 11728])).
% 1.65/1.81 tff(11734,plain,
% 1.65/1.81 (~r(z, s(s(elem!1)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11733, 11732])).
% 1.65/1.81 tff(11735,plain,
% 1.65/1.81 (b(z, s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[2071, 11734])).
% 1.65/1.81 tff(11736,plain,
% 1.65/1.81 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11722])).
% 1.65/1.81 tff(11737,plain,
% 1.65/1.81 ((~(s(elem!1) = s(s(elem!1)))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11736])).
% 1.65/1.81 tff(11738,plain,
% 1.65/1.81 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[159, 11737])).
% 1.65/1.81 tff(11739,plain,
% 1.65/1.81 (b(s(s(elem!1)), z) <=> b(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11729])).
% 1.65/1.81 tff(11740,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.65/1.81 inference(symmetry,[status(thm)],[11739])).
% 1.65/1.81 tff(11741,plain,
% 1.65/1.81 (~r(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1938, 124, 1544, 11728])).
% 1.65/1.81 tff(11742,plain,
% 1.65/1.81 (b(s(s(s(s(z)))), z)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1499, 51, 726, 11741])).
% 1.65/1.81 tff(11743,plain,
% 1.65/1.81 (b(s(s(elem!1)), z)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11742, 11740])).
% 1.65/1.81 tff(11744,plain,
% 1.65/1.81 (~r(s(s(s(z))), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5741, 11743, 162, 11738, 11735, 11728])).
% 1.65/1.81 tff(11745,plain,
% 1.65/1.81 (b(s(s(s(z))), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[5118, 11744])).
% 1.65/1.81 tff(11746,plain,
% 1.65/1.81 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11729])).
% 1.65/1.81 tff(11747,plain,
% 1.65/1.81 (b(s(z), s(s(s(s(z)))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[57, 11746])).
% 1.65/1.81 tff(11748,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11749,plain,
% 1.65/1.81 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.81 inference(rewrite,[status(thm)],[])).
% 1.65/1.81 tff(11750,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11749])).
% 1.65/1.81 tff(11751,plain,
% 1.65/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.81 inference(transitivity,[status(thm)],[11750, 11748])).
% 1.65/1.81 tff(11752,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.65/1.81 inference(quant_inst,[status(thm)],[])).
% 1.65/1.81 tff(11753,plain,
% 1.65/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11752, 11751])).
% 1.65/1.81 tff(11754,plain,
% 1.65/1.81 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11753, 238, 1817, 11747, 11745])).
% 1.65/1.81 tff(11755,plain,
% 1.65/1.81 (~b(s(elem!1), elem!1)),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11754, 11726])).
% 1.65/1.81 tff(11756,plain,
% 1.65/1.81 (b(elem!1, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[8974, 11719, 1817])).
% 1.65/1.81 tff(11757,plain,
% 1.65/1.81 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11722])).
% 1.65/1.81 tff(11758,plain,
% 1.65/1.81 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11757])).
% 1.65/1.81 tff(11759,plain,
% 1.65/1.81 (b(s(elem!1), s(z))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11745, 11758])).
% 1.65/1.81 tff(11760,plain,
% 1.65/1.81 (~b(elem!1, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1160, 11759, 11756, 57])).
% 1.65/1.81 tff(11761,plain,
% 1.65/1.81 (r(elem!1, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[629, 11760, 387])).
% 1.65/1.81 tff(11762,plain,
% 1.65/1.81 (r(elem!1, s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11719])).
% 1.65/1.81 tff(11763,plain,
% 1.65/1.81 (r(s(s(z)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11762])).
% 1.65/1.81 tff(11764,plain,
% 1.65/1.81 (r(s(s(z)), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[135, 2213, 114])).
% 1.65/1.81 tff(11765,plain,
% 1.65/1.81 (r(elem!1, s(s(elem!1)))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[11764, 11763])).
% 1.65/1.81 tff(11766,plain,
% 1.65/1.81 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1149, 11761, 150, 57, 11756])).
% 1.65/1.81 tff(11767,plain,
% 1.65/1.81 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[323, 11766, 272])).
% 1.65/1.81 tff(11768,plain,
% 1.65/1.81 (~b(s(elem!1), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[4533, 11767, 57, 11759])).
% 1.65/1.81 tff(11769,plain,
% 1.65/1.81 (r(s(elem!1), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[534, 11768, 159])).
% 1.65/1.81 tff(11770,plain,
% 1.65/1.81 (~r(s(elem!1), elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[4590, 11769, 11765, 11761])).
% 1.65/1.81 tff(11771,plain,
% 1.65/1.81 (b(s(elem!1), elem!1)),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[408, 11770, 394])).
% 1.65/1.81 tff(11772,plain,
% 1.65/1.81 ($false),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11771, 11755])).
% 1.65/1.81 tff(11773,plain,(r(s(z), s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(z)) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.81 tff(11774,plain,
% 1.65/1.81 (r(s(z), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11773, 2213, 1817, 162, 1544, 114, 150, 10090, 81])).
% 1.65/1.81 tff(11775,plain,
% 1.65/1.81 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[218, 11774, 102])).
% 1.65/1.81 tff(11776,plain,
% 1.65/1.81 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[223, 11775, 209])).
% 1.65/1.81 tff(11777,plain,
% 1.65/1.81 (~r(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[8143, 11776, 162, 102, 11774])).
% 1.65/1.81 tff(11778,plain,
% 1.65/1.81 (b(z, s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1542, 11777])).
% 1.65/1.81 tff(11779,plain,
% 1.65/1.81 (~r(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[8913, 124, 11774, 11764])).
% 1.65/1.81 tff(11780,plain,
% 1.65/1.81 (b(s(z), s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[4557, 51, 11779, 7947])).
% 1.65/1.81 tff(11781,plain,
% 1.65/1.81 (~r(s(elem!1), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11411, 11774, 415, 159, 102, 162])).
% 1.65/1.81 tff(11782,plain,
% 1.65/1.81 (b(s(elem!1), s(z))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[473, 11781, 358])).
% 1.65/1.81 tff(11783,plain,
% 1.65/1.81 (~b(z, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[11700, 238, 11782, 11780, 11778])).
% 1.65/1.81 tff(11784,plain,
% 1.65/1.81 (r(z, s(elem!1))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[3115, 51, 4923, 11783])).
% 1.65/1.81 tff(11785,plain,
% 1.65/1.81 (~b(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[10041, 238, 1817, 11780, 11778])).
% 1.65/1.81 tff(11786,plain,
% 1.65/1.81 (r(z, s(s(z)))),
% 1.65/1.81 inference(unit_resolution,[status(thm)],[1511, 51, 11785, 4848])).
% 1.65/1.81 tff(11787,plain,
% 1.65/1.81 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[1436])).
% 1.65/1.81 tff(11788,plain,
% 1.65/1.81 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.65/1.81 inference(symmetry,[status(thm)],[11787])).
% 1.65/1.81 tff(11789,plain,
% 1.65/1.81 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.81 inference(modus_ponens,[status(thm)],[192, 11788])).
% 1.65/1.81 tff(11790,plain,
% 1.65/1.81 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[1435])).
% 1.65/1.81 tff(11791,plain,
% 1.65/1.81 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.65/1.81 inference(monotonicity,[status(thm)],[11790])).
% 1.65/1.81 tff(11792,assumption,(~r(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.82 tff(11793,plain,
% 1.65/1.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11792, 11791])).
% 1.65/1.82 tff(11794,plain,
% 1.65/1.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5167, 11793])).
% 1.65/1.82 tff(11795,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2405, 375, 226])).
% 1.65/1.82 tff(11796,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11797,plain,
% 1.65/1.82 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11798,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11797])).
% 1.65/1.82 tff(11799,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11798, 11796])).
% 1.65/1.82 tff(11800,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11801,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11800, 11799])).
% 1.65/1.82 tff(11802,plain,
% 1.65/1.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11801, 238, 11795, 1786, 11794])).
% 1.65/1.82 tff(11803,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1101, 11802])).
% 1.65/1.82 tff(11804,plain,
% 1.65/1.82 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[4329, 11803, 11789])).
% 1.65/1.82 tff(11805,plain,
% 1.65/1.82 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1738, 11804])).
% 1.65/1.82 tff(11806,plain,
% 1.65/1.82 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[1435])).
% 1.65/1.82 tff(11807,plain,
% 1.65/1.82 (r(s(z), s(s(s(z))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[160, 11806])).
% 1.65/1.82 tff(11808,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11809,plain,
% 1.65/1.82 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11810,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11809])).
% 1.65/1.82 tff(11811,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11810, 11808])).
% 1.65/1.82 tff(11812,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11813,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11812, 11811])).
% 1.65/1.82 tff(11814,plain,
% 1.65/1.82 (~r(s(z), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11813, 124, 11803, 11807])).
% 1.65/1.82 tff(11815,plain,
% 1.65/1.82 (b(s(z), s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1709, 11814])).
% 1.65/1.82 tff(11816,plain,
% 1.65/1.82 (r(s(z), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[161, 3392])).
% 1.65/1.82 tff(11817,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11818,plain,
% 1.65/1.82 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(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(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11819,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11818])).
% 1.65/1.82 tff(11820,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11819, 11817])).
% 1.65/1.82 tff(11821,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11822,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11821, 11820])).
% 1.65/1.82 tff(11823,plain,
% 1.65/1.82 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11822, 124, 11816, 11803, 11807])).
% 1.65/1.82 tff(11824,plain,
% 1.65/1.82 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1781, 11823])).
% 1.65/1.82 tff(11825,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1908, 11824, 11815, 1817, 11805])).
% 1.65/1.82 tff(11826,plain,((~(s(elem!1) = s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11827,plain,
% 1.65/1.82 (~(s(elem!1) = s(s(z)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11826, 7232, 1786, 102, 1817, 11764, 11774, 11776])).
% 1.65/1.82 tff(11828,plain,
% 1.65/1.82 (~b(s(elem!1), s(s(z)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11693, 238, 1817, 11782, 11780])).
% 1.65/1.82 tff(11829,plain,
% 1.65/1.82 (r(s(elem!1), s(s(z)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[488, 11828, 11827])).
% 1.65/1.82 tff(11830,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11708, 124, 11829, 11786, 11784])).
% 1.65/1.82 tff(11831,plain,(b(s(s(z)), s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(s(s(z)), s(z)) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11832,plain,
% 1.65/1.82 (b(s(s(z)), s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(s(s(z)), s(z)) | b(s(z), s(s(s(elem!1))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11831, 8300])).
% 1.65/1.82 tff(11833,plain,
% 1.65/1.82 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11832, 150, 81, 11475, 11678, 22, 2213, 11717])).
% 1.65/1.82 tff(11834,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1904, 11833])).
% 1.65/1.82 tff(11835,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11834, 11716])).
% 1.65/1.82 tff(11836,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11324, 11835])).
% 1.65/1.82 tff(11837,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11838,plain,
% 1.65/1.82 (elem!1 = s(s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11837, 206, 1, 1457, 81, 2213])).
% 1.65/1.82 tff(11839,plain,
% 1.65/1.82 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11838])).
% 1.65/1.82 tff(11840,plain,
% 1.65/1.82 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.82 inference(commutativity,[status(thm)],[])).
% 1.65/1.82 tff(11841,plain,
% 1.65/1.82 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11838])).
% 1.65/1.82 tff(11842,plain,
% 1.65/1.82 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11841, 11840])).
% 1.65/1.82 tff(11843,plain,
% 1.65/1.82 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11842])).
% 1.65/1.82 tff(11844,plain,
% 1.65/1.82 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11843])).
% 1.65/1.82 tff(11845,plain,
% 1.65/1.82 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2097, 11838])).
% 1.65/1.82 tff(11846,plain,
% 1.65/1.82 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5222, 11845, 22])).
% 1.65/1.82 tff(11847,plain,
% 1.65/1.82 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11846, 11844])).
% 1.65/1.82 tff(11848,plain,
% 1.65/1.82 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11838])).
% 1.65/1.82 tff(11849,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11848])).
% 1.65/1.82 tff(11850,plain,
% 1.65/1.82 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11849])).
% 1.65/1.82 tff(11851,plain,
% 1.65/1.82 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7231, 124, 11678, 11475])).
% 1.65/1.82 tff(11852,plain,
% 1.65/1.82 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11851, 11850])).
% 1.65/1.82 tff(11853,plain,
% 1.65/1.82 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[935, 11852, 11847])).
% 1.65/1.82 tff(11854,plain,
% 1.65/1.82 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11853, 11839])).
% 1.65/1.82 tff(11855,plain,
% 1.65/1.82 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2958, 124, 11678, 11475])).
% 1.65/1.82 tff(11856,plain,
% 1.65/1.82 ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5236, 51, 11855])).
% 1.65/1.82 tff(11857,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11856, 11846])).
% 1.65/1.82 tff(11858,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11859,plain,
% 1.65/1.82 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11860,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11859])).
% 1.65/1.82 tff(11861,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11860, 11858])).
% 1.65/1.82 tff(11862,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11863,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11862, 11861])).
% 1.65/1.82 tff(11864,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11863, 124, 160, 1544, 861, 10004])).
% 1.65/1.82 tff(11865,plain,((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11866,plain,
% 1.65/1.82 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11865, 11507, 11475])).
% 1.65/1.82 tff(11867,plain,
% 1.65/1.82 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2879, 11845])).
% 1.65/1.82 tff(11868,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[8247, 11867, 11866])).
% 1.65/1.82 tff(11869,plain,
% 1.65/1.82 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[223, 10009, 11531])).
% 1.65/1.82 tff(11870,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[7429, 238, 11869, 11868, 11857, 11854])).
% 1.65/1.82 tff(11871,plain,((s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11872,plain,
% 1.65/1.82 (s(elem!1) = s(s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11871, 2213, 1457, 81, 1])).
% 1.65/1.82 tff(11873,plain,
% 1.65/1.82 (elem!1 = s(s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[158, 11872])).
% 1.65/1.82 tff(11874,plain,
% 1.65/1.82 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11873])).
% 1.65/1.82 tff(11875,plain,
% 1.65/1.82 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.82 inference(symmetry,[status(thm)],[11874])).
% 1.65/1.82 tff(11876,plain,
% 1.65/1.82 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11875])).
% 1.65/1.82 tff(11877,plain,
% 1.65/1.82 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2097, 11873])).
% 1.65/1.82 tff(11878,plain,
% 1.65/1.82 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2106, 11877])).
% 1.65/1.82 tff(11879,plain,
% 1.65/1.82 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11878, 11876])).
% 1.65/1.82 tff(11880,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11873])).
% 1.65/1.82 tff(11881,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.82 inference(symmetry,[status(thm)],[11880])).
% 1.65/1.82 tff(11882,plain,
% 1.65/1.82 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5343, 11872])).
% 1.65/1.82 tff(11883,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11882])).
% 1.65/1.82 tff(11884,plain,
% 1.65/1.82 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.82 inference(transitivity,[status(thm)],[11883, 11881])).
% 1.65/1.82 tff(11885,plain,
% 1.65/1.82 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11884])).
% 1.65/1.82 tff(11886,plain,
% 1.65/1.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11324, 11885])).
% 1.65/1.82 tff(11887,plain,
% 1.65/1.82 (b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1064, 11886, 11879])).
% 1.65/1.82 tff(11888,plain,
% 1.65/1.82 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5296, 11887, 11873])).
% 1.65/1.82 tff(11889,plain,
% 1.65/1.82 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11873])).
% 1.65/1.82 tff(11890,plain,
% 1.65/1.82 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(elem!1)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[58])).
% 1.65/1.82 tff(11891,plain,
% 1.65/1.82 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11890])).
% 1.65/1.82 tff(11892,plain,
% 1.65/1.82 (elem!1 = s(s(s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[7656, 11891])).
% 1.65/1.82 tff(11893,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[514, 11892])).
% 1.65/1.82 tff(11894,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11895,plain,
% 1.65/1.82 (elem!1 = s(s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11894, 11882])).
% 1.65/1.82 tff(11896,plain,
% 1.65/1.82 ((~![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)))))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11897,plain,
% 1.65/1.82 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11896, 10])).
% 1.65/1.82 tff(11898,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.65/1.82 tff(11899,plain,
% 1.65/1.82 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11898])).
% 1.65/1.82 tff(11900,plain,
% 1.65/1.82 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11899])).
% 1.65/1.82 tff(11901,plain,
% 1.65/1.82 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11900])).
% 1.65/1.82 tff(11902,plain,
% 1.65/1.82 (s(s(s(s(z)))) = elem!1),
% 1.65/1.82 inference(symmetry,[status(thm)],[11898])).
% 1.65/1.82 tff(11903,plain,
% 1.65/1.82 (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11902, 501, 11901])).
% 1.65/1.82 tff(11904,plain,
% 1.65/1.82 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11903])).
% 1.65/1.82 tff(11905,plain,
% 1.65/1.82 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[716, 11904, 11897])).
% 1.65/1.82 tff(11906,plain,
% 1.65/1.82 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11905])).
% 1.65/1.82 tff(11907,plain,
% 1.65/1.82 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11906])).
% 1.65/1.82 tff(11908,plain,
% 1.65/1.82 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[1890])).
% 1.65/1.82 tff(11909,plain,
% 1.65/1.82 (s(s(s(s(s(z))))) = s(s(z))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11908, 11907, 138])).
% 1.65/1.82 tff(11910,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1729, 11909])).
% 1.65/1.82 tff(11911,plain,((~(elem!1 = s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11912,plain,
% 1.65/1.82 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11911, 11895])).
% 1.65/1.82 tff(11913,plain,
% 1.65/1.82 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11873])).
% 1.65/1.82 tff(11914,plain,
% 1.65/1.82 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11913])).
% 1.65/1.82 tff(11915,plain,
% 1.65/1.82 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11914])).
% 1.65/1.82 tff(11916,plain,
% 1.65/1.82 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11851, 11915])).
% 1.65/1.82 tff(11917,plain,
% 1.65/1.82 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[935, 11916, 11912])).
% 1.65/1.82 tff(11918,plain,
% 1.65/1.82 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11917, 11889])).
% 1.65/1.82 tff(11919,plain,
% 1.65/1.82 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5222, 11877, 22])).
% 1.65/1.82 tff(11920,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11856, 11919])).
% 1.65/1.82 tff(11921,plain,
% 1.65/1.82 (s(elem!1) = s(s(elem!1))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11877, 11882])).
% 1.65/1.82 tff(11922,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11921])).
% 1.65/1.82 tff(11923,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11922])).
% 1.65/1.82 tff(11924,plain,
% 1.65/1.82 (b(s(s(s(s(z)))), s(elem!1))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11920, 11923])).
% 1.65/1.82 tff(11925,plain,
% 1.65/1.82 (s(elem!1) = elem!1),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[5315, 11882, 11873])).
% 1.65/1.82 tff(11926,plain,
% 1.65/1.82 (elem!1 = s(elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[393, 11925])).
% 1.65/1.82 tff(11927,plain,
% 1.65/1.82 (b(z, elem!1)),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[2080, 11873, 11685])).
% 1.65/1.82 tff(11928,plain,
% 1.65/1.82 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11921])).
% 1.65/1.82 tff(11929,plain,
% 1.65/1.82 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.65/1.82 inference(symmetry,[status(thm)],[11928])).
% 1.65/1.82 tff(11930,plain,
% 1.65/1.82 (b(elem!1, s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11889, 11929])).
% 1.65/1.82 tff(11931,plain,
% 1.65/1.82 (b(s(elem!1), s(s(s(s(z)))))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11917, 11930])).
% 1.65/1.82 tff(11932,plain,
% 1.65/1.82 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1487, 51, 11174])).
% 1.65/1.82 tff(11933,plain,
% 1.65/1.82 (b(z, s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11932, 1454])).
% 1.65/1.82 tff(11934,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.65/1.82 tff(11935,assumption,(b(s(s(s(s(z)))), s(elem!1))), introduced(assumption)).
% 1.65/1.82 tff(11936,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11937,plain,
% 1.65/1.82 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 1.65/1.82 inference(rewrite,[status(thm)],[])).
% 1.65/1.82 tff(11938,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1)))))),
% 1.65/1.82 inference(monotonicity,[status(thm)],[11937])).
% 1.65/1.82 tff(11939,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))))),
% 1.65/1.82 inference(transitivity,[status(thm)],[11938, 11936])).
% 1.65/1.82 tff(11940,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(s(z)))))))),
% 1.65/1.82 inference(quant_inst,[status(thm)],[])).
% 1.65/1.82 tff(11941,plain,
% 1.65/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1)))),
% 1.65/1.82 inference(modus_ponens,[status(thm)],[11940, 11939])).
% 1.65/1.82 tff(11942,plain,
% 1.65/1.82 ($false),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11941, 238, 11935, 11934, 11933, 2085])).
% 1.65/1.82 tff(11943,plain,(r(z, s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, elem!1)) | (~(elem!1 = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.82 tff(11944,plain,
% 1.65/1.82 (r(z, s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11943, 11931, 11927, 11926, 11924])).
% 1.65/1.82 tff(11945,plain,
% 1.65/1.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[11221, 11944, 11683])).
% 1.65/1.82 tff(11946,plain,
% 1.65/1.82 (b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.82 inference(unit_resolution,[status(thm)],[1604, 11945])).
% 1.65/1.82 tff(11947,plain,
% 1.65/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11948,plain,
% 1.65/1.83 (((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11949,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[11948])).
% 1.65/1.83 tff(11950,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[11949, 11947])).
% 1.65/1.83 tff(11951,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(11952,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[11951, 11950])).
% 1.65/1.83 tff(11953,plain,
% 1.65/1.83 (~b(s(s(elem!1)), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11952, 238, 11946, 11920, 11918])).
% 1.65/1.83 tff(11954,plain,
% 1.65/1.83 (r(s(s(elem!1)), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[5230, 51, 11953, 5385])).
% 1.65/1.83 tff(11955,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11956,plain,
% 1.65/1.83 (((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11957,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[11956])).
% 1.65/1.83 tff(11958,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.65/1.83 inference(transitivity,[status(thm)],[11957, 11955])).
% 1.65/1.83 tff(11959,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(11960,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[11959, 11958])).
% 1.65/1.83 tff(11961,plain,
% 1.65/1.83 (~r(s(s(elem!1)), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11960, 124, 11683, 11954])).
% 1.65/1.83 tff(11962,plain,
% 1.65/1.83 (b(s(s(elem!1)), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4905, 11961])).
% 1.65/1.83 tff(11963,plain,
% 1.65/1.83 (~b(s(s(s(s(s(z))))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7343, 11962, 11888, 11685])).
% 1.65/1.83 tff(11964,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11965,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(11966,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[11965, 11964])).
% 1.65/1.83 tff(11967,plain,
% 1.65/1.83 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11966, 238, 11888, 11920, 11918])).
% 1.65/1.83 tff(11968,plain,
% 1.65/1.83 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1904, 11967])).
% 1.65/1.83 tff(11969,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11970,plain,
% 1.65/1.83 (((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(11971,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[11970])).
% 1.65/1.83 tff(11972,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[11971, 11969])).
% 1.65/1.83 tff(11973,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(11974,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[11973, 11972])).
% 1.65/1.83 tff(11975,plain,
% 1.65/1.83 (~b(s(s(s(s(z)))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11974, 238, 11685, 11962, 11920])).
% 1.65/1.83 tff(11976,plain,
% 1.65/1.83 (r(s(s(s(s(z)))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[8328, 11975])).
% 1.65/1.83 tff(11977,plain,
% 1.65/1.83 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[7358, 11976, 11475, 11968])).
% 1.65/1.83 tff(11978,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 11977, 11963])).
% 1.65/1.83 tff(11979,plain,(b(s(s(z)), s(s(elem!1))) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(11980,plain,
% 1.65/1.83 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11979, 1, 81, 1457])).
% 1.65/1.83 tff(11981,plain,
% 1.65/1.83 (~r(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11454, 150, 11980, 11507, 81, 1457, 11678, 1])).
% 1.65/1.83 tff(11982,plain,
% 1.65/1.83 (b(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11309, 11981])).
% 1.65/1.83 tff(11983,plain,
% 1.65/1.83 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[1626])).
% 1.65/1.83 tff(11984,plain,
% 1.65/1.83 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[11983])).
% 1.65/1.83 tff(11985,plain,
% 1.65/1.83 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[11324, 11984])).
% 1.65/1.83 tff(11986,plain,
% 1.65/1.83 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1904, 11985])).
% 1.65/1.83 tff(11987,plain,
% 1.65/1.83 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11801, 238, 11795, 11986, 11794])).
% 1.65/1.83 tff(11988,plain,
% 1.65/1.83 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1101, 11987])).
% 1.65/1.83 tff(11989,plain,
% 1.65/1.83 (~r(s(z), s(s(s(s(s(z))))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11813, 124, 11988, 11807])).
% 1.65/1.83 tff(11990,plain,
% 1.65/1.83 (b(s(z), s(s(s(s(s(z))))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1709, 11989])).
% 1.65/1.83 tff(11991,plain,
% 1.65/1.83 (r(s(z), s(s(s(s(z)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[10004, 3392])).
% 1.65/1.83 tff(11992,plain,
% 1.65/1.83 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11822, 124, 11991, 11988, 11807])).
% 1.65/1.83 tff(11993,plain,
% 1.65/1.83 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1781, 11992])).
% 1.65/1.83 tff(11994,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11524, 11993, 11990, 1457])).
% 1.65/1.83 tff(11995,plain,((~(s(elem!1) = s(s(z)))) | (~b(z, s(z))) | r(s(s(elem!1)), s(s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(11996,plain,
% 1.65/1.83 (~(s(elem!1) = s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[11995, 11869, 11851, 11507, 1457])).
% 1.65/1.83 tff(11997,plain,
% 1.65/1.83 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[2874])).
% 1.65/1.83 tff(11998,plain,
% 1.65/1.83 (s(s(s(z))) = s(s(elem!1))),
% 1.65/1.83 inference(transitivity,[status(thm)],[716, 11997, 88])).
% 1.65/1.83 tff(11999,plain,
% 1.65/1.83 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[11998])).
% 1.65/1.83 tff(12000,plain,
% 1.65/1.83 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.65/1.83 inference(symmetry,[status(thm)],[11999])).
% 1.65/1.83 tff(12001,plain,
% 1.65/1.83 (s(elem!1) = s(s(z))),
% 1.65/1.83 inference(transitivity,[status(thm)],[18, 12000, 138])).
% 1.65/1.83 tff(12002,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[278, 12001])).
% 1.65/1.83 tff(12003,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(12004,plain,
% 1.65/1.83 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12003, 11996])).
% 1.65/1.83 tff(12005,plain,
% 1.65/1.83 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[8247, 12004, 11866])).
% 1.65/1.83 tff(12006,plain,
% 1.65/1.83 (~(elem!1 = s(z))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[280, 11996])).
% 1.65/1.83 tff(12007,plain,
% 1.65/1.83 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[223, 545, 11398])).
% 1.65/1.83 tff(12008,plain,
% 1.65/1.83 (r(s(elem!1), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[488, 3258, 4572])).
% 1.65/1.83 tff(12009,plain,
% 1.65/1.83 (b(s(z), s(elem!1))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[439, 6010, 426])).
% 1.65/1.83 tff(12010,plain,
% 1.65/1.83 (~b(elem!1, s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[9722, 370, 1817, 12009])).
% 1.65/1.83 tff(12011,plain,
% 1.65/1.83 (~b(s(z), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[9713, 12010, 1457, 1152, 370, 475, 387])).
% 1.65/1.83 tff(12012,plain,
% 1.65/1.83 (r(s(z), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[351, 12011, 6098])).
% 1.65/1.83 tff(12013,plain,
% 1.65/1.83 (~r(s(s(elem!1)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[342, 12012, 160])).
% 1.65/1.83 tff(12014,plain,
% 1.65/1.83 (b(s(s(elem!1)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[255, 12013, 167])).
% 1.65/1.83 tff(12015,plain,
% 1.65/1.83 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[246, 12014, 227, 224])).
% 1.65/1.83 tff(12016,plain,
% 1.65/1.83 (r(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[190, 179])).
% 1.65/1.83 tff(12017,plain,
% 1.65/1.83 (b(s(z), s(elem!1))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[439, 426, 6010])).
% 1.65/1.83 tff(12018,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12019,plain,
% 1.65/1.83 (((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12020,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[12019])).
% 1.65/1.83 tff(12021,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[12020, 12018])).
% 1.65/1.83 tff(12022,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(12023,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[12022, 12021])).
% 1.65/1.83 tff(12024,plain,
% 1.65/1.83 (~b(s(s(z)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12023, 238, 1817, 370, 12017])).
% 1.65/1.83 tff(12025,plain,
% 1.65/1.83 (r(s(s(z)), elem!1)),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[1275, 12024, 374])).
% 1.65/1.83 tff(12026,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12027,plain,
% 1.65/1.83 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12028,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[12027])).
% 1.65/1.83 tff(12029,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[12028, 12026])).
% 1.65/1.83 tff(12030,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(12031,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[12030, 12029])).
% 1.65/1.83 tff(12032,plain,
% 1.65/1.83 (~r(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12031, 124, 12016, 161])).
% 1.65/1.83 tff(12033,plain,
% 1.65/1.83 ((s(z) = s(s(z))) | b(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[4557, 51, 12032])).
% 1.65/1.83 tff(12034,plain,
% 1.65/1.83 (b(s(z), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12033, 4411])).
% 1.65/1.83 tff(12035,plain,
% 1.65/1.83 (~(elem!1 = s(s(elem!1)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[2097, 418])).
% 1.65/1.83 tff(12036,plain,
% 1.65/1.83 (~r(s(elem!1), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[8397, 505, 12035, 179])).
% 1.65/1.83 tff(12037,plain,
% 1.65/1.83 (b(s(elem!1), s(s(z)))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[488, 12036, 278])).
% 1.65/1.83 tff(12038,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12039,plain,
% 1.65/1.83 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12040,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[12039])).
% 1.65/1.83 tff(12041,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[12040, 12038])).
% 1.65/1.83 tff(12042,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(quant_inst,[status(thm)],[])).
% 1.65/1.83 tff(12043,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1)))),
% 1.65/1.83 inference(modus_ponens,[status(thm)],[12042, 12041])).
% 1.65/1.83 tff(12044,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12043, 238, 1817, 490, 2258, 660])).
% 1.65/1.83 tff(12045,plain,((~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(12046,plain,
% 1.65/1.83 (~b(s(z), s(elem!1))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12045, 12037, 12034, 1817])).
% 1.65/1.83 tff(12047,plain,
% 1.65/1.83 (r(s(z), s(elem!1))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[439, 12046, 433])).
% 1.65/1.83 tff(12048,plain,
% 1.65/1.83 (r(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[539, 505, 418])).
% 1.65/1.83 tff(12049,plain,
% 1.65/1.83 ($false),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[586, 124, 12048, 161, 12047])).
% 1.65/1.83 tff(12050,plain,(b(s(elem!1), s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(z) = s(elem!1)) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(s(z))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.83 tff(12051,plain,
% 1.65/1.83 (b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.83 inference(unit_resolution,[status(thm)],[12050, 426, 415, 1817, 179, 278, 161])).
% 1.65/1.83 tff(12052,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12053,plain,
% 1.65/1.83 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(rewrite,[status(thm)],[])).
% 1.65/1.83 tff(12054,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.65/1.83 inference(monotonicity,[status(thm)],[12053])).
% 1.65/1.83 tff(12055,plain,
% 1.65/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.65/1.83 inference(transitivity,[status(thm)],[12054, 12052])).
% 1.65/1.83 tff(12056,plain,
% 1.65/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12057,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12056, 12055])).
% 1.65/1.84 tff(12058,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12057, 238, 631, 290, 370, 660])).
% 1.65/1.84 tff(12059,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12060,plain,
% 1.65/1.84 (~b(elem!1, s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12059, 12051, 370, 12017])).
% 1.65/1.84 tff(12061,plain,
% 1.65/1.84 (r(elem!1, s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[629, 12060, 387])).
% 1.65/1.84 tff(12062,plain,
% 1.65/1.84 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[501])).
% 1.65/1.84 tff(12063,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), s(elem!1))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[590, 12062])).
% 1.65/1.84 tff(12064,plain,
% 1.65/1.84 (~r(s(z), s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[450, 12063, 161])).
% 1.65/1.84 tff(12065,plain,
% 1.65/1.84 (b(s(z), s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[439, 12064, 433])).
% 1.65/1.84 tff(12066,plain,
% 1.65/1.84 (~b(s(elem!1), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12045, 12065, 12034, 1817])).
% 1.65/1.84 tff(12067,plain,
% 1.65/1.84 (r(s(elem!1), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[488, 12066, 278])).
% 1.65/1.84 tff(12068,plain,
% 1.65/1.84 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[501])).
% 1.65/1.84 tff(12069,plain,
% 1.65/1.84 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.65/1.84 inference(symmetry,[status(thm)],[12068])).
% 1.65/1.84 tff(12070,plain,
% 1.65/1.84 (r(s(z), elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[161, 12069])).
% 1.65/1.84 tff(12071,plain,
% 1.65/1.84 (~r(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[342, 12070, 160])).
% 1.65/1.84 tff(12072,plain,
% 1.65/1.84 (b(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[255, 12071, 167])).
% 1.65/1.84 tff(12073,plain,
% 1.65/1.84 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[223, 2251, 209])).
% 1.65/1.84 tff(12074,plain,
% 1.65/1.84 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[501])).
% 1.65/1.84 tff(12075,plain,
% 1.65/1.84 ((s(s(z)) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12074, 1284])).
% 1.65/1.84 tff(12076,plain,
% 1.65/1.84 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.65/1.84 inference(symmetry,[status(thm)],[12075])).
% 1.65/1.84 tff(12077,plain,
% 1.65/1.84 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12076, 1972])).
% 1.65/1.84 tff(12078,plain,
% 1.65/1.84 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12077])).
% 1.65/1.84 tff(12079,plain,
% 1.65/1.84 (~(elem!1 = s(s(z)))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[1291, 12078])).
% 1.65/1.84 tff(12080,plain,
% 1.65/1.84 (~r(elem!1, s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[8611, 12067, 590])).
% 1.65/1.84 tff(12081,plain,
% 1.65/1.84 (b(elem!1, s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[763, 12080, 12079])).
% 1.65/1.84 tff(12082,plain,
% 1.65/1.84 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[2501, 12081, 12073, 501, 12072])).
% 1.65/1.84 tff(12083,plain,
% 1.65/1.84 (r(s(s(z)), s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[135, 12082, 114])).
% 1.65/1.84 tff(12084,plain,
% 1.65/1.84 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[2528])).
% 1.65/1.84 tff(12085,plain,
% 1.65/1.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[209, 12084])).
% 1.65/1.84 tff(12086,plain,
% 1.65/1.84 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[501])).
% 1.65/1.84 tff(12087,plain,
% 1.65/1.84 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12086])).
% 1.65/1.84 tff(12088,plain,
% 1.65/1.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12071, 12087])).
% 1.65/1.84 tff(12089,plain,
% 1.65/1.84 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[2549, 51, 12088])).
% 1.65/1.84 tff(12090,plain,
% 1.65/1.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12089, 12085])).
% 1.65/1.84 tff(12091,plain,
% 1.65/1.84 (b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[8397, 12067, 150, 179])).
% 1.65/1.84 tff(12092,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12093,plain,
% 1.65/1.84 (((~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))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12094,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12093])).
% 1.65/1.84 tff(12095,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12094, 12092])).
% 1.65/1.84 tff(12096,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12097,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12096, 12095])).
% 1.65/1.84 tff(12098,plain,
% 1.65/1.84 (~b(s(elem!1), s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12097, 238, 12091, 12073, 12090])).
% 1.65/1.84 tff(12099,plain,
% 1.65/1.84 (r(s(elem!1), s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[534, 12098, 159])).
% 1.65/1.84 tff(12100,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12101,plain,
% 1.65/1.84 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12102,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12101])).
% 1.65/1.84 tff(12103,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12102, 12100])).
% 1.65/1.84 tff(12104,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12105,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12104, 12103])).
% 1.65/1.84 tff(12106,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12105, 124, 12099, 12083, 12067])).
% 1.65/1.84 tff(12107,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12108,plain,
% 1.65/1.84 (~(elem!1 = s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12107, 12061, 161, 150, 179, 278, 1817, 426, 160, 22])).
% 1.65/1.84 tff(12109,plain,
% 1.65/1.84 (~(s(s(s(elem!1))) = elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[516, 12108])).
% 1.65/1.84 tff(12110,plain,
% 1.65/1.84 (~r(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[622, 124, 12061, 307])).
% 1.65/1.84 tff(12111,plain,
% 1.65/1.84 (b(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[255, 12110, 167])).
% 1.65/1.84 tff(12112,plain,
% 1.65/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[599, 12061, 307])).
% 1.65/1.84 tff(12113,plain,
% 1.65/1.84 (b(elem!1, s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[606, 12112, 150])).
% 1.65/1.84 tff(12114,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12115,plain,
% 1.65/1.84 (((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12116,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12115])).
% 1.65/1.84 tff(12117,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12116, 12114])).
% 1.65/1.84 tff(12118,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12119,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12118, 12117])).
% 1.65/1.84 tff(12120,plain,
% 1.65/1.84 (~b(s(s(s(elem!1))), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12119, 238, 12113, 12111, 224])).
% 1.65/1.84 tff(12121,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[647, 12120, 12109])).
% 1.65/1.84 tff(12122,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12123,plain,
% 1.65/1.84 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12124,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12123])).
% 1.65/1.84 tff(12125,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12124, 12122])).
% 1.65/1.84 tff(12126,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12127,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12126, 12125])).
% 1.65/1.84 tff(12128,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12127, 124, 12121, 12025, 12016])).
% 1.65/1.84 tff(12129,plain,((s(elem!1) = s(z)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12130,plain,
% 1.65/1.84 (s(s(z)) = elem!1),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12129, 12015, 161, 160, 1, 150, 1817, 307, 278, 370])).
% 1.65/1.84 tff(12131,plain,
% 1.65/1.84 (elem!1 = s(s(z))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[1231, 12130])).
% 1.65/1.84 tff(12132,plain,
% 1.65/1.84 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12131])).
% 1.65/1.84 tff(12133,plain,
% 1.65/1.84 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.65/1.84 inference(symmetry,[status(thm)],[12132])).
% 1.65/1.84 tff(12134,plain,
% 1.65/1.84 ((~r(s(z), s(s(z)))) <=> (~r(s(z), elem!1))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12133])).
% 1.65/1.84 tff(12135,plain,
% 1.65/1.84 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[9632, 12014, 227, 224])).
% 1.65/1.84 tff(12136,plain,
% 1.65/1.84 (r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[3233, 12135])).
% 1.65/1.84 tff(12137,plain,
% 1.65/1.84 (~r(s(z), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[4568, 12136, 161])).
% 1.65/1.84 tff(12138,plain,
% 1.65/1.84 (~r(s(z), elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12137, 12134])).
% 1.65/1.84 tff(12139,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12012, 12138])).
% 1.65/1.84 tff(12140,plain,((~b(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12141,plain,
% 1.65/1.84 ((~b(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12140, 8300, 10004])).
% 1.65/1.84 tff(12142,plain,
% 1.65/1.84 (~b(elem!1, s(z))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12141, 12008, 150, 1, 160, 307, 227, 1457, 1152, 3258])).
% 1.65/1.84 tff(12143,plain,
% 1.65/1.84 (r(elem!1, s(z))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[363, 12142, 330])).
% 1.65/1.84 tff(12144,plain,
% 1.65/1.84 (~r(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[263, 12143, 162])).
% 1.65/1.84 tff(12145,plain,
% 1.65/1.84 (~r(elem!1, s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[5843, 12143, 160])).
% 1.65/1.84 tff(12146,plain,
% 1.65/1.84 (r(s(s(elem!1)), elem!1) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[2484, 10004])).
% 1.65/1.84 tff(12147,plain,
% 1.65/1.84 (elem!1 = s(s(s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12146, 12145, 150, 160, 545, 12143, 12144])).
% 1.65/1.84 tff(12148,plain,
% 1.65/1.84 (s(s(s(elem!1))) = elem!1),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[2002, 12147])).
% 1.65/1.84 tff(12149,plain,
% 1.65/1.84 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12148])).
% 1.65/1.84 tff(12150,plain,
% 1.65/1.84 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12148])).
% 1.65/1.84 tff(12151,plain,
% 1.65/1.84 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.65/1.84 inference(transitivity,[status(thm)],[12150, 767])).
% 1.65/1.84 tff(12152,plain,
% 1.65/1.84 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.65/1.84 inference(symmetry,[status(thm)],[12151])).
% 1.65/1.84 tff(12153,plain,
% 1.65/1.84 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.65/1.84 inference(monotonicity,[status(thm)],[12152])).
% 1.65/1.84 tff(12154,plain,
% 1.65/1.84 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[11911, 12147])).
% 1.65/1.84 tff(12155,plain,
% 1.65/1.84 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12154, 12153])).
% 1.65/1.84 tff(12156,plain,
% 1.65/1.84 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[8247, 12155, 8245])).
% 1.65/1.84 tff(12157,plain,
% 1.65/1.84 (b(s(s(s(s(z)))), elem!1)),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12156, 12149])).
% 1.65/1.84 tff(12158,plain,
% 1.65/1.84 (b(s(s(elem!1)), elem!1)),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[255, 12144, 167])).
% 1.65/1.84 tff(12159,plain,
% 1.65/1.84 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[246, 12158, 227, 12007])).
% 1.65/1.84 tff(12160,plain,
% 1.65/1.84 ((~(elem!1 = s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~r(elem!1, s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(z)), s(s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(elem!1))))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12107, 10004, 8300])).
% 1.65/1.84 tff(12161,plain,
% 1.65/1.84 (~r(elem!1, s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12160, 12159, 150, 12147, 3258, 426, 160, 22])).
% 1.65/1.84 tff(12162,plain,
% 1.65/1.84 (b(elem!1, s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[629, 12161, 391])).
% 1.65/1.84 tff(12163,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.84 tff(12164,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.84 inference(quant_inst,[status(thm)],[])).
% 1.65/1.84 tff(12165,plain,
% 1.65/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.65/1.84 inference(modus_ponens,[status(thm)],[12164, 12163])).
% 1.65/1.84 tff(12166,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12165, 238, 12162, 12158, 12157, 5641])).
% 1.65/1.84 tff(12167,plain,((elem!1 = s(z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | b(s(elem!1), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12168,plain,
% 1.65/1.84 (b(s(elem!1), s(s(z)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12167, 307, 8245, 391, 330, 160, 227, 545, 162, 1, 150, 1457, 1152, 5641])).
% 1.65/1.84 tff(12169,plain,
% 1.65/1.84 ((~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(elem!1)))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12045, 8300])).
% 1.65/1.84 tff(12170,plain,
% 1.65/1.84 ($false),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12169, 12009, 12168, 2258])).
% 1.65/1.84 tff(12171,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(s(z)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.84 tff(12172,plain,
% 1.65/1.84 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[12171, 5641, 8245, 391, 330, 160, 227, 545, 162, 1, 150, 1457, 1152, 2258])).
% 1.65/1.84 tff(12173,plain,
% 1.65/1.84 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.84 inference(unit_resolution,[status(thm)],[323, 12172, 275])).
% 1.65/1.84 tff(12174,plain,
% 1.65/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.65/1.84 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12175,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(12176,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12175, 12174])).
% 1.65/1.85 tff(12177,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12176, 238, 12173, 12007, 1041, 5641])).
% 1.65/1.85 tff(12178,plain,((~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(elem!1)) | r(s(s(s(s(z)))), s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12179,plain,
% 1.65/1.85 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12178, 150, 3294, 11866, 1212, 12006, 11507, 11980, 10009, 11678, 1, 12005, 1457, 11687, 11982])).
% 1.65/1.85 tff(12180,plain,
% 1.65/1.85 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11856, 12179])).
% 1.65/1.85 tff(12181,plain,
% 1.65/1.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12180])).
% 1.65/1.85 tff(12182,plain,
% 1.65/1.85 (s(s(s(z))) = s(elem!1)),
% 1.65/1.85 inference(transitivity,[status(thm)],[716, 12181, 17])).
% 1.65/1.85 tff(12183,plain,
% 1.65/1.85 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12182])).
% 1.65/1.85 tff(12184,plain,
% 1.65/1.85 (s(s(z)) = elem!1),
% 1.65/1.85 inference(transitivity,[status(thm)],[144, 12183, 154])).
% 1.65/1.85 tff(12185,plain,
% 1.65/1.85 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12184])).
% 1.65/1.85 tff(12186,plain,
% 1.65/1.85 (b(s(z), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11982, 12185])).
% 1.65/1.85 tff(12187,plain,
% 1.65/1.85 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12184])).
% 1.65/1.85 tff(12188,plain,
% 1.65/1.85 (b(elem!1, s(z))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[8300, 12187])).
% 1.65/1.85 tff(12189,plain,
% 1.65/1.85 (~b(elem!1, s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[9672, 12188, 11687, 12186])).
% 1.65/1.85 tff(12190,plain,
% 1.65/1.85 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2893, 12180])).
% 1.65/1.85 tff(12191,plain,
% 1.65/1.85 (~r(elem!1, s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[9709, 12188, 1457, 11687, 12190, 12186])).
% 1.65/1.85 tff(12192,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[629, 12191, 12189, 1212])).
% 1.65/1.85 tff(12193,plain,((elem!1 = s(s(elem!1))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12194,plain,
% 1.65/1.85 (elem!1 = s(s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12193, 206, 1, 1457, 81])).
% 1.65/1.85 tff(12195,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12194])).
% 1.65/1.85 tff(12196,plain,
% 1.65/1.85 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12194])).
% 1.65/1.85 tff(12197,plain,
% 1.65/1.85 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12196, 11840])).
% 1.65/1.85 tff(12198,plain,
% 1.65/1.85 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12197])).
% 1.65/1.85 tff(12199,plain,
% 1.65/1.85 ((~(s(s(s(s(z)))) = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12198])).
% 1.65/1.85 tff(12200,plain,
% 1.65/1.85 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2097, 12194])).
% 1.65/1.85 tff(12201,plain,
% 1.65/1.85 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[5222, 12200, 22])).
% 1.65/1.85 tff(12202,plain,
% 1.65/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12201, 12199])).
% 1.65/1.85 tff(12203,plain,
% 1.65/1.85 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12194])).
% 1.65/1.85 tff(12204,plain,
% 1.65/1.85 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12203])).
% 1.65/1.85 tff(12205,plain,
% 1.65/1.85 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12204])).
% 1.65/1.85 tff(12206,plain,
% 1.65/1.85 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11851, 12205])).
% 1.65/1.85 tff(12207,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[935, 12206, 12202])).
% 1.65/1.85 tff(12208,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12207, 12195])).
% 1.65/1.85 tff(12209,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11856, 12201])).
% 1.65/1.85 tff(12210,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[7429, 238, 11869, 12005, 12209, 12208])).
% 1.65/1.85 tff(12211,plain,((s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12212,plain,
% 1.65/1.85 (s(elem!1) = s(s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12211, 1, 1457, 81])).
% 1.65/1.85 tff(12213,plain,
% 1.65/1.85 (elem!1 = s(s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[158, 12212])).
% 1.65/1.85 tff(12214,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12213])).
% 1.65/1.85 tff(12215,plain,
% 1.65/1.85 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[5343, 12212])).
% 1.65/1.85 tff(12216,plain,
% 1.65/1.85 (elem!1 = s(s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11894, 12215])).
% 1.65/1.85 tff(12217,plain,
% 1.65/1.85 (~(elem!1 = s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11911, 12216])).
% 1.65/1.85 tff(12218,plain,
% 1.65/1.85 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12213])).
% 1.65/1.85 tff(12219,plain,
% 1.65/1.85 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12218])).
% 1.65/1.85 tff(12220,plain,
% 1.65/1.85 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12219])).
% 1.65/1.85 tff(12221,plain,
% 1.65/1.85 (~r(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11851, 12220])).
% 1.65/1.85 tff(12222,plain,
% 1.65/1.85 (b(elem!1, s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[935, 12221, 12217])).
% 1.65/1.85 tff(12223,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12222, 12214])).
% 1.65/1.85 tff(12224,plain,
% 1.65/1.85 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2097, 12213])).
% 1.65/1.85 tff(12225,plain,
% 1.65/1.85 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[5222, 12224, 22])).
% 1.65/1.85 tff(12226,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11856, 12225])).
% 1.65/1.85 tff(12227,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12228,plain,
% 1.65/1.85 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12229,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12228])).
% 1.65/1.85 tff(12230,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12229, 12227])).
% 1.65/1.85 tff(12231,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(12232,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12231, 12230])).
% 1.65/1.85 tff(12233,plain,
% 1.65/1.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12232, 238, 11980, 12226, 12223])).
% 1.65/1.85 tff(12234,plain,
% 1.65/1.85 (r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1564, 12233])).
% 1.65/1.85 tff(12235,plain,
% 1.65/1.85 ((s(s(s(s(s(z))))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12213])).
% 1.65/1.85 tff(12236,plain,
% 1.65/1.85 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12235])).
% 1.65/1.85 tff(12237,plain,
% 1.65/1.85 ((~(s(s(s(s(s(z))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12236])).
% 1.65/1.85 tff(12238,plain,
% 1.65/1.85 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2106, 12224])).
% 1.65/1.85 tff(12239,plain,
% 1.65/1.85 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12238, 12237])).
% 1.65/1.85 tff(12240,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12213])).
% 1.65/1.85 tff(12241,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12240])).
% 1.65/1.85 tff(12242,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12215])).
% 1.65/1.85 tff(12243,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.85 inference(transitivity,[status(thm)],[12242, 12241])).
% 1.65/1.85 tff(12244,plain,
% 1.65/1.85 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12243])).
% 1.65/1.85 tff(12245,plain,
% 1.65/1.85 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11324, 12244])).
% 1.65/1.85 tff(12246,plain,
% 1.65/1.85 (b(s(s(s(s(s(z))))), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1064, 12245, 12239])).
% 1.65/1.85 tff(12247,plain,
% 1.65/1.85 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[5296, 12246, 12213])).
% 1.65/1.85 tff(12248,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12249,plain,
% 1.65/1.85 (((~b(s(s(elem!1)), s(s(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(s(s(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(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12250,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(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(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12249])).
% 1.65/1.85 tff(12251,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(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(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12250, 12248])).
% 1.65/1.85 tff(12252,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(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(s(s(s(z))))), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(12253,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12252, 12251])).
% 1.65/1.85 tff(12254,plain,
% 1.65/1.85 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12253, 238, 11980, 12247, 12223])).
% 1.65/1.85 tff(12255,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1738, 12254])).
% 1.65/1.85 tff(12256,plain,
% 1.65/1.85 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11966, 238, 12247, 12226, 12223])).
% 1.65/1.85 tff(12257,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1904, 12256])).
% 1.65/1.85 tff(12258,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1928, 12257, 12255, 12234])).
% 1.65/1.85 tff(12259,plain,((s(elem!1) = s(z)) | (~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12260,plain,
% 1.65/1.85 (s(elem!1) = s(z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12259, 1457, 81])).
% 1.65/1.85 tff(12261,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12260])).
% 1.65/1.85 tff(12262,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12261])).
% 1.65/1.85 tff(12263,plain,
% 1.65/1.85 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12262])).
% 1.65/1.85 tff(12264,plain,
% 1.65/1.85 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11677, 12263])).
% 1.65/1.85 tff(12265,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[11248, 12260])).
% 1.65/1.85 tff(12266,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12265, 12264])).
% 1.65/1.85 tff(12267,plain,((~b(z, s(z))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12268,plain,
% 1.65/1.85 (~b(z, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12267, 81])).
% 1.65/1.85 tff(12269,plain,
% 1.65/1.85 (r(z, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1542, 12268])).
% 1.65/1.85 tff(12270,plain,
% 1.65/1.85 (~(s(s(elem!1)) = s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[271, 10886])).
% 1.65/1.85 tff(12271,plain,
% 1.65/1.85 (b(z, s(z)) | r(s(z), s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1) | b(s(s(z)), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[10881, 8300])).
% 1.65/1.85 tff(12272,plain,
% 1.65/1.85 (s(s(z)) = elem!1),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12271, 2213, 81, 12268, 24])).
% 1.65/1.85 tff(12273,plain,
% 1.65/1.85 (elem!1 = s(s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1231, 12272])).
% 1.65/1.85 tff(12274,plain,
% 1.65/1.85 (s(elem!1) = s(s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12273])).
% 1.65/1.85 tff(12275,plain,
% 1.65/1.85 (r(s(elem!1), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12274])).
% 1.65/1.85 tff(12276,plain,
% 1.65/1.85 (r(elem!1, s(s(elem!1))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12273])).
% 1.65/1.85 tff(12277,plain,
% 1.65/1.85 (r(s(s(z)), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12276])).
% 1.65/1.85 tff(12278,plain,
% 1.65/1.85 (r(elem!1, s(s(elem!1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[11679, 12277])).
% 1.65/1.85 tff(12279,plain,
% 1.65/1.85 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[365])).
% 1.65/1.85 tff(12280,plain,
% 1.65/1.85 (r(s(elem!1), s(s(z))) <=> r(s(elem!1), elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12279])).
% 1.65/1.85 tff(12281,plain,
% 1.65/1.85 ((elem!1 = s(elem!1)) <=> (s(s(z)) = s(elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[365])).
% 1.65/1.85 tff(12282,plain,
% 1.65/1.85 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12281, 1245])).
% 1.65/1.85 tff(12283,plain,
% 1.65/1.85 ((~(elem!1 = s(elem!1))) <=> (~(s(elem!1) = s(s(z))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12282])).
% 1.65/1.85 tff(12284,plain,
% 1.65/1.85 (~(s(elem!1) = s(s(z)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[1212, 12283])).
% 1.65/1.85 tff(12285,plain,
% 1.65/1.85 ((~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[9380, 8300])).
% 1.65/1.85 tff(12286,plain,
% 1.65/1.85 (~b(s(elem!1), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12285, 1152, 1137])).
% 1.65/1.85 tff(12287,plain,
% 1.65/1.85 (r(s(elem!1), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[488, 12286, 12284])).
% 1.65/1.85 tff(12288,plain,
% 1.65/1.85 (r(s(elem!1), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12287, 12280])).
% 1.65/1.85 tff(12289,plain,
% 1.65/1.85 ((~(elem!1 = s(s(z)))) | b(elem!1, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[8974, 8300])).
% 1.65/1.85 tff(12290,plain,
% 1.65/1.85 (b(elem!1, s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12289, 365])).
% 1.65/1.85 tff(12291,plain,
% 1.65/1.85 (~b(elem!1, s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1160, 1152, 1137, 12290])).
% 1.65/1.85 tff(12292,plain,
% 1.65/1.85 (r(elem!1, s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[629, 12291, 1212])).
% 1.65/1.85 tff(12293,plain,
% 1.65/1.85 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1149, 12292, 1137, 150, 12290])).
% 1.65/1.85 tff(12294,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[323, 12293, 3294])).
% 1.65/1.85 tff(12295,plain,
% 1.65/1.85 (~b(s(elem!1), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[4533, 12294, 1137, 1152])).
% 1.65/1.85 tff(12296,plain,
% 1.65/1.85 (r(s(elem!1), s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[534, 12295, 206])).
% 1.65/1.85 tff(12297,plain,
% 1.65/1.85 (~r(s(elem!1), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[4590, 12296, 591, 12292])).
% 1.65/1.85 tff(12298,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12297, 12288])).
% 1.65/1.85 tff(12299,plain,((~b(s(elem!1), s(z))) | (~(elem!1 = s(s(z)))) | (~r(elem!1, s(s(elem!1)))) | (s(elem!1) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12300,plain,
% 1.65/1.85 (~b(s(elem!1), s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12299, 12273, 12278, 10886, 57, 150])).
% 1.65/1.85 tff(12301,plain,
% 1.65/1.85 (r(s(elem!1), s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[473, 12300, 1])).
% 1.65/1.85 tff(12302,plain,
% 1.65/1.85 (r(s(s(s(z))), s(z))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12301, 12275])).
% 1.65/1.85 tff(12303,plain,
% 1.65/1.85 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[8420, 12302, 12269])).
% 1.65/1.85 tff(12304,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1624, 12303])).
% 1.65/1.85 tff(12305,plain,
% 1.65/1.85 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12273])).
% 1.65/1.85 tff(12306,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12305])).
% 1.65/1.85 tff(12307,plain,
% 1.65/1.85 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12274])).
% 1.65/1.85 tff(12308,plain,
% 1.65/1.85 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12307])).
% 1.65/1.85 tff(12309,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12308])).
% 1.65/1.85 tff(12310,plain,
% 1.65/1.85 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(elem!1)), elem!1)),
% 1.65/1.85 inference(transitivity,[status(thm)],[12309, 12306])).
% 1.65/1.85 tff(12311,plain,
% 1.65/1.85 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(elem!1)), elem!1))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12310])).
% 1.65/1.85 tff(12312,plain,
% 1.65/1.85 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12307])).
% 1.65/1.85 tff(12313,plain,
% 1.65/1.85 (b(s(z), s(s(s(s(z)))))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[57, 12312])).
% 1.65/1.85 tff(12314,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12315,plain,
% 1.65/1.85 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12316,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12315])).
% 1.65/1.85 tff(12317,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12316, 12314])).
% 1.65/1.85 tff(12318,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.65/1.85 inference(quant_inst,[status(thm)],[])).
% 1.65/1.85 tff(12319,plain,
% 1.65/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12318, 12317])).
% 1.65/1.85 tff(12320,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12319, 238, 1817, 1587, 2765, 1784])).
% 1.65/1.85 tff(12321,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12322,plain,
% 1.65/1.85 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12321, 8300])).
% 1.65/1.85 tff(12323,plain,
% 1.65/1.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12322, 12304, 12313])).
% 1.65/1.85 tff(12324,plain,
% 1.65/1.85 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12323, 12311])).
% 1.65/1.85 tff(12325,plain,
% 1.65/1.85 (r(s(s(elem!1)), elem!1)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[255, 12324, 167])).
% 1.65/1.85 tff(12326,plain,
% 1.65/1.85 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1385, 12272])).
% 1.65/1.85 tff(12327,plain,
% 1.65/1.85 (b(s(elem!1), z) <=> b(s(s(s(z))), z)),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12274])).
% 1.65/1.85 tff(12328,plain,
% 1.65/1.85 (b(s(s(s(z))), z) <=> b(s(elem!1), z)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12327])).
% 1.65/1.85 tff(12329,plain,
% 1.65/1.85 (~r(s(s(s(z))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2825, 124, 12302, 12269])).
% 1.65/1.85 tff(12330,plain,
% 1.65/1.85 (b(s(s(s(z))), z)),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1524, 12329])).
% 1.65/1.85 tff(12331,plain,
% 1.65/1.85 (b(s(elem!1), z)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12330, 12328])).
% 1.65/1.85 tff(12332,plain,
% 1.65/1.85 (b(z, s(elem!1)) <=> b(z, s(s(s(z))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[12274])).
% 1.65/1.85 tff(12333,plain,
% 1.65/1.85 (b(z, s(s(s(z)))) <=> b(z, s(elem!1))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12332])).
% 1.65/1.85 tff(12334,plain,
% 1.65/1.85 (~r(z, s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[2816, 124, 12302, 12269])).
% 1.65/1.85 tff(12335,plain,
% 1.65/1.85 (b(z, s(s(s(z))))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1475, 12334])).
% 1.65/1.85 tff(12336,plain,
% 1.65/1.85 (b(z, s(elem!1))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[12335, 12333])).
% 1.65/1.85 tff(12337,plain,
% 1.65/1.85 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[5906, 365])).
% 1.65/1.85 tff(12338,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.65/1.85 inference(symmetry,[status(thm)],[12337])).
% 1.65/1.85 tff(12339,plain,
% 1.65/1.85 (r(s(s(s(elem!1))), elem!1)),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[1717, 12338])).
% 1.65/1.85 tff(12340,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.65/1.85 tff(12341,plain,
% 1.65/1.85 ($false),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12340, 12339])).
% 1.65/1.85 tff(12342,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | r(s(s(s(elem!1))), elem!1) | (~(elem!1 = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.85 tff(12343,plain,
% 1.65/1.85 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[12342, 10179, 365])).
% 1.65/1.85 tff(12344,plain,
% 1.65/1.85 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.85 inference(unit_resolution,[status(thm)],[1738, 12343])).
% 1.65/1.85 tff(12345,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[4974])).
% 1.65/1.85 tff(12346,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(symmetry,[status(thm)],[12345])).
% 1.65/1.85 tff(12347,plain,
% 1.65/1.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.85 inference(monotonicity,[status(thm)],[5906, 4974])).
% 1.65/1.85 tff(12348,plain,
% 1.65/1.85 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(transitivity,[status(thm)],[12347, 12346])).
% 1.65/1.85 tff(12349,plain,
% 1.65/1.85 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.85 inference(modus_ponens,[status(thm)],[210, 12348])).
% 1.65/1.85 tff(12350,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12351,plain,
% 1.65/1.85 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.85 inference(rewrite,[status(thm)],[])).
% 1.65/1.85 tff(12352,plain,
% 1.65/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12351])).
% 1.65/1.86 tff(12353,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12352, 12350])).
% 1.65/1.86 tff(12354,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12355,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), z))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12354, 12353])).
% 1.65/1.86 tff(12356,plain,
% 1.65/1.86 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12355, 124, 2026, 2008])).
% 1.65/1.86 tff(12357,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 12356])).
% 1.65/1.86 tff(12358,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12359,plain,
% 1.65/1.86 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(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(z))))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12360,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12359])).
% 1.65/1.86 tff(12361,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12360, 12358])).
% 1.65/1.86 tff(12362,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12363,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12362, 12361])).
% 1.65/1.86 tff(12364,plain,
% 1.65/1.86 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12363, 124, 192, 2008])).
% 1.65/1.86 tff(12365,plain,
% 1.65/1.86 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1764, 12364])).
% 1.65/1.86 tff(12366,plain,
% 1.65/1.86 (~r(z, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[9101, 192, 2026])).
% 1.65/1.86 tff(12367,plain,
% 1.65/1.86 ((z = s(s(z))) | b(z, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1511, 51, 12366])).
% 1.65/1.86 tff(12368,plain,
% 1.65/1.86 (b(z, s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12367, 1450])).
% 1.65/1.86 tff(12369,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12370,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12371,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12370, 12369])).
% 1.65/1.86 tff(12372,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12371, 238, 1906, 12368, 12365, 12357])).
% 1.65/1.86 tff(12373,plain,((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12374,plain,
% 1.65/1.86 (~r(z, s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12373, 12349, 192, 12344])).
% 1.65/1.86 tff(12375,plain,
% 1.65/1.86 (b(z, s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[2071, 12374])).
% 1.65/1.86 tff(12376,plain,
% 1.65/1.86 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[8353, 12375, 8344, 8345])).
% 1.65/1.86 tff(12377,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[323, 12376, 275])).
% 1.65/1.86 tff(12378,plain,
% 1.65/1.86 (~r(elem!1, s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1149, 12377, 1137, 150, 12290])).
% 1.65/1.86 tff(12379,plain,
% 1.65/1.86 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[365])).
% 1.65/1.86 tff(12380,plain,
% 1.65/1.86 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12379, 1284])).
% 1.65/1.86 tff(12381,plain,
% 1.65/1.86 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.65/1.86 inference(symmetry,[status(thm)],[12380])).
% 1.65/1.86 tff(12382,plain,
% 1.65/1.86 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.65/1.86 inference(transitivity,[status(thm)],[12381, 641])).
% 1.65/1.86 tff(12383,plain,
% 1.65/1.86 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12382])).
% 1.65/1.86 tff(12384,plain,
% 1.65/1.86 (~(s(s(s(elem!1))) = elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[1291, 12383])).
% 1.65/1.86 tff(12385,plain,
% 1.65/1.86 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[3182, 210, 192])).
% 1.65/1.86 tff(12386,plain,
% 1.65/1.86 (b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[190, 12385])).
% 1.65/1.86 tff(12387,plain,
% 1.65/1.86 (b(elem!1, s(s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[4820, 12386, 4808])).
% 1.65/1.86 tff(12388,plain,
% 1.65/1.86 (~b(elem!1, s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[2721, 12377, 210, 150, 12387, 12384])).
% 1.65/1.86 tff(12389,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[629, 12388, 12378, 391])).
% 1.65/1.86 tff(12390,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~(elem!1 = s(s(z)))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12391,plain,
% 1.65/1.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12390, 12336, 150, 57, 12270, 10890, 12331, 11679, 12273, 12326, 12325])).
% 1.65/1.86 tff(12392,plain,
% 1.65/1.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[223, 12391, 10168])).
% 1.65/1.86 tff(12393,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[5912, 12392, 12273])).
% 1.65/1.86 tff(12394,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12395,plain,
% 1.65/1.86 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12396,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12395])).
% 1.65/1.86 tff(12397,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12396, 12394])).
% 1.65/1.86 tff(12398,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12399,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12398, 12397])).
% 1.65/1.86 tff(12400,plain,
% 1.65/1.86 (~b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12399, 238, 12313, 12393, 12304])).
% 1.65/1.86 tff(12401,plain,
% 1.65/1.86 (r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1781, 12400])).
% 1.65/1.86 tff(12402,plain,
% 1.65/1.86 (~r(s(s(s(s(s(z))))), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[3947, 124, 12401, 12269])).
% 1.65/1.86 tff(12403,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), z)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1846, 51, 1006, 12402])).
% 1.65/1.86 tff(12404,plain,
% 1.65/1.86 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[3580, 124, 12401, 12302])).
% 1.65/1.86 tff(12405,plain,
% 1.65/1.86 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1101, 12404])).
% 1.65/1.86 tff(12406,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12407,plain,
% 1.65/1.86 (((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12408,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12407])).
% 1.65/1.86 tff(12409,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12408, 12406])).
% 1.65/1.86 tff(12410,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12411,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12410, 12409])).
% 1.65/1.86 tff(12412,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12411, 238, 12330, 12335, 12405, 12403])).
% 1.65/1.86 tff(12413,plain,(b(s(s(z)), s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12414,plain,
% 1.65/1.86 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12413, 150, 1, 81, 24])).
% 1.65/1.86 tff(12415,plain,
% 1.65/1.86 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[11464, 12414, 57])).
% 1.65/1.86 tff(12416,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[323, 12415, 12270])).
% 1.65/1.86 tff(12417,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12418,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12419,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12418, 12417])).
% 1.65/1.86 tff(12420,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12419, 238, 8300, 1137, 227, 23])).
% 1.65/1.86 tff(12421,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12422,plain,
% 1.65/1.86 (~b(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12421, 12414, 57])).
% 1.65/1.86 tff(12423,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[112, 12422])).
% 1.65/1.86 tff(12424,plain,
% 1.65/1.86 (~r(s(elem!1), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[315, 12423, 12416])).
% 1.65/1.86 tff(12425,plain,
% 1.65/1.86 (b(s(elem!1), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[473, 12424, 1])).
% 1.65/1.86 tff(12426,plain,
% 1.65/1.86 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[3161, 8300])).
% 1.65/1.86 tff(12427,plain,
% 1.65/1.86 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12426, 12414, 57])).
% 1.65/1.86 tff(12428,plain,
% 1.65/1.86 (r(s(s(elem!1)), elem!1)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[255, 12427, 167])).
% 1.65/1.86 tff(12429,plain,
% 1.65/1.86 (~r(elem!1, s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[263, 12423, 12428])).
% 1.65/1.86 tff(12430,plain,
% 1.65/1.86 ((~b(s(z), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(z)) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = elem!1) | (s(s(elem!1)) = elem!1) | (~b(s(s(z)), s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[9383, 8300])).
% 1.65/1.86 tff(12431,plain,
% 1.65/1.86 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12430, 12423, 57, 167, 1, 10891, 12270, 12414])).
% 1.65/1.86 tff(12432,plain,
% 1.65/1.86 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1624, 12431])).
% 1.65/1.86 tff(12433,plain,
% 1.65/1.86 (~(s(s(z)) = elem!1)),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[4855, 12432, 12422])).
% 1.65/1.86 tff(12434,plain,
% 1.65/1.86 (r(elem!1, s(z)) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (elem!1 = s(s(elem!1))) | b(s(s(elem!1)), elem!1) | b(s(z), s(s(s(elem!1)))) | (s(s(z)) = elem!1) | b(elem!1, s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[10791, 8300])).
% 1.65/1.86 tff(12435,plain,
% 1.65/1.86 (b(elem!1, s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12434, 12433, 81, 57, 22, 150, 12427, 12429, 12269])).
% 1.65/1.86 tff(12436,plain,
% 1.65/1.86 ((~r(elem!1, s(elem!1))) | (~r(z, s(z))) | b(s(z), s(s(s(elem!1)))) | r(elem!1, s(z)) | (elem!1 = s(s(elem!1))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[10663, 8300])).
% 1.65/1.86 tff(12437,plain,
% 1.65/1.86 (~r(elem!1, s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12436, 12433, 81, 12269, 57, 12429, 150, 22])).
% 1.65/1.86 tff(12438,plain,
% 1.65/1.86 (b(elem!1, s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[629, 12437, 10890])).
% 1.65/1.86 tff(12439,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[1160, 12438, 12435, 57, 12425])).
% 1.65/1.86 tff(12440,plain,((elem!1 = s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (s(elem!1) = s(z)) | r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12441,plain,
% 1.65/1.86 (elem!1 = s(s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12440, 24, 1, 81])).
% 1.65/1.86 tff(12442,plain,
% 1.65/1.86 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[2097, 12441])).
% 1.65/1.86 tff(12443,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12442])).
% 1.65/1.86 tff(12444,plain,
% 1.65/1.86 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12441])).
% 1.65/1.86 tff(12445,plain,
% 1.65/1.86 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12444, 12443])).
% 1.65/1.86 tff(12446,plain,
% 1.65/1.86 (~r(s(s(z)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[8206, 57, 12269])).
% 1.65/1.86 tff(12447,plain,
% 1.65/1.86 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12441])).
% 1.65/1.86 tff(12448,plain,
% 1.65/1.86 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.65/1.86 inference(symmetry,[status(thm)],[12447])).
% 1.65/1.86 tff(12449,plain,
% 1.65/1.86 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(z)) = elem!1))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12448])).
% 1.65/1.86 tff(12450,plain,
% 1.65/1.86 (~(s(s(z)) = elem!1)),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[22, 12449])).
% 1.65/1.86 tff(12451,plain,
% 1.65/1.86 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[11244, 12450, 81, 24, 12446])).
% 1.65/1.86 tff(12452,plain,
% 1.65/1.86 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[11464, 12451, 57])).
% 1.65/1.86 tff(12453,plain,
% 1.65/1.86 (r(elem!1, s(elem!1))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[2940, 12452, 10229, 12442])).
% 1.65/1.86 tff(12454,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12453, 12445])).
% 1.65/1.86 tff(12455,plain,
% 1.65/1.86 (~b(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12421, 12451, 57])).
% 1.65/1.86 tff(12456,plain,
% 1.65/1.86 (r(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[112, 12455])).
% 1.65/1.86 tff(12457,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12458,plain,
% 1.65/1.86 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.86 inference(rewrite,[status(thm)],[])).
% 1.65/1.86 tff(12459,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.65/1.86 inference(monotonicity,[status(thm)],[12458])).
% 1.65/1.86 tff(12460,plain,
% 1.65/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.65/1.86 inference(transitivity,[status(thm)],[12459, 12457])).
% 1.65/1.86 tff(12461,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.65/1.86 inference(quant_inst,[status(thm)],[])).
% 1.65/1.86 tff(12462,plain,
% 1.65/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.86 inference(modus_ponens,[status(thm)],[12461, 12460])).
% 1.65/1.86 tff(12463,plain,
% 1.65/1.86 ($false),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12462, 124, 12456, 12454, 10004])).
% 1.65/1.86 tff(12464,plain,(r(s(z), s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.86 tff(12465,plain,
% 1.65/1.86 (r(s(z), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12464, 1, 81])).
% 1.65/1.86 tff(12466,plain,
% 1.65/1.86 ((~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1))))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[8143, 10004])).
% 1.65/1.86 tff(12467,plain,
% 1.65/1.86 (~r(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12466, 11399, 1545, 160])).
% 1.65/1.86 tff(12468,plain,
% 1.65/1.86 (b(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[112, 12467])).
% 1.65/1.86 tff(12469,plain,
% 1.65/1.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[223, 10009, 11398])).
% 1.65/1.86 tff(12470,plain,
% 1.65/1.86 (~r(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12466, 12469, 1545, 160])).
% 1.65/1.86 tff(12471,plain,
% 1.65/1.86 (b(s(s(elem!1)), s(z))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[112, 12470])).
% 1.65/1.86 tff(12472,plain,
% 1.65/1.86 (b(s(z), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[11309, 10025])).
% 1.65/1.86 tff(12473,plain,
% 1.65/1.86 (~b(s(elem!1), s(s(z)))),
% 1.65/1.86 inference(unit_resolution,[status(thm)],[12169, 12009, 12472])).
% 1.65/1.87 tff(12474,plain,
% 1.65/1.87 (~b(s(s(elem!1)), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[8921, 238, 8300, 12472, 12471])).
% 1.65/1.87 tff(12475,plain,
% 1.65/1.87 (r(s(s(elem!1)), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[5230, 51, 12474, 5385])).
% 1.65/1.87 tff(12476,plain,
% 1.65/1.87 ((~(s(elem!1) = s(s(z)))) | b(s(elem!1), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2858, 8300])).
% 1.65/1.87 tff(12477,plain,
% 1.65/1.87 (~(s(elem!1) = s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12476, 1808])).
% 1.65/1.87 tff(12478,plain,
% 1.65/1.87 (r(s(elem!1), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[488, 12477, 4572])).
% 1.65/1.87 tff(12479,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12480,plain,
% 1.65/1.87 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12481,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12480])).
% 1.65/1.87 tff(12482,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12481, 12479])).
% 1.65/1.87 tff(12483,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12484,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12483, 12482])).
% 1.65/1.87 tff(12485,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12484, 124, 307, 12478, 5414, 8970])).
% 1.65/1.87 tff(12486,plain,(b(s(elem!1), s(z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(z)))) | b(s(elem!1), s(s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12487,plain,
% 1.65/1.87 (b(s(elem!1), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12486, 307, 12475, 12473, 1])).
% 1.65/1.87 tff(12488,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12489,plain,
% 1.65/1.87 (((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(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(z), s(s(z)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12490,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12489])).
% 1.65/1.87 tff(12491,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12490, 12488])).
% 1.65/1.87 tff(12492,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12493,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12492, 12491])).
% 1.65/1.87 tff(12494,plain,
% 1.65/1.87 (~b(s(s(z)), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12493, 238, 8300, 12487, 12472])).
% 1.65/1.87 tff(12495,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[9607, 124, 307, 192, 4689])).
% 1.65/1.87 tff(12496,plain,((~r(s(s(z)), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12497,plain,
% 1.65/1.87 (~r(s(s(z)), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12496, 307, 192])).
% 1.65/1.87 tff(12498,plain,
% 1.65/1.87 (s(s(z)) = s(elem!1)),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1260, 51, 12497, 12494])).
% 1.65/1.87 tff(12499,plain,
% 1.65/1.87 (s(s(s(z))) = s(s(elem!1))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12498])).
% 1.65/1.87 tff(12500,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12499])).
% 1.65/1.87 tff(12501,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12500])).
% 1.65/1.87 tff(12502,plain,
% 1.65/1.87 ((~b(s(s(s(s(s(z))))), s(s(elem!1)))) <=> (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12501])).
% 1.65/1.87 tff(12503,plain,
% 1.65/1.87 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12499])).
% 1.65/1.87 tff(12504,plain,
% 1.65/1.87 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12503])).
% 1.65/1.87 tff(12505,plain,
% 1.65/1.87 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12504])).
% 1.65/1.87 tff(12506,plain,
% 1.65/1.87 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12505, 1008])).
% 1.65/1.87 tff(12507,plain,
% 1.65/1.87 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12506])).
% 1.65/1.87 tff(12508,plain,
% 1.65/1.87 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12507])).
% 1.65/1.87 tff(12509,plain,
% 1.65/1.87 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[2782, 12508])).
% 1.65/1.87 tff(12510,plain,
% 1.65/1.87 ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[8140, 10004])).
% 1.65/1.87 tff(12511,plain,
% 1.65/1.87 (~r(z, s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12510, 160, 1545])).
% 1.65/1.87 tff(12512,plain,
% 1.65/1.87 (b(z, s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[3795, 51, 12511, 3785])).
% 1.65/1.87 tff(12513,plain,
% 1.65/1.87 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[10835, 10004])).
% 1.65/1.87 tff(12514,plain,
% 1.65/1.87 (~r(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12513, 12512, 1545, 12469, 12509])).
% 1.65/1.87 tff(12515,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1781, 12514])).
% 1.65/1.87 tff(12516,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12517,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12518,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12517, 12516])).
% 1.65/1.87 tff(12519,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12518, 238, 12471, 12009, 12515])).
% 1.65/1.87 tff(12520,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12519, 12502])).
% 1.65/1.87 tff(12521,plain,
% 1.65/1.87 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(s(z))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12498])).
% 1.65/1.87 tff(12522,plain,
% 1.65/1.87 (r(s(elem!1), s(s(s(z)))) <=> r(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12521])).
% 1.65/1.87 tff(12523,plain,
% 1.65/1.87 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12499])).
% 1.65/1.87 tff(12524,plain,
% 1.65/1.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(z))))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12523])).
% 1.65/1.87 tff(12525,plain,
% 1.65/1.87 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12524, 12522])).
% 1.65/1.87 tff(12526,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12527,plain,
% 1.65/1.87 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12528,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12527])).
% 1.65/1.87 tff(12529,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12528, 12526])).
% 1.65/1.87 tff(12530,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12531,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12530, 12529])).
% 1.65/1.87 tff(12532,plain,
% 1.65/1.87 (~b(s(elem!1), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12531, 238, 12487, 12472, 12471])).
% 1.65/1.87 tff(12533,plain,
% 1.65/1.87 (r(s(elem!1), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[534, 12532, 206])).
% 1.65/1.87 tff(12534,plain,
% 1.65/1.87 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12533, 12525])).
% 1.65/1.87 tff(12535,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12536,plain,
% 1.65/1.87 (((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12537,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12536])).
% 1.65/1.87 tff(12538,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12537, 12535])).
% 1.65/1.87 tff(12539,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12540,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12539, 12538])).
% 1.65/1.87 tff(12541,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12540, 238, 12487, 12009, 12515])).
% 1.65/1.87 tff(12542,plain,
% 1.65/1.87 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[10847, 12541, 12498])).
% 1.65/1.87 tff(12543,plain,
% 1.65/1.87 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1738, 12542])).
% 1.65/1.87 tff(12544,plain,
% 1.65/1.87 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[4329, 12543, 12534])).
% 1.65/1.87 tff(12545,plain,
% 1.65/1.87 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[1101, 12544])).
% 1.65/1.87 tff(12546,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12545, 12520])).
% 1.65/1.87 tff(12547,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12548,plain,
% 1.65/1.87 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12547, 192, 206, 1, 1545, 160])).
% 1.65/1.87 tff(12549,plain,
% 1.65/1.87 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[323, 12548, 3294])).
% 1.65/1.87 tff(12550,plain,
% 1.65/1.87 ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[4743, 10004])).
% 1.65/1.87 tff(12551,plain,
% 1.65/1.87 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12550, 306])).
% 1.65/1.87 tff(12552,plain,
% 1.65/1.87 (b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[539, 12551, 418])).
% 1.65/1.87 tff(12553,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[298, 11409, 12552, 289, 12469])).
% 1.65/1.87 tff(12554,plain,((~r(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12555,plain,
% 1.65/1.87 (~r(s(elem!1), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12554, 12549, 206, 418, 160])).
% 1.65/1.87 tff(12556,plain,
% 1.65/1.87 (b(s(elem!1), s(z))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[473, 12555, 1])).
% 1.65/1.87 tff(12557,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12558,plain,
% 1.65/1.87 (((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12559,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12558])).
% 1.65/1.87 tff(12560,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12559, 12557])).
% 1.65/1.87 tff(12561,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.65/1.87 inference(quant_inst,[status(thm)],[])).
% 1.65/1.87 tff(12562,plain,
% 1.65/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12561, 12560])).
% 1.65/1.87 tff(12563,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12562, 238, 12549, 12556, 12472, 12471])).
% 1.65/1.87 tff(12564,plain,((~r(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12565,plain,
% 1.65/1.87 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12564, 159, 1, 415, 160, 1545])).
% 1.65/1.87 tff(12566,plain,
% 1.65/1.87 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[135, 12565, 22])).
% 1.65/1.87 tff(12567,plain,
% 1.65/1.87 (~b(s(z), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[11304, 12566, 12468])).
% 1.65/1.87 tff(12568,plain,
% 1.65/1.87 (r(s(z), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[11309, 12567])).
% 1.65/1.87 tff(12569,plain,
% 1.65/1.87 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[10049, 12568])).
% 1.65/1.87 tff(12570,plain,
% 1.65/1.87 (b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[3233, 12569])).
% 1.65/1.87 tff(12571,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[6287, 238, 12566, 11399, 12468, 12570])).
% 1.65/1.87 tff(12572,plain,((elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12573,plain,
% 1.65/1.87 (elem!1 = s(s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12572, 1, 12465, 12269])).
% 1.65/1.87 tff(12574,plain,
% 1.65/1.87 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12573])).
% 1.65/1.87 tff(12575,plain,
% 1.65/1.87 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12574])).
% 1.65/1.87 tff(12576,plain,
% 1.65/1.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[10022, 12465])).
% 1.65/1.87 tff(12577,plain,
% 1.65/1.87 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[2097, 12573])).
% 1.65/1.87 tff(12578,plain,
% 1.65/1.87 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12577])).
% 1.65/1.87 tff(12579,plain,
% 1.65/1.87 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12573])).
% 1.65/1.87 tff(12580,plain,
% 1.65/1.87 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.87 inference(transitivity,[status(thm)],[12579, 12578])).
% 1.65/1.87 tff(12581,plain,
% 1.65/1.87 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12580])).
% 1.65/1.87 tff(12582,plain,
% 1.65/1.87 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.65/1.87 inference(monotonicity,[status(thm)],[12577])).
% 1.65/1.87 tff(12583,plain,
% 1.65/1.87 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.65/1.87 inference(symmetry,[status(thm)],[12582])).
% 1.65/1.87 tff(12584,plain,
% 1.65/1.87 (r(s(z), s(elem!1))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[10004, 12583])).
% 1.65/1.87 tff(12585,plain,
% 1.65/1.87 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[6009, 12584, 12465])).
% 1.65/1.87 tff(12586,plain,
% 1.65/1.87 (~r(elem!1, s(elem!1))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[7696, 12585, 12573])).
% 1.65/1.87 tff(12587,plain,
% 1.65/1.87 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.87 inference(modus_ponens,[status(thm)],[12586, 12581])).
% 1.65/1.87 tff(12588,plain,
% 1.65/1.87 (~r(z, s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12510, 12465, 12269])).
% 1.65/1.87 tff(12589,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.65/1.87 tff(12590,plain,
% 1.65/1.87 ($false),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[3795, 51, 9232, 3785, 12589])).
% 1.65/1.87 tff(12591,plain,(b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.87 tff(12592,plain,
% 1.65/1.87 (b(z, s(s(s(elem!1))))),
% 1.65/1.87 inference(unit_resolution,[status(thm)],[12591, 12588])).
% 1.65/1.87 tff(12593,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12594,plain,
% 1.65/1.87 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.65/1.87 inference(rewrite,[status(thm)],[])).
% 1.65/1.87 tff(12595,plain,
% 1.65/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12594])).
% 1.65/1.88 tff(12596,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12595, 12593])).
% 1.65/1.88 tff(12597,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12598,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12597, 12596])).
% 1.65/1.88 tff(12599,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12598, 124, 160, 2026, 1545])).
% 1.65/1.88 tff(12600,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(12601,plain,
% 1.65/1.88 (~r(z, s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12600, 12465, 12269])).
% 1.65/1.88 tff(12602,plain,
% 1.65/1.88 (b(z, s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[2071, 12601])).
% 1.65/1.88 tff(12603,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.65/1.88 tff(12604,plain,
% 1.65/1.88 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[2549, 51, 12603])).
% 1.65/1.88 tff(12605,plain,
% 1.65/1.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12604, 2596])).
% 1.65/1.88 tff(12606,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12607,plain,
% 1.65/1.88 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12608,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12607])).
% 1.65/1.88 tff(12609,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12608, 12606])).
% 1.65/1.88 tff(12610,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12611,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12610, 12609])).
% 1.65/1.88 tff(12612,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12611, 238, 7733, 2078, 12605, 9918])).
% 1.65/1.88 tff(12613,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(12614,plain,
% 1.65/1.88 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12613, 12602, 12592, 12587, 12576])).
% 1.65/1.88 tff(12615,plain,
% 1.65/1.88 (~b(s(z), s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5363, 12614, 81])).
% 1.65/1.88 tff(12616,plain,
% 1.65/1.88 (elem!1 = s(s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12572, 1, 160, 1545])).
% 1.65/1.88 tff(12617,plain,
% 1.65/1.88 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[2097, 12616])).
% 1.65/1.88 tff(12618,plain,
% 1.65/1.88 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12617])).
% 1.65/1.88 tff(12619,plain,
% 1.65/1.88 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12616])).
% 1.65/1.88 tff(12620,plain,
% 1.65/1.88 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12619, 12618])).
% 1.65/1.88 tff(12621,plain,
% 1.65/1.88 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12620])).
% 1.65/1.88 tff(12622,plain,
% 1.65/1.88 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12617])).
% 1.65/1.88 tff(12623,plain,
% 1.65/1.88 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.65/1.88 inference(symmetry,[status(thm)],[12622])).
% 1.65/1.88 tff(12624,plain,
% 1.65/1.88 (r(s(z), s(elem!1))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[10004, 12623])).
% 1.65/1.88 tff(12625,plain,
% 1.65/1.88 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[6009, 12624, 160])).
% 1.65/1.88 tff(12626,plain,
% 1.65/1.88 (~r(elem!1, s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7696, 12625, 12616])).
% 1.65/1.88 tff(12627,plain,
% 1.65/1.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12626, 12621])).
% 1.65/1.88 tff(12628,plain,
% 1.65/1.88 (b(z, s(s(s(elem!1))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12591, 12511])).
% 1.65/1.88 tff(12629,plain,
% 1.65/1.88 (~r(z, s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12600, 160, 1545])).
% 1.65/1.88 tff(12630,plain,
% 1.65/1.88 (b(z, s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[2071, 12629])).
% 1.65/1.88 tff(12631,plain,
% 1.65/1.88 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12613, 12630, 12628, 12627, 11398])).
% 1.65/1.88 tff(12632,plain,
% 1.65/1.88 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12631])).
% 1.65/1.88 tff(12633,plain,
% 1.65/1.88 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12617])).
% 1.65/1.88 tff(12634,plain,
% 1.65/1.88 (b(s(elem!1), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12633, 12632])).
% 1.65/1.88 tff(12635,plain,
% 1.65/1.88 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12616])).
% 1.65/1.88 tff(12636,plain,
% 1.65/1.88 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12635])).
% 1.65/1.88 tff(12637,plain,
% 1.65/1.88 (~(s(s(s(z))) = elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7046, 12616])).
% 1.65/1.88 tff(12638,plain,
% 1.65/1.88 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12637, 12636])).
% 1.65/1.88 tff(12639,plain,
% 1.65/1.88 (~r(s(s(s(z))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[9499, 113, 1545, 12638])).
% 1.65/1.88 tff(12640,plain,
% 1.65/1.88 (b(s(s(s(z))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5118, 12639])).
% 1.65/1.88 tff(12641,plain,
% 1.65/1.88 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5222, 12617, 22])).
% 1.65/1.88 tff(12642,plain,
% 1.65/1.88 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[9930, 113, 1545, 12641, 12629])).
% 1.65/1.88 tff(12643,plain,
% 1.65/1.88 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1624, 12642])).
% 1.65/1.88 tff(12644,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12645,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z)))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12646,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(z))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12645, 12644])).
% 1.65/1.88 tff(12647,plain,
% 1.65/1.88 (~b(s(s(s(z))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12646, 238, 8300, 2258, 1456])).
% 1.65/1.88 tff(12648,plain,
% 1.65/1.88 (r(s(s(s(z))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[2298, 51, 12647, 149])).
% 1.65/1.88 tff(12649,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12650,plain,
% 1.65/1.88 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12651,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12650])).
% 1.65/1.88 tff(12652,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12651, 12649])).
% 1.65/1.88 tff(12653,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12654,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12653, 12652])).
% 1.65/1.88 tff(12655,plain,
% 1.65/1.88 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12654, 238, 8300, 2258, 1784])).
% 1.65/1.88 tff(12656,plain,
% 1.65/1.88 (r(s(s(z)), s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1604, 12655])).
% 1.65/1.88 tff(12657,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12658,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12659,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12658, 12657])).
% 1.65/1.88 tff(12660,plain,
% 1.65/1.88 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12659, 238, 2258, 1784, 1456])).
% 1.65/1.88 tff(12661,plain,
% 1.65/1.88 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5167, 12660])).
% 1.65/1.88 tff(12662,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[8889, 124, 12661, 12656, 12648])).
% 1.65/1.88 tff(12663,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(12664,plain,
% 1.65/1.88 (~b(s(z), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12663, 12643, 12640])).
% 1.65/1.88 tff(12665,plain,
% 1.65/1.88 (r(s(z), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[11309, 12664])).
% 1.65/1.88 tff(12666,plain,
% 1.65/1.88 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[10049, 12665])).
% 1.65/1.88 tff(12667,plain,
% 1.65/1.88 (b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[3233, 12666])).
% 1.65/1.88 tff(12668,plain,
% 1.65/1.88 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[11379, 12665, 160, 12643])).
% 1.65/1.88 tff(12669,plain,
% 1.65/1.88 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1738, 12668])).
% 1.65/1.88 tff(12670,plain,
% 1.65/1.88 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[11390, 12669, 12641, 12667])).
% 1.65/1.88 tff(12671,plain,
% 1.65/1.88 (b(s(z), s(s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[1968, 8300, 10004])).
% 1.65/1.88 tff(12672,plain,
% 1.65/1.88 (~r(s(elem!1), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12671, 12670, 2])).
% 1.65/1.88 tff(12673,plain,
% 1.65/1.88 (b(s(elem!1), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[473, 12672, 1])).
% 1.65/1.88 tff(12674,plain,
% 1.65/1.88 (b(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12673, 12634])).
% 1.65/1.88 tff(12675,plain,
% 1.65/1.88 ($false),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[82, 12674])).
% 1.65/1.88 tff(12676,plain,(b(s(s(elem!1)), s(z)) | (s(elem!1) = s(z)) | b(s(z), s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.88 tff(12677,plain,
% 1.65/1.88 (b(s(s(elem!1)), s(z))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12676, 1, 12615, 12465, 12269])).
% 1.65/1.88 tff(12678,plain,
% 1.65/1.88 (b(elem!1, s(z))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12677, 12575])).
% 1.65/1.88 tff(12679,plain,
% 1.65/1.88 (b(elem!1, s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12573])).
% 1.65/1.88 tff(12680,plain,
% 1.65/1.88 (b(s(s(elem!1)), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.65/1.88 inference(symmetry,[status(thm)],[12679])).
% 1.65/1.88 tff(12681,plain,
% 1.65/1.88 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12614])).
% 1.65/1.88 tff(12682,plain,
% 1.65/1.88 (b(s(elem!1), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12577])).
% 1.65/1.88 tff(12683,plain,
% 1.65/1.88 (b(s(elem!1), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12682, 12681, 12680])).
% 1.65/1.88 tff(12684,plain,
% 1.65/1.88 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12577])).
% 1.65/1.88 tff(12685,plain,
% 1.65/1.88 ((s(s(s(elem!1))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.65/1.88 inference(symmetry,[status(thm)],[12684])).
% 1.65/1.88 tff(12686,plain,
% 1.65/1.88 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12685])).
% 1.65/1.88 tff(12687,plain,
% 1.65/1.88 (~(s(elem!1) = s(s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[1291, 12686])).
% 1.65/1.88 tff(12688,plain,
% 1.65/1.88 (r(elem!1, s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[5325, 5327])).
% 1.65/1.88 tff(12689,plain,
% 1.65/1.88 ((~r(elem!1, s(elem!1))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12688])).
% 1.65/1.88 tff(12690,plain,
% 1.65/1.88 (r(s(z), s(elem!1))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[10004, 7898])).
% 1.65/1.88 tff(12691,plain,
% 1.65/1.88 (~r(s(s(elem!1)), s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[6009, 12690, 160])).
% 1.65/1.88 tff(12692,plain,
% 1.65/1.88 (~r(elem!1, s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[7696, 12691, 2073])).
% 1.65/1.88 tff(12693,plain,
% 1.65/1.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12692, 12689])).
% 1.65/1.88 tff(12694,plain,
% 1.65/1.88 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12613, 12630, 12628, 12693, 11398])).
% 1.65/1.88 tff(12695,plain,
% 1.65/1.88 (b(s(s(s(s(z)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12694])).
% 1.65/1.88 tff(12696,plain,
% 1.65/1.88 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.88 inference(symmetry,[status(thm)],[12695])).
% 1.65/1.88 tff(12697,plain,
% 1.65/1.88 ((~b(s(s(s(s(z)))), s(s(elem!1)))) <=> (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12696])).
% 1.65/1.88 tff(12698,plain,
% 1.65/1.88 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[2073])).
% 1.65/1.88 tff(12699,plain,
% 1.65/1.88 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.65/1.88 inference(monotonicity,[status(thm)],[2575])).
% 1.65/1.88 tff(12700,plain,
% 1.65/1.88 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12699])).
% 1.65/1.88 tff(12701,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12702,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12703,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12702, 12701])).
% 1.65/1.88 tff(12704,plain,
% 1.65/1.88 (~b(s(s(s(z))), s(s(elem!1)))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12703, 238, 2258, 23, 1456])).
% 1.65/1.88 tff(12705,plain,
% 1.65/1.88 (~b(s(s(s(z))), elem!1)),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12704, 12700])).
% 1.65/1.88 tff(12706,plain,
% 1.65/1.88 (r(s(s(s(z))), elem!1)),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[5094, 12705, 9465])).
% 1.65/1.88 tff(12707,plain,
% 1.65/1.88 (r(s(s(s(z))), s(s(elem!1)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12706, 12698])).
% 1.65/1.88 tff(12708,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12709,plain,
% 1.65/1.88 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12710,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12709])).
% 1.65/1.88 tff(12711,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12710, 12708])).
% 1.65/1.88 tff(12712,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.65/1.88 inference(quant_inst,[status(thm)],[])).
% 1.65/1.88 tff(12713,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.65/1.88 inference(modus_ponens,[status(thm)],[12712, 12711])).
% 1.65/1.88 tff(12714,plain,
% 1.65/1.88 (~b(s(s(z)), s(s(s(z))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[12713, 238, 8300, 2258, 1456])).
% 1.65/1.88 tff(12715,plain,
% 1.65/1.88 (r(s(s(z)), s(s(s(z))))),
% 1.65/1.88 inference(unit_resolution,[status(thm)],[4334, 12714])).
% 1.65/1.88 tff(12716,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12717,plain,
% 1.65/1.88 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.65/1.88 inference(rewrite,[status(thm)],[])).
% 1.65/1.88 tff(12718,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 1.65/1.88 inference(monotonicity,[status(thm)],[12717])).
% 1.65/1.88 tff(12719,plain,
% 1.65/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 1.65/1.88 inference(transitivity,[status(thm)],[12718, 12716])).
% 1.65/1.88 tff(12720,plain,
% 1.65/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(12721,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12720, 12719])).
% 1.65/1.89 tff(12722,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12721, 124, 192, 12715, 12707, 12648])).
% 1.65/1.89 tff(12723,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12724,plain,
% 1.65/1.89 (~b(s(s(s(z))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12723, 192, 2073, 12472, 23])).
% 1.65/1.89 tff(12725,plain,
% 1.65/1.89 (r(s(s(s(z))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5118, 12724])).
% 1.65/1.89 tff(12726,plain,
% 1.65/1.89 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8420, 12725, 1545])).
% 1.65/1.89 tff(12727,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1624, 12726])).
% 1.65/1.89 tff(12728,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(12729,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(12730,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12729, 12728])).
% 1.65/1.89 tff(12731,plain,
% 1.65/1.89 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12730, 238, 12472, 23, 12727])).
% 1.65/1.89 tff(12732,plain,
% 1.65/1.89 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12731, 12697])).
% 1.65/1.89 tff(12733,plain,
% 1.65/1.89 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12694])).
% 1.65/1.89 tff(12734,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12733])).
% 1.65/1.89 tff(12735,plain,
% 1.65/1.89 ((~b(s(s(elem!1)), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(z))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12734])).
% 1.65/1.89 tff(12736,plain,
% 1.65/1.89 (~b(s(s(elem!1)), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8921, 238, 8300, 12472, 23])).
% 1.65/1.89 tff(12737,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12736, 12735])).
% 1.65/1.89 tff(12738,plain,
% 1.65/1.89 (r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3233, 12737])).
% 1.65/1.89 tff(12739,plain,
% 1.65/1.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[9958, 238, 8300, 12472, 12727])).
% 1.65/1.89 tff(12740,plain,
% 1.65/1.89 (r(s(s(s(s(z)))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1564, 12739])).
% 1.65/1.89 tff(12741,plain,
% 1.65/1.89 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3010, 12740, 12738])).
% 1.65/1.89 tff(12742,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8247, 12741, 2963])).
% 1.65/1.89 tff(12743,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12742, 12732])).
% 1.65/1.89 tff(12744,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12745,plain,
% 1.65/1.89 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12744, 12677, 12269, 12573, 12465])).
% 1.65/1.89 tff(12746,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[135, 12745, 22])).
% 1.65/1.89 tff(12747,plain,
% 1.65/1.89 (~b(s(z), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11304, 12746, 12677])).
% 1.65/1.89 tff(12748,plain,
% 1.65/1.89 (r(s(z), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11309, 12747])).
% 1.65/1.89 tff(12749,plain,
% 1.65/1.89 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10049, 12748])).
% 1.65/1.89 tff(12750,plain,
% 1.65/1.89 (~r(s(elem!1), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3017, 12749, 12577])).
% 1.65/1.89 tff(12751,plain,
% 1.65/1.89 (b(s(elem!1), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[488, 12750, 12687])).
% 1.65/1.89 tff(12752,plain,
% 1.65/1.89 (b(elem!1, s(s(z)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12751, 12683])).
% 1.65/1.89 tff(12753,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(12754,plain,
% 1.65/1.89 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(12755,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12754])).
% 1.65/1.89 tff(12756,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12755, 12753])).
% 1.65/1.89 tff(12757,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(12758,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12757, 12756])).
% 1.65/1.89 tff(12759,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12758, 238, 8300, 370, 753, 2765])).
% 1.65/1.89 tff(12760,plain,((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12761,plain,
% 1.65/1.89 (~b(s(z), s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12760, 12752, 12678])).
% 1.65/1.89 tff(12762,plain,
% 1.65/1.89 (s(elem!1) = elem!1),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5315, 12614, 12573])).
% 1.65/1.89 tff(12763,plain,
% 1.65/1.89 (elem!1 = s(elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[393, 12762])).
% 1.65/1.89 tff(12764,plain,
% 1.65/1.89 (b(z, elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2080, 12602, 12573])).
% 1.65/1.89 tff(12765,plain,
% 1.65/1.89 (b(s(s(z)), s(elem!1)) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12577])).
% 1.65/1.89 tff(12766,plain,
% 1.65/1.89 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12765])).
% 1.65/1.89 tff(12767,plain,
% 1.65/1.89 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12614])).
% 1.65/1.89 tff(12768,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12767])).
% 1.65/1.89 tff(12769,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(elem!1))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12768, 12766])).
% 1.65/1.89 tff(12770,plain,
% 1.65/1.89 (b(s(s(z)), s(elem!1))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12746, 12769])).
% 1.65/1.89 tff(12771,plain,
% 1.65/1.89 (r(z, s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2188, 12770, 12764, 12763, 12751])).
% 1.65/1.89 tff(12772,plain,
% 1.65/1.89 (~r(s(z), s(s(s(s(z)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10639, 12771, 12269, 12748])).
% 1.65/1.89 tff(12773,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[6600, 12772, 12761])).
% 1.65/1.89 tff(12774,plain,((s(elem!1) = s(z)) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12775,plain,
% 1.65/1.89 (s(elem!1) = s(z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12774, 81])).
% 1.65/1.89 tff(12776,plain,
% 1.65/1.89 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12775])).
% 1.65/1.89 tff(12777,plain,
% 1.65/1.89 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12776])).
% 1.65/1.89 tff(12778,plain,
% 1.65/1.89 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12775])).
% 1.65/1.89 tff(12779,plain,
% 1.65/1.89 (elem!1 = z),
% 1.65/1.89 inference(transitivity,[status(thm)],[155, 12778, 26])).
% 1.65/1.89 tff(12780,plain,
% 1.65/1.89 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12779])).
% 1.65/1.89 tff(12781,plain,
% 1.65/1.89 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12780])).
% 1.65/1.89 tff(12782,plain,
% 1.65/1.89 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12781, 12777])).
% 1.65/1.89 tff(12783,plain,
% 1.65/1.89 (r(elem!1, s(elem!1))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12269, 12782])).
% 1.65/1.89 tff(12784,plain,
% 1.65/1.89 (b(elem!1, s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10246, 12783, 12775, 81])).
% 1.65/1.89 tff(12785,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11248, 12775])).
% 1.65/1.89 tff(12786,plain,
% 1.65/1.89 (s(s(z)) = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[357, 12775])).
% 1.65/1.89 tff(12787,plain,
% 1.65/1.89 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12786])).
% 1.65/1.89 tff(12788,plain,
% 1.65/1.89 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12787, 3730])).
% 1.65/1.89 tff(12789,plain,
% 1.65/1.89 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12788])).
% 1.65/1.89 tff(12790,plain,
% 1.65/1.89 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[4960, 12786])).
% 1.65/1.89 tff(12791,plain,
% 1.65/1.89 (~(s(s(z)) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1385, 12790])).
% 1.65/1.89 tff(12792,plain,
% 1.65/1.89 (~(elem!1 = s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12791, 12789])).
% 1.65/1.89 tff(12793,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12786])).
% 1.65/1.89 tff(12794,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12793])).
% 1.65/1.89 tff(12795,plain,
% 1.65/1.89 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12794])).
% 1.65/1.89 tff(12796,plain,
% 1.65/1.89 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[10088, 12795])).
% 1.65/1.89 tff(12797,plain,
% 1.65/1.89 (b(s(elem!1), s(z)) <=> b(s(z), s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12775])).
% 1.65/1.89 tff(12798,plain,
% 1.65/1.89 (b(s(z), s(z)) <=> b(s(elem!1), s(z))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12797])).
% 1.65/1.89 tff(12799,plain,
% 1.65/1.89 ((~b(s(z), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12798])).
% 1.65/1.89 tff(12800,plain,
% 1.65/1.89 (b(s(elem!1), s(elem!1)) <=> b(s(z), s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12775, 12775])).
% 1.65/1.89 tff(12801,plain,
% 1.65/1.89 ((~b(s(elem!1), s(elem!1))) <=> (~b(s(z), s(z)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12800])).
% 1.65/1.89 tff(12802,plain,
% 1.65/1.89 ((~![X: $i] : (~b(X, X))) | (~b(s(elem!1), s(elem!1)))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(12803,plain,
% 1.65/1.89 (~b(s(elem!1), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12802, 837])).
% 1.65/1.89 tff(12804,plain,
% 1.65/1.89 (~b(s(z), s(z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12803, 12801])).
% 1.65/1.89 tff(12805,plain,
% 1.65/1.89 (~b(s(elem!1), s(z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12804, 12799])).
% 1.65/1.89 tff(12806,plain,
% 1.65/1.89 (b(s(elem!1), s(z)) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(elem!1))) | b(z, s(z)) | b(s(s(z)), s(s(elem!1))) | (s(s(z)) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10592, 8300])).
% 1.65/1.89 tff(12807,plain,
% 1.65/1.89 (r(s(z), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12806, 12805, 81, 12268, 12796, 12791])).
% 1.65/1.89 tff(12808,plain,
% 1.65/1.89 (r(elem!1, s(z))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12269, 12781])).
% 1.65/1.89 tff(12809,plain,
% 1.65/1.89 (~r(elem!1, s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5843, 12808, 12807])).
% 1.65/1.89 tff(12810,plain,
% 1.65/1.89 (b(elem!1, s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[606, 12809, 12792])).
% 1.65/1.89 tff(12811,plain,
% 1.65/1.89 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12786])).
% 1.65/1.89 tff(12812,plain,
% 1.65/1.89 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12811])).
% 1.65/1.89 tff(12813,plain,
% 1.65/1.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[1291, 12812])).
% 1.65/1.89 tff(12814,plain,
% 1.65/1.89 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10022, 12807])).
% 1.65/1.89 tff(12815,plain,
% 1.65/1.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[223, 12814, 12813])).
% 1.65/1.89 tff(12816,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3306, 12815, 12810, 12785, 12784])).
% 1.65/1.89 tff(12817,plain,(b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12818,plain,
% 1.65/1.89 (~b(z, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11467, 113, 1137, 159, 22])).
% 1.65/1.89 tff(12819,plain,
% 1.65/1.89 (r(z, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1542, 12818])).
% 1.65/1.89 tff(12820,plain,
% 1.65/1.89 (~r(s(s(elem!1)), z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[4026, 124, 113, 12819])).
% 1.65/1.89 tff(12821,plain,
% 1.65/1.89 (b(s(s(elem!1)), z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[4905, 12820])).
% 1.65/1.89 tff(12822,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(12823,plain,
% 1.65/1.89 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.65/1.89 inference(rewrite,[status(thm)],[])).
% 1.65/1.89 tff(12824,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12823])).
% 1.65/1.89 tff(12825,plain,
% 1.65/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12824, 12822])).
% 1.65/1.89 tff(12826,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.65/1.89 inference(quant_inst,[status(thm)],[])).
% 1.65/1.89 tff(12827,plain,
% 1.65/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12826, 12825])).
% 1.65/1.89 tff(12828,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12827, 238, 1137, 226, 12817, 4047])).
% 1.65/1.89 tff(12829,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12830,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12829, 12821, 1137])).
% 1.65/1.89 tff(12831,plain,
% 1.65/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[223, 12830, 209])).
% 1.65/1.89 tff(12832,plain,
% 1.65/1.89 ((~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8306, 8300])).
% 1.65/1.89 tff(12833,plain,
% 1.65/1.89 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12832, 12831, 12817])).
% 1.65/1.89 tff(12834,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[135, 12833, 22])).
% 1.65/1.89 tff(12835,plain,
% 1.65/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11464, 12834, 1137])).
% 1.65/1.89 tff(12836,plain,
% 1.65/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[323, 12835, 272])).
% 1.65/1.89 tff(12837,plain,
% 1.65/1.89 (~r(s(elem!1), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[315, 12836, 113])).
% 1.65/1.89 tff(12838,plain,
% 1.65/1.89 (b(s(elem!1), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[473, 12837, 1])).
% 1.65/1.89 tff(12839,plain,
% 1.65/1.89 (~b(s(s(elem!1)), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12426, 12834, 1137])).
% 1.65/1.89 tff(12840,plain,
% 1.65/1.89 (r(s(s(elem!1)), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[255, 12839, 167])).
% 1.65/1.89 tff(12841,plain,
% 1.65/1.89 (~r(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[263, 12840, 113])).
% 1.65/1.89 tff(12842,plain,
% 1.65/1.89 (~r(s(s(s(s(z)))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12430, 12834, 1137, 167, 1, 394, 272, 113])).
% 1.65/1.89 tff(12843,plain,
% 1.65/1.89 (b(s(s(s(s(z)))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1624, 12842])).
% 1.65/1.89 tff(12844,plain,
% 1.65/1.89 (~(s(elem!1) = s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8538, 12843, 82, 12817, 12819, 12831, 421])).
% 1.65/1.89 tff(12845,plain,
% 1.65/1.89 (~(elem!1 = s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[280, 12844])).
% 1.65/1.89 tff(12846,plain,
% 1.65/1.89 (b(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[363, 12845, 12841])).
% 1.65/1.89 tff(12847,plain,
% 1.65/1.89 (~b(elem!1, s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1160, 12846, 1137, 12838])).
% 1.65/1.89 tff(12848,plain,
% 1.65/1.89 (~(s(s(z)) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[4855, 12843, 82])).
% 1.65/1.89 tff(12849,plain,
% 1.65/1.89 ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (s(s(z)) = elem!1) | (s(s(z)) = s(s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[10620, 8300])).
% 1.65/1.89 tff(12850,plain,
% 1.65/1.89 (~r(elem!1, s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12849, 12846, 1137, 22, 150, 12848])).
% 1.65/1.89 tff(12851,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[629, 12850, 12847, 387])).
% 1.65/1.89 tff(12852,plain,(b(s(s(elem!1)), s(z)) | (~b(s(z), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12853,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12852, 150, 1137, 1])).
% 1.65/1.89 tff(12854,plain,
% 1.65/1.89 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8310, 8300])).
% 1.65/1.89 tff(12855,plain,
% 1.65/1.89 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12854, 12853, 12817])).
% 1.65/1.89 tff(12856,plain,
% 1.65/1.89 (r(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[135, 12855, 22])).
% 1.65/1.89 tff(12857,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3192, 12853, 12817, 1137])).
% 1.65/1.89 tff(12858,plain,
% 1.65/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[223, 12857, 209])).
% 1.65/1.89 tff(12859,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12832, 12858, 12856, 12817])).
% 1.65/1.89 tff(12860,plain,((elem!1 = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12861,plain,
% 1.65/1.89 (elem!1 = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12860, 1, 1137])).
% 1.65/1.89 tff(12862,plain,
% 1.65/1.89 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12861])).
% 1.65/1.89 tff(12863,plain,
% 1.65/1.89 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2097, 12861])).
% 1.65/1.89 tff(12864,plain,
% 1.65/1.89 (~(s(s(elem!1)) = s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[271, 7735])).
% 1.65/1.89 tff(12865,plain,
% 1.65/1.89 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2879, 12863])).
% 1.65/1.89 tff(12866,plain,
% 1.65/1.89 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5222, 12863, 22])).
% 1.65/1.89 tff(12867,plain,
% 1.65/1.89 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12861])).
% 1.65/1.89 tff(12868,plain,
% 1.65/1.89 ((~(s(s(s(z))) = elem!1)) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12867])).
% 1.65/1.89 tff(12869,plain,
% 1.65/1.89 (~(s(s(s(z))) = elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[7046, 12861])).
% 1.65/1.89 tff(12870,plain,
% 1.65/1.89 (~(s(s(s(z))) = s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12869, 12868])).
% 1.65/1.89 tff(12871,plain,
% 1.65/1.89 (s(elem!1) = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11467, 1457, 1137, 162, 22])).
% 1.65/1.89 tff(12872,plain,
% 1.65/1.89 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5343, 12871])).
% 1.65/1.89 tff(12873,plain,
% 1.65/1.89 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12872])).
% 1.65/1.89 tff(12874,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12873])).
% 1.65/1.89 tff(12875,plain,
% 1.65/1.89 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12874])).
% 1.65/1.89 tff(12876,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[10088, 12875])).
% 1.65/1.89 tff(12877,plain,
% 1.65/1.89 (b(s(z), elem!1)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3083, 12861, 1137])).
% 1.65/1.89 tff(12878,plain,
% 1.65/1.89 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[9449, 1457, 12877, 12863, 1, 12870, 12817])).
% 1.65/1.89 tff(12879,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12878, 12876])).
% 1.65/1.89 tff(12880,plain,((~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12881,plain,
% 1.65/1.89 (~b(z, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12880, 162, 1137, 1])).
% 1.65/1.89 tff(12882,plain,
% 1.65/1.89 (r(z, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1542, 12881])).
% 1.65/1.89 tff(12883,plain,
% 1.65/1.89 (~r(s(s(s(z))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[9499, 12882, 12870, 162])).
% 1.65/1.89 tff(12884,plain,
% 1.65/1.89 (b(s(s(s(z))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5118, 12883])).
% 1.65/1.89 tff(12885,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[9933, 12884, 12817, 12866, 12865])).
% 1.65/1.89 tff(12886,plain,
% 1.65/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[223, 545, 12885])).
% 1.65/1.89 tff(12887,plain,
% 1.65/1.89 (~r(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12832, 12886, 12817])).
% 1.65/1.89 tff(12888,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[135, 12887, 22])).
% 1.65/1.89 tff(12889,plain,
% 1.65/1.89 (~b(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[11464, 12888, 1137])).
% 1.65/1.89 tff(12890,plain,
% 1.65/1.89 (r(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[323, 12889, 12864])).
% 1.65/1.89 tff(12891,plain,
% 1.65/1.89 (~r(s(elem!1), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[315, 12890, 162])).
% 1.65/1.89 tff(12892,plain,
% 1.65/1.89 (b(s(elem!1), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[473, 12891, 1])).
% 1.65/1.89 tff(12893,plain,
% 1.65/1.89 (b(s(s(s(elem!1))), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[5664, 12892, 12863])).
% 1.65/1.89 tff(12894,plain,
% 1.65/1.89 ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8376, 8300])).
% 1.65/1.89 tff(12895,plain,
% 1.65/1.89 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12894, 12893, 12817])).
% 1.65/1.89 tff(12896,plain,
% 1.65/1.89 (s(s(elem!1)) = elem!1),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12861, 4108])).
% 1.65/1.89 tff(12897,plain,
% 1.65/1.89 (~(elem!1 = s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1802, 12877])).
% 1.65/1.89 tff(12898,plain,
% 1.65/1.89 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12863])).
% 1.65/1.89 tff(12899,plain,
% 1.65/1.89 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12898])).
% 1.65/1.89 tff(12900,plain,
% 1.65/1.89 (b(s(z), s(elem!1))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12817, 12899])).
% 1.65/1.89 tff(12901,plain,
% 1.65/1.89 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12861])).
% 1.65/1.89 tff(12902,plain,
% 1.65/1.89 ((s(s(z)) = s(s(elem!1))) <=> (s(s(z)) = elem!1)),
% 1.65/1.89 inference(symmetry,[status(thm)],[12901])).
% 1.65/1.89 tff(12903,plain,
% 1.65/1.89 ((s(s(z)) = s(s(elem!1))) <=> (elem!1 = s(s(z)))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12902, 1972])).
% 1.65/1.89 tff(12904,plain,
% 1.65/1.89 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(elem!1 = s(s(z))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12903])).
% 1.65/1.89 tff(12905,plain,
% 1.65/1.89 (~(elem!1 = s(s(z)))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[22, 12904])).
% 1.65/1.89 tff(12906,plain,
% 1.65/1.89 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2920, 545])).
% 1.65/1.89 tff(12907,plain,
% 1.65/1.89 (r(elem!1, s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2940, 12889, 12863, 12906])).
% 1.65/1.89 tff(12908,plain,
% 1.65/1.89 (~(s(elem!1) = s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[379, 12897])).
% 1.65/1.89 tff(12909,plain,
% 1.65/1.89 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8385, 8300])).
% 1.65/1.89 tff(12910,plain,
% 1.65/1.89 (~b(s(elem!1), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12909, 12892, 12817])).
% 1.65/1.89 tff(12911,plain,
% 1.65/1.89 (r(s(elem!1), s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[488, 12910, 12908])).
% 1.65/1.89 tff(12912,plain,
% 1.65/1.89 (~r(elem!1, s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[8611, 12911, 12907])).
% 1.65/1.89 tff(12913,plain,
% 1.65/1.89 (b(elem!1, s(s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[763, 12912, 12905])).
% 1.65/1.89 tff(12914,plain,
% 1.65/1.89 ((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[9722, 8300])).
% 1.65/1.89 tff(12915,plain,
% 1.65/1.89 (~b(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12914, 12913, 12900])).
% 1.65/1.89 tff(12916,plain,
% 1.65/1.89 (r(elem!1, s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[363, 12915, 12897])).
% 1.65/1.89 tff(12917,plain,
% 1.65/1.89 ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1378, 10004])).
% 1.65/1.89 tff(12918,plain,
% 1.65/1.89 (~r(elem!1, s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12917, 12916])).
% 1.65/1.89 tff(12919,plain,
% 1.65/1.89 (elem!1 = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[166, 163])).
% 1.65/1.89 tff(12920,plain,
% 1.65/1.89 (s(elem!1) = s(s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[2097, 12919])).
% 1.65/1.89 tff(12921,plain,
% 1.65/1.89 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(elem!1))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12920])).
% 1.65/1.89 tff(12922,plain,
% 1.65/1.89 ((~b(elem!1, s(elem!1))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12921])).
% 1.65/1.89 tff(12923,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.65/1.89 tff(12924,plain,
% 1.65/1.89 (~b(elem!1, s(s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12923, 12922])).
% 1.65/1.89 tff(12925,plain,
% 1.65/1.89 (elem!1 = s(s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[1319, 12924, 1313])).
% 1.65/1.89 tff(12926,plain,
% 1.65/1.89 (s(s(s(elem!1))) = elem!1),
% 1.65/1.89 inference(symmetry,[status(thm)],[12925])).
% 1.65/1.89 tff(12927,plain,
% 1.65/1.89 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12926])).
% 1.65/1.89 tff(12928,plain,
% 1.65/1.89 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12927])).
% 1.65/1.89 tff(12929,plain,
% 1.65/1.89 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), elem!1)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[163])).
% 1.65/1.89 tff(12930,plain,
% 1.65/1.89 (b(s(s(z)), elem!1)),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[227, 12929])).
% 1.65/1.89 tff(12931,plain,
% 1.65/1.89 (b(s(s(z)), s(s(s(elem!1))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12930, 12928])).
% 1.65/1.89 tff(12932,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[179, 12931])).
% 1.65/1.89 tff(12933,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(z)), s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))) | b(elem!1, s(elem!1)) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12934,plain,
% 1.65/1.89 (b(elem!1, s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12933, 12918, 12896, 12888, 12895])).
% 1.65/1.89 tff(12935,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[12934, 12862])).
% 1.65/1.89 tff(12936,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12889, 12935])).
% 1.65/1.89 tff(12937,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12938,plain,
% 1.65/1.89 (~r(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12937, 1, 545, 1137])).
% 1.65/1.89 tff(12939,plain,
% 1.65/1.89 (b(s(s(elem!1)), s(z))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[112, 12938])).
% 1.65/1.89 tff(12940,plain,
% 1.65/1.89 (~b(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12854, 12939, 12817])).
% 1.65/1.89 tff(12941,plain,
% 1.65/1.89 (r(s(s(z)), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[135, 12940, 22])).
% 1.65/1.89 tff(12942,plain,
% 1.65/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[3192, 12939, 12817, 1137])).
% 1.65/1.89 tff(12943,plain,
% 1.65/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[223, 12942, 545])).
% 1.65/1.89 tff(12944,plain,
% 1.65/1.89 ($false),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12832, 12943, 12941, 12817])).
% 1.65/1.89 tff(12945,plain,((s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.89 tff(12946,plain,
% 1.65/1.89 (s(elem!1) = s(z)),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[12945, 10007, 57])).
% 1.65/1.89 tff(12947,plain,
% 1.65/1.89 (s(s(z)) = s(s(elem!1))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[357, 12946])).
% 1.65/1.89 tff(12948,plain,
% 1.65/1.89 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.65/1.89 inference(unit_resolution,[status(thm)],[4960, 12947])).
% 1.65/1.89 tff(12949,plain,
% 1.65/1.89 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12946])).
% 1.65/1.89 tff(12950,plain,
% 1.65/1.89 (elem!1 = z),
% 1.65/1.89 inference(transitivity,[status(thm)],[155, 12949, 26])).
% 1.65/1.89 tff(12951,plain,
% 1.65/1.89 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = z)),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12950])).
% 1.65/1.89 tff(12952,plain,
% 1.65/1.89 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.65/1.89 inference(symmetry,[status(thm)],[12951])).
% 1.65/1.89 tff(12953,plain,
% 1.65/1.89 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.65/1.89 inference(transitivity,[status(thm)],[12952, 9219])).
% 1.65/1.89 tff(12954,plain,
% 1.65/1.89 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12953])).
% 1.65/1.89 tff(12955,plain,
% 1.65/1.89 (~(elem!1 = s(s(s(z))))),
% 1.65/1.89 inference(modus_ponens,[status(thm)],[1469, 12954])).
% 1.65/1.89 tff(12956,plain,
% 1.65/1.89 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.65/1.89 inference(monotonicity,[status(thm)],[12950])).
% 1.65/1.89 tff(12957,plain,
% 1.65/1.89 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.65/1.89 inference(symmetry,[status(thm)],[12956])).
% 1.65/1.89 tff(12958,plain,
% 1.65/1.89 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12947])).
% 1.65/1.90 tff(12959,plain,
% 1.65/1.90 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12958])).
% 1.65/1.90 tff(12960,plain,
% 1.65/1.90 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(z))))),
% 1.65/1.90 inference(symmetry,[status(thm)],[12959])).
% 1.65/1.90 tff(12961,plain,
% 1.65/1.90 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12950])).
% 1.65/1.90 tff(12962,plain,
% 1.65/1.90 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.65/1.90 inference(transitivity,[status(thm)],[12961, 12960, 12957])).
% 1.65/1.90 tff(12963,plain,
% 1.65/1.90 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12962])).
% 1.65/1.90 tff(12964,plain,
% 1.65/1.90 (b(s(s(elem!1)), s(elem!1))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[11248, 12946])).
% 1.65/1.90 tff(12965,plain,
% 1.65/1.90 (~(s(elem!1) = s(s(elem!1)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[5343, 10007])).
% 1.65/1.90 tff(12966,plain,
% 1.65/1.90 (~r(s(elem!1), s(s(elem!1)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[3876, 12946, 24])).
% 1.65/1.90 tff(12967,plain,
% 1.65/1.90 (b(s(elem!1), s(s(elem!1)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[534, 12966, 12965])).
% 1.65/1.90 tff(12968,plain,
% 1.65/1.90 (~b(s(elem!1), s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[4533, 12967, 57, 12964])).
% 1.65/1.90 tff(12969,plain,
% 1.65/1.90 (~(s(elem!1) = s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[12476, 12968])).
% 1.65/1.90 tff(12970,plain,
% 1.65/1.90 (~(elem!1 = s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[280, 12969])).
% 1.65/1.90 tff(12971,plain,
% 1.65/1.90 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12947])).
% 1.65/1.90 tff(12972,plain,
% 1.65/1.90 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 1.65/1.90 inference(symmetry,[status(thm)],[12971])).
% 1.65/1.90 tff(12973,plain,
% 1.65/1.90 (b(s(z), s(s(z)))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[57, 12972])).
% 1.65/1.90 tff(12974,plain,
% 1.65/1.90 ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[8666, 8300])).
% 1.65/1.90 tff(12975,plain,
% 1.65/1.90 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[12974, 12973, 12817])).
% 1.65/1.90 tff(12976,plain,
% 1.65/1.90 (r(s(s(s(elem!1))), s(s(z)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[3233, 12975])).
% 1.65/1.90 tff(12977,plain,
% 1.65/1.90 (~b(z, s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[8848, 12976, 12817])).
% 1.65/1.90 tff(12978,plain,
% 1.65/1.90 (~b(elem!1, s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[5709, 12977, 12946])).
% 1.65/1.90 tff(12979,plain,
% 1.65/1.90 (r(elem!1, s(z))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[363, 12978, 12970])).
% 1.65/1.90 tff(12980,plain,
% 1.65/1.90 (~r(elem!1, s(s(s(elem!1))))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[12917, 12979])).
% 1.65/1.90 tff(12981,plain,
% 1.65/1.90 (~r(elem!1, s(s(s(z))))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[12980, 12963])).
% 1.65/1.90 tff(12982,plain,
% 1.65/1.90 (b(elem!1, s(s(s(z))))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[5079, 12981, 12955])).
% 1.65/1.90 tff(12983,plain,
% 1.65/1.90 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12946])).
% 1.65/1.90 tff(12984,plain,
% 1.65/1.90 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.90 inference(symmetry,[status(thm)],[12983])).
% 1.65/1.90 tff(12985,plain,
% 1.65/1.90 (b(s(elem!1), s(s(s(elem!1))))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[12817, 12984])).
% 1.65/1.90 tff(12986,plain,
% 1.65/1.90 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[298, 12985, 12964, 12967])).
% 1.65/1.90 tff(12987,plain,
% 1.65/1.90 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.65/1.90 inference(unit_resolution,[status(thm)],[223, 12986, 10007])).
% 1.65/1.90 tff(12988,plain,
% 1.65/1.90 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12946])).
% 1.65/1.90 tff(12989,plain,
% 1.65/1.90 (b(s(s(elem!1)), s(z))),
% 1.65/1.90 inference(modus_ponens,[status(thm)],[12964, 12988])).
% 1.65/1.90 tff(12990,plain,
% 1.65/1.90 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.90 inference(monotonicity,[status(thm)],[12947])).
% 1.65/1.90 tff(12991,plain,
% 1.65/1.90 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.65/1.90 inference(transitivity,[status(thm)],[12990, 3730])).
% 1.65/1.90 tff(12992,plain,
% 1.65/1.90 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.65/1.90 inference(transitivity,[status(thm)],[12991, 4108])).
% 1.75/1.90 tff(12993,plain,
% 1.75/1.90 ((~(s(s(z)) = elem!1)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12992])).
% 1.75/1.90 tff(12994,plain,
% 1.75/1.90 (~(s(s(z)) = elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1385, 12948])).
% 1.75/1.90 tff(12995,plain,
% 1.75/1.90 (~(s(s(elem!1)) = elem!1)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[12994, 12993])).
% 1.75/1.90 tff(12996,plain,
% 1.75/1.90 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2920, 10007])).
% 1.75/1.90 tff(12997,plain,
% 1.75/1.90 (r(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1542, 12977])).
% 1.75/1.90 tff(12998,plain,
% 1.75/1.90 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12950])).
% 1.75/1.90 tff(12999,plain,
% 1.75/1.90 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.75/1.90 inference(transitivity,[status(thm)],[12998, 3716])).
% 1.75/1.90 tff(13000,plain,
% 1.75/1.90 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.75/1.90 inference(symmetry,[status(thm)],[12999])).
% 1.75/1.90 tff(13001,plain,
% 1.75/1.90 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13000])).
% 1.75/1.90 tff(13002,plain,
% 1.75/1.90 (~(elem!1 = s(s(s(elem!1))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[821, 13001])).
% 1.75/1.90 tff(13003,plain,
% 1.75/1.90 (b(elem!1, s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1319, 12980, 13002])).
% 1.75/1.90 tff(13004,plain,
% 1.75/1.90 (r(elem!1, s(elem!1)) <=> r(elem!1, s(z))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12946])).
% 1.75/1.90 tff(13005,plain,
% 1.75/1.90 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13004])).
% 1.75/1.90 tff(13006,plain,
% 1.75/1.90 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12950])).
% 1.75/1.90 tff(13007,plain,
% 1.75/1.90 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13006])).
% 1.75/1.90 tff(13008,plain,
% 1.75/1.90 (r(z, s(z)) <=> r(elem!1, s(elem!1))),
% 1.75/1.90 inference(transitivity,[status(thm)],[13007, 13005])).
% 1.75/1.90 tff(13009,plain,
% 1.75/1.90 (r(elem!1, s(elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[12997, 13008])).
% 1.75/1.90 tff(13010,plain,
% 1.75/1.90 (~(elem!1 = s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[4995, 12994])).
% 1.75/1.90 tff(13011,plain,
% 1.75/1.90 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(z, s(s(s(elem!1)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12961])).
% 1.75/1.90 tff(13012,plain,
% 1.75/1.90 (~r(z, s(s(s(elem!1))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[12980, 13011])).
% 1.75/1.90 tff(13013,plain,
% 1.75/1.90 (b(z, s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[3795, 51, 13012, 3785])).
% 1.75/1.90 tff(13014,plain,
% 1.75/1.90 (~(elem!1 = s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[386, 12965])).
% 1.75/1.90 tff(13015,plain,
% 1.75/1.90 (~(s(elem!1) = elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[393, 13014])).
% 1.75/1.90 tff(13016,plain,
% 1.75/1.90 ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (s(elem!1) = elem!1) | (elem!1 = s(s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[10552, 8300])).
% 1.75/1.90 tff(13017,plain,
% 1.75/1.90 (~b(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13016, 12982, 13015, 12946, 13013, 13010, 12987, 12967, 13009, 13003, 12997, 57, 12996])).
% 1.75/1.90 tff(13018,plain,
% 1.75/1.90 (~b(s(s(elem!1)), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[11589, 13017, 12946])).
% 1.75/1.90 tff(13019,plain,
% 1.75/1.90 (r(s(s(elem!1)), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[255, 13018, 12995])).
% 1.75/1.90 tff(13020,plain,
% 1.75/1.90 (r(s(s(s(s(s(z))))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[10196, 13019, 12946, 12989, 12964, 12987, 12982])).
% 1.75/1.90 tff(13021,plain,
% 1.75/1.90 ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1826, 10004])).
% 1.75/1.90 tff(13022,plain,
% 1.75/1.90 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13021, 13020])).
% 1.75/1.90 tff(13023,plain,
% 1.75/1.90 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1814, 13022, 12948])).
% 1.75/1.90 tff(13024,plain,
% 1.75/1.90 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5751, 13023, 12947])).
% 1.75/1.90 tff(13025,plain,
% 1.75/1.90 (~r(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[10217, 13019, 12946, 12997, 57, 12989, 10007, 13013, 12964, 12982])).
% 1.75/1.90 tff(13026,plain,
% 1.75/1.90 (b(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1624, 13025])).
% 1.75/1.90 tff(13027,plain,
% 1.75/1.90 (~b(s(s(s(z))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9868, 13026, 12817])).
% 1.75/1.90 tff(13028,plain,
% 1.75/1.90 (r(s(s(s(z))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5118, 13027])).
% 1.75/1.90 tff(13029,plain,
% 1.75/1.90 ((~r(s(s(s(z))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9297, 8300])).
% 1.75/1.90 tff(13030,plain,
% 1.75/1.90 (~r(s(z), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13029, 13028, 12947, 12987, 12997, 13024])).
% 1.75/1.90 tff(13031,plain,
% 1.75/1.90 (b(s(z), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5701, 13030])).
% 1.75/1.90 tff(13032,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[12950])).
% 1.75/1.90 tff(13033,plain,
% 1.75/1.90 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.75/1.90 inference(transitivity,[status(thm)],[13000, 641])).
% 1.75/1.90 tff(13034,plain,
% 1.75/1.90 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13033])).
% 1.75/1.90 tff(13035,plain,
% 1.75/1.90 (~(s(s(s(elem!1))) = elem!1)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[821, 13034])).
% 1.75/1.90 tff(13036,plain,
% 1.75/1.90 (~r(s(s(s(elem!1))), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1182, 13019, 12987])).
% 1.75/1.90 tff(13037,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[647, 13036, 13035])).
% 1.75/1.90 tff(13038,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), z)),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13037, 13032])).
% 1.75/1.90 tff(13039,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9329, 238, 12817, 13013, 13038, 13031])).
% 1.75/1.90 tff(13040,plain,(r(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(13041,plain,
% 1.75/1.90 ((s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[11526, 13040])).
% 1.75/1.90 tff(13042,plain,
% 1.75/1.90 (~b(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13041, 23, 22])).
% 1.75/1.90 tff(13043,plain,
% 1.75/1.90 (r(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1542, 13042])).
% 1.75/1.90 tff(13044,plain,
% 1.75/1.90 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12854, 12817])).
% 1.75/1.90 tff(13045,plain,
% 1.75/1.90 (~b(s(s(z)), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13044, 23])).
% 1.75/1.90 tff(13046,plain,
% 1.75/1.90 (r(s(s(z)), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[135, 13045, 22])).
% 1.75/1.90 tff(13047,plain,
% 1.75/1.90 ((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~(elem!1 = s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12744, 13040])).
% 1.75/1.90 tff(13048,plain,
% 1.75/1.90 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13047, 13046, 23, 13043])).
% 1.75/1.90 tff(13049,plain,
% 1.75/1.90 ((elem!1 = s(s(elem!1))) | (s(elem!1) = s(z)) | (~r(z, s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12572, 13040])).
% 1.75/1.90 tff(13050,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13049, 13048, 13043, 1])).
% 1.75/1.90 tff(13051,plain,((~b(s(s(elem!1)), s(z))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(13052,plain,
% 1.75/1.90 (~b(s(s(elem!1)), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13051, 1])).
% 1.75/1.90 tff(13053,plain,
% 1.75/1.90 (b(s(z), s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[8046, 10004])).
% 1.75/1.90 tff(13054,plain,
% 1.75/1.90 (b(s(z), s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13053, 12817])).
% 1.75/1.90 tff(13055,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13054, 2])).
% 1.75/1.90 tff(13056,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(z)) | (s(elem!1) = s(z)) | b(s(z), s(s(elem!1))) | (~r(z, s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12676, 13040])).
% 1.75/1.90 tff(13057,plain,
% 1.75/1.90 (~r(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13056, 82, 1, 2])).
% 1.75/1.90 tff(13058,plain,
% 1.75/1.90 (b(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1542, 13057])).
% 1.75/1.90 tff(13059,plain,
% 1.75/1.90 ((~b(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[8848, 12817])).
% 1.75/1.90 tff(13060,plain,
% 1.75/1.90 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13059, 13058])).
% 1.75/1.90 tff(13061,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[3233, 13060])).
% 1.75/1.90 tff(13062,plain,
% 1.75/1.90 ((~b(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9751, 12817])).
% 1.75/1.90 tff(13063,plain,
% 1.75/1.90 (elem!1 = s(s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13062, 13058, 1, 226, 113])).
% 1.75/1.90 tff(13064,plain,
% 1.75/1.90 (s(elem!1) = s(s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2097, 13063])).
% 1.75/1.90 tff(13065,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13064])).
% 1.75/1.90 tff(13066,plain,
% 1.75/1.90 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13063])).
% 1.75/1.90 tff(13067,plain,
% 1.75/1.90 (b(elem!1, s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.90 inference(transitivity,[status(thm)],[13066, 13065])).
% 1.75/1.90 tff(13068,plain,
% 1.75/1.90 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13064])).
% 1.75/1.90 tff(13069,plain,
% 1.75/1.90 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13068])).
% 1.75/1.90 tff(13070,plain,
% 1.75/1.90 (r(s(z), s(elem!1))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[10004, 13069])).
% 1.75/1.90 tff(13071,plain,
% 1.75/1.90 ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[6009, 13040])).
% 1.75/1.90 tff(13072,plain,
% 1.75/1.90 (~r(s(s(elem!1)), s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13071, 13070])).
% 1.75/1.90 tff(13073,plain,
% 1.75/1.90 (~r(elem!1, s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[7696, 13072, 13063])).
% 1.75/1.90 tff(13074,plain,
% 1.75/1.90 (b(elem!1, s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[629, 13073, 391])).
% 1.75/1.90 tff(13075,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13074, 13067])).
% 1.75/1.90 tff(13076,plain,
% 1.75/1.90 ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12974, 12817])).
% 1.75/1.90 tff(13077,plain,
% 1.75/1.90 (~b(s(z), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13076, 13061])).
% 1.75/1.90 tff(13078,plain,
% 1.75/1.90 (r(s(z), s(s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[11309, 13077])).
% 1.75/1.90 tff(13079,plain,
% 1.75/1.90 ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9625, 13040])).
% 1.75/1.90 tff(13080,plain,
% 1.75/1.90 (~r(s(s(z)), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13079, 13078])).
% 1.75/1.90 tff(13081,plain,
% 1.75/1.90 (b(s(s(z)), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[135, 13080, 22])).
% 1.75/1.90 tff(13082,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2498, 238, 13081, 226, 13075, 13061])).
% 1.75/1.90 tff(13083,plain,(b(s(s(elem!1)), s(z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (elem!1 = s(elem!1)) | (s(elem!1) = s(z)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(13084,plain,
% 1.75/1.90 (elem!1 = s(elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13083, 13055, 13052, 1, 2])).
% 1.75/1.90 tff(13085,plain,
% 1.75/1.90 ((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(s(z), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2572, 12817])).
% 1.75/1.90 tff(13086,plain,
% 1.75/1.90 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13085, 2])).
% 1.75/1.90 tff(13087,plain,
% 1.75/1.90 (~(s(elem!1) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5343, 13086])).
% 1.75/1.90 tff(13088,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[386, 13087, 13084])).
% 1.75/1.90 tff(13089,plain,(b(s(z), s(s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(13090,plain,
% 1.75/1.90 (b(s(z), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13089, 1])).
% 1.75/1.90 tff(13091,plain,
% 1.75/1.90 (elem!1 = s(s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12860, 13090, 1])).
% 1.75/1.90 tff(13092,plain,
% 1.75/1.90 (r(s(s(elem!1)), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[112, 13052])).
% 1.75/1.90 tff(13093,plain,
% 1.75/1.90 (~b(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12880, 13090, 13092, 1])).
% 1.75/1.90 tff(13094,plain,
% 1.75/1.90 (r(z, s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1542, 13093])).
% 1.75/1.90 tff(13095,plain,
% 1.75/1.90 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~(elem!1 = s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9522, 12817])).
% 1.75/1.90 tff(13096,plain,
% 1.75/1.90 (~b(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13095, 13094, 22, 13090, 13091])).
% 1.75/1.90 tff(13097,plain,
% 1.75/1.90 (s(elem!1) = s(s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2097, 13091])).
% 1.75/1.90 tff(13098,plain,
% 1.75/1.90 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5222, 13097, 22])).
% 1.75/1.90 tff(13099,plain,
% 1.75/1.90 ((~r(z, s(s(elem!1)))) | (~r(z, s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[12600, 13040])).
% 1.75/1.90 tff(13100,plain,
% 1.75/1.90 (~r(z, s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13099, 13094])).
% 1.75/1.90 tff(13101,plain,
% 1.75/1.90 (~r(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9930, 13100, 13094, 13092, 13098])).
% 1.75/1.90 tff(13102,plain,
% 1.75/1.90 ($false),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1624, 13101, 13096])).
% 1.75/1.90 tff(13103,plain,(s(elem!1) = s(z)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.90 tff(13104,plain,
% 1.75/1.90 (s(s(z)) = s(s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[357, 13103])).
% 1.75/1.90 tff(13105,plain,
% 1.75/1.90 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13104])).
% 1.75/1.90 tff(13106,plain,
% 1.75/1.90 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13105])).
% 1.75/1.90 tff(13107,plain,
% 1.75/1.90 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[1291, 13106])).
% 1.75/1.90 tff(13108,plain,
% 1.75/1.90 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[10022, 13040])).
% 1.75/1.90 tff(13109,plain,
% 1.75/1.90 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[223, 13108])).
% 1.75/1.90 tff(13110,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13109, 13107])).
% 1.75/1.90 tff(13111,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(elem!1))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[11248, 13103])).
% 1.75/1.90 tff(13112,plain,
% 1.75/1.90 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = elem!1)),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13104])).
% 1.75/1.90 tff(13113,plain,
% 1.75/1.90 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.75/1.90 inference(transitivity,[status(thm)],[13112, 3730])).
% 1.75/1.90 tff(13114,plain,
% 1.75/1.90 ((~(s(s(z)) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13113])).
% 1.75/1.90 tff(13115,plain,
% 1.75/1.90 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[4960, 13104])).
% 1.75/1.90 tff(13116,plain,
% 1.75/1.90 (~(s(s(z)) = elem!1)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1385, 13115])).
% 1.75/1.90 tff(13117,plain,
% 1.75/1.90 (~(elem!1 = s(s(elem!1)))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13116, 13114])).
% 1.75/1.90 tff(13118,plain,
% 1.75/1.90 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13104])).
% 1.75/1.90 tff(13119,plain,
% 1.75/1.90 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13104])).
% 1.75/1.90 tff(13120,plain,
% 1.75/1.90 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13119])).
% 1.75/1.90 tff(13121,plain,
% 1.75/1.90 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13120])).
% 1.75/1.90 tff(13122,plain,
% 1.75/1.90 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13121])).
% 1.75/1.90 tff(13123,plain,
% 1.75/1.90 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13119])).
% 1.75/1.90 tff(13124,plain,
% 1.75/1.90 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13120])).
% 1.75/1.90 tff(13125,plain,
% 1.75/1.90 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13124])).
% 1.75/1.90 tff(13126,plain,
% 1.75/1.90 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(s(z)))) = s(s(s(elem!1)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13125])).
% 1.75/1.90 tff(13127,plain,
% 1.75/1.90 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[5165, 13126])).
% 1.75/1.90 tff(13128,plain,
% 1.75/1.90 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[2893, 13115])).
% 1.75/1.90 tff(13129,plain,
% 1.75/1.90 ((~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9933, 12817])).
% 1.75/1.90 tff(13130,plain,
% 1.75/1.90 (~b(s(s(s(z))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13129, 13110, 13128, 13127])).
% 1.75/1.90 tff(13131,plain,
% 1.75/1.90 (r(s(s(s(z))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5118, 13130])).
% 1.75/1.90 tff(13132,plain,
% 1.75/1.90 (r(s(s(s(elem!1))), s(z))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13131, 13123])).
% 1.75/1.90 tff(13133,plain,
% 1.75/1.90 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[8674, 12817])).
% 1.75/1.90 tff(13134,plain,
% 1.75/1.90 (~b(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13133, 1457])).
% 1.75/1.90 tff(13135,plain,
% 1.75/1.90 (r(s(s(s(s(z)))), s(z))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1624, 13134])).
% 1.75/1.90 tff(13136,plain,
% 1.75/1.90 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9285, 124, 13135, 13132])).
% 1.75/1.90 tff(13137,plain,
% 1.75/1.90 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13136, 13122])).
% 1.75/1.90 tff(13138,plain,
% 1.75/1.90 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5167, 13137])).
% 1.75/1.90 tff(13139,plain,
% 1.75/1.90 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13119, 13104])).
% 1.75/1.90 tff(13140,plain,
% 1.75/1.90 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13139])).
% 1.75/1.90 tff(13141,plain,
% 1.75/1.90 (b(s(s(s(z))), s(s(z)))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13110, 13140])).
% 1.75/1.90 tff(13142,plain,
% 1.75/1.90 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13119])).
% 1.75/1.90 tff(13143,plain,
% 1.75/1.90 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.75/1.90 inference(symmetry,[status(thm)],[13142])).
% 1.75/1.90 tff(13144,plain,
% 1.75/1.90 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13143])).
% 1.75/1.90 tff(13145,plain,
% 1.75/1.90 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[11865, 13040])).
% 1.75/1.90 tff(13146,plain,
% 1.75/1.90 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13145, 13135])).
% 1.75/1.90 tff(13147,plain,
% 1.75/1.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13146, 13144])).
% 1.75/1.90 tff(13148,plain,
% 1.75/1.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[5176, 13147])).
% 1.75/1.90 tff(13149,plain,
% 1.75/1.90 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[9652, 13148, 13141, 13138])).
% 1.75/1.90 tff(13150,plain,
% 1.75/1.90 (r(s(s(z)), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[1604, 13149])).
% 1.75/1.90 tff(13151,plain,
% 1.75/1.90 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13150, 13118])).
% 1.75/1.90 tff(13152,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13103])).
% 1.75/1.90 tff(13153,plain,
% 1.75/1.90 (b(s(s(elem!1)), s(z))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13111, 13152])).
% 1.75/1.90 tff(13154,plain,
% 1.75/1.90 (~b(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[6971, 238, 12817, 13153, 1457])).
% 1.75/1.90 tff(13155,plain,
% 1.75/1.90 (r(s(s(elem!1)), z)),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[4905, 13154])).
% 1.75/1.90 tff(13156,plain,
% 1.75/1.90 (b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[8247, 13146, 13127])).
% 1.75/1.90 tff(13157,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(13158,plain,
% 1.75/1.90 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(13159,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 1.75/1.90 inference(monotonicity,[status(thm)],[13158])).
% 1.75/1.90 tff(13160,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.75/1.90 inference(transitivity,[status(thm)],[13159, 13157])).
% 1.75/1.90 tff(13161,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.75/1.90 inference(quant_inst,[status(thm)],[])).
% 1.75/1.90 tff(13162,plain,
% 1.75/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.75/1.90 inference(modus_ponens,[status(thm)],[13161, 13160])).
% 1.75/1.90 tff(13163,plain,
% 1.75/1.90 (~b(s(z), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[13162, 238, 13110, 12817, 13156])).
% 1.75/1.90 tff(13164,plain,
% 1.75/1.90 (r(s(z), s(s(s(s(z)))))),
% 1.75/1.90 inference(unit_resolution,[status(thm)],[6600, 13163])).
% 1.75/1.90 tff(13165,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(13166,plain,
% 1.75/1.90 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.90 inference(rewrite,[status(thm)],[])).
% 1.75/1.90 tff(13167,plain,
% 1.75/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13166])).
% 1.75/1.91 tff(13168,plain,
% 1.75/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)))),
% 1.75/1.91 inference(transitivity,[status(thm)],[13167, 13165])).
% 1.75/1.91 tff(13169,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(13170,plain,
% 1.75/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(s(elem!1)), z))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[13169, 13168])).
% 1.75/1.91 tff(13171,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[13170, 124, 13040, 13164, 13155, 13151])).
% 1.75/1.91 tff(13172,plain,(~b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.91 tff(13173,plain,
% 1.75/1.91 (r(z, s(z))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[1542, 13172])).
% 1.75/1.91 tff(13174,plain,
% 1.75/1.91 (~r(z, s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[13099, 13173])).
% 1.75/1.91 tff(13175,plain,
% 1.75/1.91 (~r(elem!1, s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[7136, 13174, 13103])).
% 1.75/1.91 tff(13176,plain,
% 1.75/1.91 (b(elem!1, s(s(elem!1)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[606, 13175, 13117])).
% 1.75/1.91 tff(13177,plain,
% 1.75/1.91 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13103])).
% 1.75/1.91 tff(13178,plain,
% 1.75/1.91 (elem!1 = z),
% 1.75/1.91 inference(transitivity,[status(thm)],[155, 13177, 26])).
% 1.75/1.91 tff(13179,plain,
% 1.75/1.91 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13178])).
% 1.75/1.91 tff(13180,plain,
% 1.75/1.91 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.75/1.91 inference(transitivity,[status(thm)],[13179, 3716])).
% 1.75/1.91 tff(13181,plain,
% 1.75/1.91 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 1.75/1.91 inference(symmetry,[status(thm)],[13180])).
% 1.75/1.91 tff(13182,plain,
% 1.75/1.91 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13181])).
% 1.75/1.91 tff(13183,plain,
% 1.75/1.91 (~(elem!1 = s(s(s(elem!1))))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[821, 13182])).
% 1.75/1.91 tff(13184,plain,
% 1.75/1.91 ((elem!1 = s(z)) <=> (z = s(z))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13178])).
% 1.75/1.91 tff(13185,plain,
% 1.75/1.91 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.75/1.91 inference(transitivity,[status(thm)],[13184, 2036])).
% 1.75/1.91 tff(13186,plain,
% 1.75/1.91 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.75/1.91 inference(symmetry,[status(thm)],[13185])).
% 1.75/1.91 tff(13187,plain,
% 1.75/1.91 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 1.75/1.91 inference(monotonicity,[status(thm)],[13186])).
% 1.75/1.91 tff(13188,plain,
% 1.75/1.91 (~(elem!1 = s(z))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[72, 13187])).
% 1.75/1.91 tff(13189,plain,
% 1.75/1.91 (~b(elem!1, s(z))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[5709, 13172, 13103])).
% 1.75/1.91 tff(13190,plain,
% 1.75/1.91 (r(elem!1, s(z))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[363, 13189, 13188])).
% 1.75/1.91 tff(13191,plain,
% 1.75/1.91 (~r(elem!1, s(s(s(elem!1))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[12917, 13190])).
% 1.75/1.91 tff(13192,plain,
% 1.75/1.91 (b(elem!1, s(s(s(elem!1))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[1319, 13191, 13183])).
% 1.75/1.91 tff(13193,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[3306, 13192, 13176, 13111, 13110])).
% 1.75/1.91 % SZS output end Proof
% 1.75/1.91 % E exiting
%------------------------------------------------------------------------------