%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA167-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:21 PM UTC 2026
% Result : Unsatisfiable 1.14s 1.39s
% Output : Proof 2.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA167-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n014.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 00:45:08 EDT 2026
% 0.13/0.33 % CPUTime :
% 1.14/1.39 % SZS status Unsatisfiable
% 1.14/1.39 % SZS output start Proof
% 1.14/1.39 tff(r_type, type, (
% 1.14/1.39 r: ( $i * $i ) > $o)).
% 1.14/1.39 tff(s_type, type, (
% 1.14/1.39 s: $i > $i)).
% 1.14/1.39 tff(elem_1_type, type, (
% 1.14/1.39 elem_1: $i)).
% 1.14/1.39 tff(z_type, type, (
% 1.14/1.39 z: $i)).
% 1.14/1.39 tff(b_type, type, (
% 1.14/1.39 b: ( $i * $i ) > $o)).
% 1.14/1.39 tff(inj_0_type, type, (
% 1.14/1.39 inj_0: $i > $i)).
% 1.14/1.39 tff(1,plain,
% 1.14/1.39 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(2,plain,
% 1.14/1.39 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(3,plain,
% 1.14/1.39 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(4,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.14/1.39 tff(5,plain,
% 1.14/1.39 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.14/1.39 tff(6,plain,(
% 1.14/1.39 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.14/1.39 inference(skolemize,[status(sab)],[5])).
% 1.14/1.39 tff(7,plain,
% 1.14/1.39 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.14/1.39 tff(8,plain,
% 1.14/1.39 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 1.14/1.39 tff(9,plain,
% 1.14/1.39 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(10,plain,
% 1.14/1.39 (inj_0(s(s(z))) = s(z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.14/1.39 tff(11,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.14/1.39 tff(12,plain,
% 1.14/1.39 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[11])).
% 1.14/1.39 tff(13,plain,
% 1.14/1.39 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.14/1.39 inference(symmetry,[status(thm)],[12])).
% 1.14/1.39 tff(14,plain,
% 1.14/1.39 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(15,plain,
% 1.14/1.39 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[14, 8])).
% 1.14/1.39 tff(16,plain,
% 1.14/1.39 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[15])).
% 1.14/1.39 tff(17,plain,
% 1.14/1.39 (s(s(s(z))) = s(s(z))),
% 1.14/1.39 inference(symmetry,[status(thm)],[11])).
% 1.14/1.39 tff(18,plain,
% 1.14/1.39 (s(s(s(z))) = s(z)),
% 1.14/1.39 inference(transitivity,[status(thm)],[17, 16, 13, 10])).
% 1.14/1.39 tff(19,plain,
% 1.14/1.39 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(20,plain,
% 1.14/1.39 (inj_0(s(z)) = z),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[19, 8])).
% 1.14/1.39 tff(21,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.14/1.39 tff(22,plain,
% 1.14/1.39 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[21])).
% 1.14/1.39 tff(23,plain,
% 1.14/1.39 (s(s(z)) = z),
% 1.14/1.39 inference(transitivity,[status(thm)],[16, 22, 20])).
% 1.14/1.39 tff(24,plain,
% 1.14/1.39 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.14/1.39 inference(bind,[status(th)],[])).
% 1.14/1.39 tff(25,plain,
% 1.14/1.39 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.39 inference(quant_intro,[status(thm)],[24])).
% 1.14/1.39 tff(26,plain,
% 1.14/1.39 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(27,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.14/1.39 tff(28,plain,
% 1.14/1.39 (![X: $i] : (~(s(X) = z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.14/1.39 tff(29,plain,(
% 1.14/1.39 ![X: $i] : (~(s(X) = z))),
% 1.14/1.39 inference(skolemize,[status(sab)],[28])).
% 1.14/1.39 tff(30,plain,
% 1.14/1.39 (![X: $i] : (~(s(X) = z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.14/1.39 tff(31,plain,
% 1.14/1.39 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(32,plain,
% 1.14/1.39 (~(s(s(z)) = z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.14/1.39 tff(33,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[32, 23])).
% 1.14/1.39 tff(34,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(35,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[34, 18])).
% 1.14/1.39 tff(36,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(37,assumption,(r(z, s(z))), introduced(assumption)).
% 1.14/1.40 tff(38,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.14/1.40 tff(39,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.14/1.40 tff(40,assumption,(~r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.14/1.40 tff(41,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.14/1.40 tff(42,plain,
% 1.14/1.40 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.14/1.40 inference(monotonicity,[status(thm)],[41])).
% 1.14/1.40 tff(43,plain,
% 1.14/1.40 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(44,plain,
% 1.14/1.40 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[43, 8])).
% 1.14/1.40 tff(45,plain,
% 1.14/1.40 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.14/1.40 inference(symmetry,[status(thm)],[44])).
% 1.14/1.40 tff(46,plain,
% 1.14/1.40 (s(s(s(s(z)))) = z),
% 1.14/1.40 inference(transitivity,[status(thm)],[45, 42, 20])).
% 1.14/1.40 tff(47,plain,
% 1.14/1.40 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(48,plain,
% 1.14/1.40 (~(s(s(s(s(z)))) = z)),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[47, 30])).
% 1.14/1.40 tff(49,plain,
% 1.14/1.40 ($false),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[48, 46])).
% 1.14/1.40 tff(50,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(51,plain,
% 1.14/1.40 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.40 inference(bind,[status(th)],[])).
% 1.14/1.40 tff(52,plain,
% 1.14/1.40 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(quant_intro,[status(thm)],[51])).
% 1.14/1.40 tff(53,plain,
% 1.14/1.40 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(54,plain,
% 1.14/1.40 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.14/1.40 inference(bind,[status(th)],[])).
% 1.14/1.40 tff(55,plain,
% 1.14/1.40 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(quant_intro,[status(thm)],[54])).
% 1.14/1.40 tff(56,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.14/1.40 tff(57,plain,
% 1.14/1.40 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.14/1.40 tff(58,plain,
% 1.14/1.40 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.14/1.40 tff(59,plain,(
% 1.14/1.40 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(skolemize,[status(sab)],[58])).
% 1.14/1.40 tff(60,plain,
% 1.14/1.40 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 1.14/1.40 tff(61,plain,
% 1.14/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.14/1.40 inference(rewrite,[status(thm)],[])).
% 1.14/1.40 tff(62,plain,
% 1.14/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.14/1.40 inference(quant_inst,[status(thm)],[])).
% 1.14/1.40 tff(63,plain,
% 1.14/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.14/1.40 tff(64,plain,
% 1.14/1.40 ($false),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[63, 60, 50, 39, 40])).
% 1.14/1.40 tff(65,plain,(r(s(s(s(s(s(z))))), s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.40 tff(66,plain,
% 1.14/1.40 (r(s(s(s(s(s(z))))), s(z))),
% 1.14/1.40 inference(unit_resolution,[status(thm)],[65, 39])).
% 1.14/1.40 tff(67,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.14/1.40 tff(68,plain,
% 1.14/1.40 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.14/1.40 inference(bind,[status(th)],[])).
% 1.14/1.40 tff(69,plain,
% 1.14/1.40 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[68])).
% 1.24/1.40 tff(70,plain,
% 1.24/1.40 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(71,plain,
% 1.24/1.40 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(72,plain,
% 1.24/1.40 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[71])).
% 1.24/1.40 tff(73,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.24/1.40 tff(74,plain,
% 1.24/1.40 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.24/1.40 tff(75,plain,
% 1.24/1.40 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 1.24/1.40 tff(76,plain,(
% 1.24/1.40 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(skolemize,[status(sab)],[75])).
% 1.24/1.40 tff(77,plain,
% 1.24/1.40 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 1.24/1.40 tff(78,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(79,plain,
% 1.24/1.40 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(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))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(80,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[79])).
% 1.24/1.40 tff(81,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[80, 78])).
% 1.24/1.40 tff(82,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(83,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.24/1.40 tff(84,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[83, 77, 67, 66])).
% 1.24/1.40 tff(85,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.40 tff(86,plain,
% 1.24/1.40 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[85])).
% 1.24/1.40 tff(87,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.40 tff(88,plain,
% 1.24/1.40 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[87])).
% 1.24/1.40 tff(89,plain,
% 1.24/1.40 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[88])).
% 1.24/1.40 tff(90,plain,
% 1.24/1.40 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(91,plain,
% 1.24/1.40 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[90, 8])).
% 1.24/1.40 tff(92,plain,
% 1.24/1.40 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[91])).
% 1.24/1.40 tff(93,plain,
% 1.24/1.40 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[92, 89, 44, 88])).
% 1.24/1.40 tff(94,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.40 tff(95,plain,
% 1.24/1.40 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[94])).
% 1.24/1.40 tff(96,plain,
% 1.24/1.40 (s(s(z)) = s(s(s(s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[16, 95, 44])).
% 1.24/1.40 tff(97,plain,
% 1.24/1.40 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[96])).
% 1.24/1.40 tff(98,plain,
% 1.24/1.40 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[97])).
% 1.24/1.40 tff(99,plain,
% 1.24/1.40 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[94])).
% 1.24/1.40 tff(100,plain,
% 1.24/1.40 (s(s(s(s(s(z))))) = s(z)),
% 1.24/1.40 inference(transitivity,[status(thm)],[99, 92, 98, 10])).
% 1.24/1.40 tff(101,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[50, 100])).
% 1.24/1.40 tff(102,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(103,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[102, 93])).
% 1.24/1.40 tff(104,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(105,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[104, 86])).
% 1.24/1.40 tff(106,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(107,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.40 tff(108,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.40 tff(109,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(110,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(111,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.24/1.40 tff(112,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[111, 60, 108, 107, 106])).
% 1.24/1.40 tff(113,plain,(b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(114,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[113, 84])).
% 1.24/1.40 tff(115,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.24/1.40 tff(116,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.24/1.40 tff(117,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.40 tff(118,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.24/1.40 tff(119,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(120,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(121,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.24/1.40 tff(122,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[121, 77, 116, 118, 117])).
% 1.24/1.40 tff(123,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(124,plain,
% 1.24/1.40 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[123, 116, 66])).
% 1.24/1.40 tff(125,plain,
% 1.24/1.40 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(126,plain,
% 1.24/1.40 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[125])).
% 1.24/1.40 tff(127,plain,
% 1.24/1.40 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[126])).
% 1.24/1.40 tff(128,plain,
% 1.24/1.40 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[102, 127])).
% 1.24/1.40 tff(129,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(130,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(131,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[130, 129])).
% 1.24/1.40 tff(132,plain,
% 1.24/1.40 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[131, 60])).
% 1.24/1.40 tff(133,plain,
% 1.24/1.40 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[132, 128])).
% 1.24/1.40 tff(134,plain,
% 1.24/1.40 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[133, 124])).
% 1.24/1.40 tff(135,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.24/1.40 tff(136,plain,
% 1.24/1.40 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[121, 77, 116, 66])).
% 1.24/1.40 tff(137,plain,
% 1.24/1.40 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[133, 136])).
% 1.24/1.40 tff(138,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(139,plain,
% 1.24/1.40 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[138])).
% 1.24/1.40 tff(140,plain,
% 1.24/1.40 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[139])).
% 1.24/1.40 tff(141,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.40 tff(142,plain,
% 1.24/1.40 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.24/1.40 inference(symmetry,[status(thm)],[141])).
% 1.24/1.40 tff(143,plain,
% 1.24/1.40 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[142])).
% 1.24/1.40 tff(144,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[104, 143])).
% 1.24/1.40 tff(145,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(146,plain,
% 1.24/1.40 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[145, 140])).
% 1.24/1.40 tff(147,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(148,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(149,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.24/1.40 tff(150,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[149, 77, 67, 116])).
% 1.24/1.40 tff(151,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(152,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(153,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.24/1.40 tff(154,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[153, 60])).
% 1.24/1.40 tff(155,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[154, 150, 146])).
% 1.24/1.40 tff(156,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[111, 60, 84, 106])).
% 1.24/1.40 tff(157,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(158,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(159,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[158])).
% 1.24/1.40 tff(160,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[159, 157])).
% 1.24/1.40 tff(161,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
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% 1.24/1.40 inference(modus_ponens,[status(thm)],[161, 160])).
% 1.24/1.40 tff(163,plain,
% 1.24/1.40 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[162, 77, 67, 116])).
% 1.24/1.40 tff(164,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(165,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(166,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[165, 164])).
% 1.24/1.40 tff(167,plain,
% 1.24/1.40 ((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)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[166, 60])).
% 1.24/1.40 tff(168,plain,
% 1.24/1.40 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[167, 163, 145])).
% 1.24/1.40 tff(169,plain,
% 1.24/1.40 (r(s(s(s(s(s(z))))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[63, 60, 50, 39])).
% 1.24/1.40 tff(170,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.40 tff(171,plain,
% 1.24/1.40 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(172,plain,
% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
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% 1.24/1.40 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.24/1.40 tff(174,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[173, 77, 170, 67, 169])).
% 1.24/1.40 tff(175,plain,((~r(s(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))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(176,plain,
% 1.24/1.40 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[175, 67, 39])).
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% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(178,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(179,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.24/1.40 tff(180,plain,
% 1.24/1.40 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[179, 60])).
% 1.24/1.40 tff(181,plain,
% 1.24/1.40 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[180, 104])).
% 1.24/1.40 tff(182,plain,
% 1.24/1.40 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[181, 176])).
% 1.24/1.40 tff(183,plain,
% 1.24/1.40 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 1.24/1.40 inference(bind,[status(th)],[])).
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% 1.24/1.40 inference(quant_intro,[status(thm)],[183])).
% 1.24/1.40 tff(185,plain,
% 1.24/1.40 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(186,plain,
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% 1.24/1.40 inference(bind,[status(th)],[])).
% 1.24/1.40 tff(187,plain,
% 1.24/1.40 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.40 inference(quant_intro,[status(thm)],[186])).
% 1.24/1.40 tff(188,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) | (~b(X0, X4))) | (~b(X2, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.24/1.40 tff(189,plain,
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% 1.24/1.41 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.24/1.41 tff(190,plain,
% 1.24/1.41 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.24/1.41 tff(191,plain,(
% 1.24/1.41 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.41 inference(skolemize,[status(sab)],[190])).
% 1.24/1.41 tff(192,plain,
% 1.24/1.41 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.24/1.41 tff(193,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(194,plain,
% 1.24/1.41 (((~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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(195,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[194])).
% 1.24/1.41 tff(196,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[195, 193])).
% 1.24/1.41 tff(197,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(198,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.24/1.41 tff(199,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[198, 192, 182, 168, 156, 155, 137])).
% 1.24/1.41 tff(200,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(201,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[200, 116, 39])).
% 1.24/1.41 tff(202,plain,
% 1.24/1.41 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(203,plain,
% 1.24/1.41 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[202])).
% 1.24/1.41 tff(204,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(205,plain,
% 1.24/1.41 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[204])).
% 1.24/1.41 tff(206,plain,
% 1.24/1.41 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.24/1.41 inference(symmetry,[status(thm)],[205])).
% 1.24/1.41 tff(207,plain,
% 1.24/1.41 (s(s(s(z))) = z),
% 1.24/1.41 inference(transitivity,[status(thm)],[92, 206, 20])).
% 1.24/1.41 tff(208,plain,
% 1.24/1.41 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(209,plain,
% 1.24/1.41 (~(s(s(s(z))) = z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[208, 30])).
% 1.24/1.41 tff(210,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[209, 207])).
% 1.24/1.41 tff(211,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(212,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[211, 203])).
% 1.24/1.41 tff(213,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(214,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(215,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.24/1.41 tff(216,plain,
% 1.24/1.41 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[215, 60])).
% 1.24/1.41 tff(217,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[216, 212])).
% 1.24/1.41 tff(218,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[217, 201])).
% 1.24/1.41 tff(219,plain,
% 1.24/1.41 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[123, 116, 118])).
% 1.24/1.41 tff(220,plain,
% 1.24/1.41 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[133, 219])).
% 1.24/1.41 tff(221,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(222,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(223,plain,
% 1.24/1.41 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(224,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[223])).
% 1.24/1.41 tff(225,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[224, 222])).
% 1.24/1.41 tff(226,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(227,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.24/1.41 tff(228,plain,
% 1.24/1.41 (~r(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[227, 77, 37, 116])).
% 1.24/1.41 tff(229,plain,
% 1.24/1.41 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.24/1.41 inference(commutativity,[status(thm)],[])).
% 1.24/1.41 tff(230,plain,
% 1.24/1.41 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.24/1.41 inference(symmetry,[status(thm)],[229])).
% 1.24/1.41 tff(231,plain,
% 1.24/1.41 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[230])).
% 1.24/1.41 tff(232,plain,
% 1.24/1.41 (~(z = s(s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[209, 231])).
% 1.24/1.41 tff(233,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(234,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(235,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.24/1.41 tff(236,plain,
% 1.24/1.41 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[235, 60])).
% 1.24/1.41 tff(237,plain,
% 1.24/1.41 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[236, 232])).
% 1.24/1.41 tff(238,plain,
% 1.24/1.41 (b(z, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[237, 228])).
% 1.24/1.41 tff(239,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.24/1.41 tff(240,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(241,plain,
% 1.24/1.41 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(242,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[241])).
% 1.24/1.41 tff(243,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[242, 240])).
% 1.24/1.41 tff(244,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(245,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.24/1.41 tff(246,plain,
% 1.24/1.41 (~r(s(s(s(z))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[245, 77, 37, 116])).
% 1.24/1.41 tff(247,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.41 tff(248,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.41 tff(249,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(250,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(251,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.24/1.41 tff(252,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[251, 60, 209, 248, 247])).
% 1.24/1.41 tff(253,plain,(b(s(s(s(z))), z) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(254,plain,
% 1.24/1.41 (b(s(s(s(z))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[253, 246])).
% 1.24/1.41 tff(255,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(256,plain,
% 1.24/1.41 (((~b(z, s(s(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(257,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[256])).
% 1.24/1.41 tff(258,plain,
% 1.24/1.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[257, 255])).
% 1.24/1.41 tff(259,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(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)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(260,plain,
% 1.24/1.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[259, 258])).
% 1.24/1.41 tff(261,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[260, 192, 254, 239, 238, 221])).
% 1.24/1.41 tff(262,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(263,plain,
% 1.24/1.41 (~b(s(s(s(s(s(z))))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[262, 37, 116, 220])).
% 1.24/1.41 tff(264,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.24/1.41 tff(265,plain,
% 1.24/1.41 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(266,plain,
% 1.24/1.41 (~(s(s(s(s(s(z))))) = z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[265, 30])).
% 1.24/1.41 tff(267,plain,
% 1.24/1.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(268,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(269,plain,
% 1.24/1.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.24/1.41 tff(270,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[269, 60, 266, 264, 135])).
% 1.24/1.41 tff(271,plain,(b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(272,plain,
% 1.24/1.41 (r(s(s(s(s(s(z))))), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[271, 263])).
% 1.24/1.41 tff(273,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(274,plain,
% 1.24/1.41 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(275,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[274])).
% 1.24/1.41 tff(276,plain,
% 1.24/1.41 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[275, 273])).
% 1.24/1.41 tff(277,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(278,plain,
% 1.24/1.41 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.24/1.41 tff(279,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[278, 77, 37, 272, 118])).
% 1.24/1.41 tff(280,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(281,plain,
% 1.24/1.42 (~r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[280, 116, 66])).
% 1.24/1.42 tff(282,plain,
% 1.24/1.42 ((z = s(z)) <=> (s(z) = z)),
% 1.24/1.42 inference(commutativity,[status(thm)],[])).
% 1.24/1.42 tff(283,plain,
% 1.24/1.42 ((s(z) = z) <=> (z = s(z))),
% 1.24/1.42 inference(symmetry,[status(thm)],[282])).
% 1.24/1.42 tff(284,plain,
% 1.24/1.42 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[283])).
% 1.24/1.42 tff(285,plain,
% 1.24/1.42 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(286,plain,
% 1.24/1.42 (~(s(z) = z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[285, 30])).
% 1.24/1.42 tff(287,plain,
% 1.24/1.42 (~(z = s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[286, 284])).
% 1.24/1.42 tff(288,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(289,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(290,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.24/1.42 tff(291,plain,
% 1.24/1.42 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[290, 60])).
% 1.24/1.42 tff(292,plain,
% 1.24/1.42 (b(z, s(z)) | r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[291, 287])).
% 1.24/1.42 tff(293,plain,
% 1.24/1.42 (b(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[292, 281])).
% 1.24/1.42 tff(294,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(295,plain,
% 1.24/1.42 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[181, 294])).
% 1.24/1.42 tff(296,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.24/1.42 tff(297,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.42 tff(298,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(299,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(300,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.24/1.42 tff(301,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[300, 77, 170, 296, 297])).
% 1.24/1.42 tff(302,plain,((~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))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(303,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[302, 296, 170])).
% 1.24/1.42 tff(304,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(305,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(306,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.24/1.42 tff(307,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[306, 60, 48, 303])).
% 1.24/1.42 tff(308,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(309,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(310,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(311,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[310, 309])).
% 1.24/1.42 tff(312,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[311, 77, 170, 308, 118])).
% 1.24/1.42 tff(313,plain,((~r(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(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(314,plain,
% 1.24/1.42 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[313, 118, 170])).
% 1.24/1.42 tff(315,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(316,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(317,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[316, 315])).
% 1.24/1.42 tff(318,plain,
% 1.24/1.42 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[317, 60])).
% 1.24/1.42 tff(319,plain,
% 1.24/1.42 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[318, 211])).
% 1.24/1.42 tff(320,plain,
% 1.24/1.42 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[319, 314])).
% 1.24/1.42 tff(321,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(322,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(323,plain,
% 1.24/1.42 (((~r(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))))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(324,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[323])).
% 1.24/1.42 tff(325,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[324, 322])).
% 1.24/1.42 tff(326,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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))))), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(327,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[326, 325])).
% 1.24/1.42 tff(328,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[327, 77, 170, 321, 296])).
% 1.24/1.42 tff(329,plain,((~r(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))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(330,plain,
% 1.24/1.42 (~r(z, s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[329, 296, 170])).
% 1.24/1.42 tff(331,plain,
% 1.24/1.42 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.24/1.42 inference(commutativity,[status(thm)],[])).
% 1.24/1.42 tff(332,plain,
% 1.24/1.42 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[331])).
% 1.24/1.42 tff(333,plain,
% 1.24/1.42 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[332])).
% 1.24/1.42 tff(334,plain,
% 1.24/1.42 (~(z = s(s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[48, 333])).
% 1.24/1.42 tff(335,plain,
% 1.24/1.42 (((~![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))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(336,plain,
% 1.24/1.42 ((~![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))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(337,plain,
% 1.24/1.42 ((~![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)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[336, 335])).
% 1.24/1.42 tff(338,plain,
% 1.24/1.42 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[337, 60])).
% 1.24/1.42 tff(339,plain,
% 1.24/1.42 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[338, 334])).
% 1.24/1.42 tff(340,plain,
% 1.24/1.42 (b(z, s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[339, 330])).
% 1.24/1.42 tff(341,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(342,plain,
% 1.24/1.42 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(343,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[342])).
% 1.24/1.42 tff(344,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[343, 341])).
% 1.24/1.42 tff(345,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(346,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[345, 344])).
% 1.24/1.42 tff(347,plain,
% 1.24/1.42 (~b(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[346, 192, 340, 320, 307])).
% 1.24/1.42 tff(348,plain,
% 1.24/1.42 (((~![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))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(349,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(350,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.24/1.42 tff(351,plain,
% 1.24/1.42 (b(s(z), z) | r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[350, 60, 286])).
% 1.24/1.42 tff(352,plain,
% 1.24/1.42 (r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[351, 347])).
% 1.24/1.42 tff(353,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(354,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(355,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.24/1.42 tff(356,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[355, 77, 352, 296, 118])).
% 1.24/1.42 tff(357,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(358,plain,
% 1.24/1.42 (~r(s(s(s(s(s(z))))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[357, 295, 66])).
% 1.24/1.42 tff(359,plain,
% 1.24/1.42 (b(s(s(s(s(s(z))))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[271, 358])).
% 1.24/1.42 tff(360,plain,
% 1.24/1.42 (~r(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[262, 359, 116, 134])).
% 1.24/1.42 tff(361,plain,
% 1.24/1.42 (b(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[292, 360])).
% 1.24/1.42 tff(362,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(363,plain,
% 1.24/1.42 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(364,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[363])).
% 1.24/1.42 tff(365,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[364, 362])).
% 1.24/1.42 tff(366,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(367,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[366, 365])).
% 1.24/1.42 tff(368,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[367, 77, 116, 66])).
% 1.24/1.42 tff(369,assumption,(~b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.42 tff(370,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.42 tff(371,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(372,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(373,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.24/1.42 tff(374,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[373, 60, 102, 370, 369])).
% 1.24/1.42 tff(375,plain,(b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(376,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[375, 368])).
% 1.24/1.42 tff(377,assumption,(s(z) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(378,plain,
% 1.24/1.42 (s(s(s(s(s(z))))) = s(z)),
% 1.24/1.42 inference(symmetry,[status(thm)],[377])).
% 1.24/1.42 tff(379,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[50, 378])).
% 1.24/1.42 tff(380,plain,(~(s(z) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(381,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[367, 77, 116, 118])).
% 1.24/1.42 tff(382,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[375, 381])).
% 1.24/1.42 tff(383,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(384,plain,
% 1.24/1.42 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(385,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(386,plain,
% 1.24/1.42 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[385, 384])).
% 1.24/1.42 tff(387,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[386, 77, 308, 116, 383])).
% 1.24/1.42 tff(388,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(389,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[388, 308, 116])).
% 1.24/1.42 tff(390,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[167, 145])).
% 1.24/1.42 tff(391,plain,
% 1.24/1.42 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[390, 389])).
% 1.24/1.42 tff(392,plain,
% 1.24/1.42 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[313, 308, 118])).
% 1.24/1.42 tff(393,plain,
% 1.24/1.42 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[181, 392])).
% 1.24/1.42 tff(394,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.42 tff(395,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(396,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.42 tff(397,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(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(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(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(z)))), s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(398,plain,
% 1.24/1.42 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(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(z)))), s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(399,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[398])).
% 1.24/1.42 tff(400,plain,
% 1.24/1.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[399, 397])).
% 1.24/1.42 tff(401,plain,
% 1.24/1.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(402,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.24/1.43 tff(403,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[402, 192, 396, 395, 394, 221])).
% 1.24/1.43 tff(404,plain,((~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)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(405,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[404, 393, 391, 220])).
% 1.24/1.43 tff(406,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[154, 146])).
% 1.24/1.43 tff(407,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[406, 405])).
% 1.24/1.43 tff(408,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.24/1.43 tff(409,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.43 tff(410,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(411,plain,
% 1.24/1.43 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(412,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[411])).
% 1.24/1.43 tff(413,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[412, 410])).
% 1.24/1.43 tff(414,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(415,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[414, 413])).
% 1.24/1.43 tff(416,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[415, 77, 308, 409, 408])).
% 1.24/1.43 tff(417,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(418,plain,
% 1.24/1.43 (~r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[417, 308, 407])).
% 1.24/1.43 tff(419,plain,
% 1.24/1.43 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.24/1.43 inference(commutativity,[status(thm)],[])).
% 1.24/1.43 tff(420,plain,
% 1.24/1.43 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.24/1.43 inference(symmetry,[status(thm)],[419])).
% 1.24/1.43 tff(421,plain,
% 1.24/1.43 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[420])).
% 1.24/1.43 tff(422,plain,
% 1.24/1.43 (~(s(z) = s(s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[34, 421])).
% 1.24/1.43 tff(423,plain,
% 1.24/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(424,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(425,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.24/1.43 tff(426,plain,
% 1.24/1.43 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[425, 60])).
% 1.24/1.43 tff(427,plain,
% 1.24/1.43 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[426, 422])).
% 1.24/1.43 tff(428,plain,
% 1.24/1.43 (b(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[427, 418])).
% 1.24/1.43 tff(429,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(430,plain,
% 1.24/1.43 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(431,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[430])).
% 1.24/1.43 tff(432,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[431, 429])).
% 1.24/1.43 tff(433,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(434,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.24/1.43 tff(435,plain,
% 1.24/1.43 (~b(s(z), s(s(s(s(s(z))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[434, 192, 428, 220, 382])).
% 1.24/1.43 tff(436,plain,
% 1.24/1.43 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(437,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(438,plain,
% 1.24/1.43 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[437, 436])).
% 1.24/1.43 tff(439,plain,
% 1.24/1.43 (r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[438, 60, 435, 380])).
% 1.24/1.43 tff(440,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.43 tff(441,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.43 tff(442,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(443,plain,
% 1.24/1.43 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(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(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(444,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[443])).
% 1.24/1.43 tff(445,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[444, 442])).
% 1.24/1.43 tff(446,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(447,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.24/1.43 tff(448,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[447, 192, 396, 395, 441, 440])).
% 1.24/1.43 tff(449,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(450,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[449, 393, 391, 382])).
% 1.24/1.43 tff(451,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[113, 450])).
% 1.24/1.43 tff(452,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(453,plain,
% 1.24/1.43 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(454,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[453])).
% 1.24/1.43 tff(455,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[454, 452])).
% 1.24/1.43 tff(456,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(457,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[456, 455])).
% 1.24/1.43 tff(458,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[457, 77, 308, 451, 439])).
% 1.24/1.43 tff(459,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(460,plain,
% 1.24/1.43 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[459, 116, 66])).
% 1.24/1.43 tff(461,plain,
% 1.24/1.43 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[319, 460])).
% 1.24/1.43 tff(462,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.43 tff(463,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[175, 170, 39])).
% 1.24/1.43 tff(464,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[217, 463])).
% 1.24/1.43 tff(465,assumption,(b(z, s(z))), introduced(assumption)).
% 1.24/1.43 tff(466,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(467,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(468,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[467])).
% 1.24/1.43 tff(469,plain,
% 1.24/1.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[468, 466])).
% 1.24/1.43 tff(470,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(471,plain,
% 1.24/1.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[470, 469])).
% 1.24/1.43 tff(472,plain,
% 1.24/1.43 (~b(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[471, 192, 465, 464, 38])).
% 1.24/1.43 tff(473,plain,
% 1.24/1.43 (r(z, s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[339, 472])).
% 1.24/1.43 tff(474,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(475,plain,
% 1.24/1.43 (((~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)))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(476,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[475])).
% 1.24/1.43 tff(477,plain,
% 1.24/1.43 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[476, 474])).
% 1.24/1.43 tff(478,plain,
% 1.24/1.43 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(479,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.24/1.44 tff(480,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[479, 77, 170, 473, 462])).
% 1.24/1.44 tff(481,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(482,plain,
% 1.24/1.44 (~r(z, s(s(s(s(s(z))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[481, 361, 39, 295, 461])).
% 1.24/1.44 tff(483,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(484,plain,
% 1.24/1.44 (s(s(s(s(s(z))))) = z),
% 1.24/1.44 inference(symmetry,[status(thm)],[483])).
% 1.24/1.44 tff(485,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[266, 484])).
% 1.24/1.44 tff(486,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(487,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.44 tff(488,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.44 tff(489,plain,
% 1.24/1.44 (((~![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)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(490,plain,
% 1.24/1.44 ((~![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)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(491,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.24/1.44 tff(492,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[491, 60, 488, 487, 486])).
% 1.24/1.44 tff(493,plain,(b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(494,plain,
% 1.24/1.44 (b(z, s(s(s(s(s(z))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[493, 482])).
% 1.24/1.44 tff(495,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(496,plain,
% 1.24/1.44 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(497,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[496])).
% 1.24/1.44 tff(498,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[497, 495])).
% 1.24/1.44 tff(499,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(500,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[499, 498])).
% 1.24/1.44 tff(501,plain,
% 1.24/1.44 (~b(s(s(s(z))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[500, 192, 494, 359, 376])).
% 1.24/1.44 tff(502,plain,
% 1.24/1.44 (r(s(s(s(z))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[253, 501])).
% 1.24/1.44 tff(503,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.24/1.44 tff(504,assumption,(r(s(z), z)), introduced(assumption)).
% 1.24/1.44 tff(505,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(506,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(507,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[506, 505])).
% 1.24/1.44 tff(508,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[507, 77, 504, 503, 116])).
% 1.24/1.44 tff(509,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(510,plain,
% 1.24/1.44 (~r(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[509, 502, 116])).
% 1.24/1.44 tff(511,plain,
% 1.24/1.44 (b(s(z), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[351, 510])).
% 1.24/1.44 tff(512,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.24/1.44 tff(513,plain,
% 1.24/1.44 (~b(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[471, 192, 465, 512, 38])).
% 1.24/1.44 tff(514,plain,
% 1.24/1.44 (r(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[339, 513])).
% 1.24/1.44 tff(515,assumption,(b(s(z), z)), introduced(assumption)).
% 1.24/1.44 tff(516,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(517,plain,
% 1.24/1.44 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(518,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[517])).
% 1.24/1.44 tff(519,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[518, 516])).
% 1.24/1.44 tff(520,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(521,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.24/1.44 tff(522,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[521, 192, 515, 465, 512])).
% 1.24/1.44 tff(523,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.44 tff(524,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.24/1.44 tff(525,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[306, 60, 48, 524, 523])).
% 1.24/1.44 tff(526,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(527,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[526, 522])).
% 1.24/1.44 tff(528,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(529,plain,
% 1.24/1.44 (~r(s(s(s(s(s(z))))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[357, 170, 66])).
% 1.24/1.44 tff(530,plain,
% 1.24/1.44 (b(s(s(s(s(s(z))))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[271, 529])).
% 1.24/1.44 tff(531,assumption,(~b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(532,plain,
% 1.24/1.44 (((~![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))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(533,plain,
% 1.24/1.44 ((~![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))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(534,plain,
% 1.24/1.44 ((~![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)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.24/1.44 tff(535,plain,
% 1.24/1.44 ((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)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[534, 60])).
% 1.24/1.44 tff(536,plain,
% 1.24/1.44 (r(s(elem!1), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[535, 531, 528])).
% 1.24/1.44 tff(537,assumption,(r(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.44 tff(538,assumption,(r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(539,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(540,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(541,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.24/1.44 tff(542,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[541, 77, 170, 537, 538])).
% 1.24/1.44 tff(543,plain,((~r(s(elem!1), 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(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(544,plain,
% 1.24/1.44 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[543, 537, 170])).
% 1.24/1.44 tff(545,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.24/1.44 tff(546,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(547,plain,
% 1.24/1.44 (((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(548,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[547])).
% 1.24/1.44 tff(549,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[548, 546])).
% 1.24/1.44 tff(550,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(551,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.24/1.44 tff(552,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[551, 77, 545, 537, 321])).
% 1.24/1.44 tff(553,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(554,plain,
% 1.24/1.44 (~r(s(elem!1), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[553, 537, 321])).
% 1.24/1.44 tff(555,plain,
% 1.24/1.44 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(556,plain,
% 1.24/1.44 (~(s(elem!1) = z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[555, 30])).
% 1.24/1.44 tff(557,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(558,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(559,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.24/1.44 tff(560,plain,
% 1.24/1.44 (b(s(elem!1), z) | r(s(elem!1), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[559, 60, 556])).
% 1.24/1.44 tff(561,plain,
% 1.24/1.44 (b(s(elem!1), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[560, 554])).
% 1.24/1.44 tff(562,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(563,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(564,plain,
% 1.24/1.44 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(565,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[564])).
% 1.24/1.44 tff(566,plain,
% 1.24/1.44 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[565, 563])).
% 1.24/1.44 tff(567,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(elem!1))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(568,plain,
% 1.24/1.44 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.24/1.44 tff(569,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[568, 77, 562, 537, 321])).
% 1.24/1.44 tff(570,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(571,plain,
% 1.24/1.44 (~r(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[570, 537, 321])).
% 1.24/1.44 tff(572,plain,
% 1.24/1.44 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.24/1.44 inference(commutativity,[status(thm)],[])).
% 1.24/1.44 tff(573,plain,
% 1.24/1.44 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.24/1.44 inference(symmetry,[status(thm)],[572])).
% 1.24/1.44 tff(574,plain,
% 1.24/1.44 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[573])).
% 1.24/1.44 tff(575,plain,
% 1.24/1.44 (~(z = s(elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[556, 574])).
% 1.24/1.44 tff(576,plain,
% 1.24/1.44 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(577,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(578,plain,
% 1.24/1.44 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.24/1.44 tff(579,plain,
% 1.24/1.44 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[578, 60])).
% 1.24/1.44 tff(580,plain,
% 1.24/1.44 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[579, 575])).
% 1.24/1.44 tff(581,plain,
% 1.24/1.44 (b(z, s(elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[580, 571])).
% 1.24/1.44 tff(582,assumption,(b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(583,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.24/1.44 tff(584,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.24/1.44 tff(585,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(586,plain,
% 1.24/1.44 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(587,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[586])).
% 1.24/1.44 tff(588,plain,
% 1.24/1.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[587, 585])).
% 1.24/1.44 tff(589,plain,
% 1.24/1.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(590,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.24/1.45 tff(591,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[590, 192, 584, 583, 582, 239])).
% 1.24/1.45 tff(592,plain,((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(593,plain,
% 1.24/1.45 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[592, 581, 239, 561])).
% 1.24/1.45 tff(594,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(595,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(596,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.24/1.45 tff(597,plain,
% 1.24/1.45 ((s(s(s(s(s(z))))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(elem!1)) | r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[596, 60])).
% 1.24/1.45 tff(598,plain,
% 1.24/1.45 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[597, 593, 544])).
% 1.24/1.45 tff(599,plain,
% 1.24/1.45 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[598])).
% 1.24/1.45 tff(600,plain,
% 1.24/1.45 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[599])).
% 1.24/1.45 tff(601,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[600])).
% 1.24/1.45 tff(602,plain,
% 1.24/1.45 (~r(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[479, 77, 170, 321])).
% 1.24/1.45 tff(603,plain,
% 1.24/1.45 (b(z, s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[491, 60, 602, 486])).
% 1.24/1.45 tff(604,plain,
% 1.24/1.45 (~b(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[500, 192, 603, 239, 440])).
% 1.24/1.45 tff(605,plain,
% 1.24/1.45 (r(s(s(s(z))), z)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[253, 604])).
% 1.24/1.45 tff(606,plain,
% 1.24/1.45 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.24/1.45 inference(commutativity,[status(thm)],[])).
% 1.24/1.45 tff(607,plain,
% 1.24/1.45 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[606])).
% 1.24/1.45 tff(608,plain,
% 1.24/1.45 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[607])).
% 1.24/1.45 tff(609,plain,
% 1.24/1.45 (~(s(z) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[50, 608])).
% 1.24/1.45 tff(610,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(611,plain,
% 1.24/1.45 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(612,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[611])).
% 1.24/1.45 tff(613,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[612, 610])).
% 1.24/1.45 tff(614,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(615,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.24/1.45 tff(616,plain,
% 1.24/1.45 (~b(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[615, 192, 515, 603, 239])).
% 1.24/1.45 tff(617,plain,
% 1.24/1.45 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[438, 60, 616])).
% 1.24/1.45 tff(618,plain,
% 1.24/1.45 (r(s(z), s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[617, 609])).
% 1.24/1.45 tff(619,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.45 tff(620,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(621,plain,
% 1.24/1.45 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(622,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[621])).
% 1.24/1.45 tff(623,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[622, 620])).
% 1.24/1.45 tff(624,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(625,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.24/1.45 tff(626,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[625, 77, 170, 308, 619])).
% 1.24/1.45 tff(627,plain,((~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)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(628,plain,
% 1.24/1.45 (~r(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[627, 618, 170])).
% 1.24/1.45 tff(629,plain,
% 1.24/1.45 (b(s(z), s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[319, 628])).
% 1.24/1.45 tff(630,plain,
% 1.24/1.45 ((s(s(s(s(s(z))))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[598])).
% 1.24/1.45 tff(631,plain,
% 1.24/1.45 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[630])).
% 1.24/1.45 tff(632,plain,
% 1.24/1.45 (~(s(elem!1) = s(z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[50, 631])).
% 1.24/1.45 tff(633,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(634,assumption,(~r(z, s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(635,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.24/1.45 tff(636,plain,
% 1.24/1.45 (s(elem!1) = s(z)),
% 1.24/1.45 inference(symmetry,[status(thm)],[635])).
% 1.24/1.45 tff(637,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[115, 636])).
% 1.24/1.45 tff(638,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(639,plain,
% 1.24/1.45 (~(s(z) = s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[638, 115])).
% 1.24/1.45 tff(640,plain,
% 1.24/1.45 (b(z, s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[580, 634])).
% 1.24/1.45 tff(641,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(642,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(643,plain,
% 1.24/1.45 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(644,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[643])).
% 1.24/1.45 tff(645,plain,
% 1.24/1.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z)))),
% 1.24/1.45 inference(transitivity,[status(thm)],[644, 642])).
% 1.24/1.45 tff(646,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(647,plain,
% 1.24/1.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), z))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[646, 645])).
% 1.24/1.45 tff(648,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[647, 192, 584, 515, 583, 641])).
% 1.24/1.45 tff(649,plain,((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(650,plain,
% 1.24/1.45 (~b(s(z), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[649, 583, 640, 515])).
% 1.24/1.45 tff(651,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(652,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(653,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(654,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(655,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(656,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.24/1.45 tff(657,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[656, 60, 653, 652, 651])).
% 1.24/1.45 tff(658,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(659,plain,
% 1.24/1.45 (r(s(z), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[658, 650, 639])).
% 1.24/1.45 tff(660,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.24/1.45 tff(661,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(662,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(663,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.24/1.45 tff(664,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[663, 77, 538, 660, 118])).
% 1.24/1.45 tff(665,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(666,plain,
% 1.24/1.45 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[665, 659, 66])).
% 1.24/1.45 tff(667,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.24/1.45 tff(668,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.24/1.45 tff(669,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(670,plain,
% 1.24/1.45 (((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(671,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[670])).
% 1.24/1.45 tff(672,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[671, 669])).
% 1.24/1.45 tff(673,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(674,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[673, 672])).
% 1.24/1.45 tff(675,plain,
% 1.24/1.45 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[674, 77, 668, 667])).
% 1.24/1.45 tff(676,plain,
% 1.24/1.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(677,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(678,plain,
% 1.24/1.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.24/1.45 tff(679,plain,
% 1.24/1.45 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[678, 60])).
% 1.24/1.45 tff(680,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(elem!1)),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[679, 675, 633])).
% 1.24/1.45 tff(681,plain,
% 1.24/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(682,plain,
% 1.24/1.45 (inj_0(s(elem!1)) = elem!1),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[681, 8])).
% 1.24/1.45 tff(683,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.24/1.45 tff(684,plain,
% 1.24/1.45 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[683])).
% 1.24/1.45 tff(685,plain,
% 1.24/1.45 (s(s(s(z))) = elem!1),
% 1.24/1.45 inference(transitivity,[status(thm)],[92, 684, 682])).
% 1.24/1.45 tff(686,plain,
% 1.24/1.45 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[685])).
% 1.24/1.45 tff(687,plain,
% 1.24/1.45 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[686])).
% 1.24/1.45 tff(688,plain,
% 1.24/1.45 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[683])).
% 1.24/1.45 tff(689,plain,
% 1.24/1.45 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[688])).
% 1.24/1.45 tff(690,plain,
% 1.24/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(691,plain,
% 1.24/1.45 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[690, 8])).
% 1.24/1.45 tff(692,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.24/1.45 tff(693,plain,
% 1.24/1.45 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[692])).
% 1.24/1.45 tff(694,plain,
% 1.24/1.45 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[693])).
% 1.24/1.45 tff(695,plain,
% 1.24/1.45 (elem!1 = inj_0(s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[682])).
% 1.24/1.45 tff(696,plain,
% 1.24/1.45 (elem!1 = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[695, 694, 691, 689])).
% 1.24/1.45 tff(697,plain,
% 1.24/1.45 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[696, 687])).
% 1.24/1.45 tff(698,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[102, 697])).
% 1.24/1.45 tff(699,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(700,plain,
% 1.24/1.45 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[699, 680])).
% 1.24/1.45 tff(701,plain,
% 1.24/1.45 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(commutativity,[status(thm)],[])).
% 1.24/1.45 tff(702,plain,
% 1.24/1.45 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.24/1.45 inference(symmetry,[status(thm)],[701])).
% 1.24/1.45 tff(703,plain,
% 1.24/1.45 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.45 inference(commutativity,[status(thm)],[])).
% 1.24/1.45 tff(704,plain,
% 1.24/1.45 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[703])).
% 1.24/1.45 tff(705,plain,
% 1.24/1.45 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[692, 704])).
% 1.24/1.45 tff(706,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.45 tff(707,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[706, 705])).
% 1.24/1.45 tff(708,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(709,plain,
% 1.24/1.45 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[708, 680])).
% 1.24/1.45 tff(710,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.45 tff(711,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(elem!1)),
% 1.24/1.45 inference(symmetry,[status(thm)],[710])).
% 1.24/1.45 tff(712,plain,
% 1.24/1.45 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[711])).
% 1.24/1.45 tff(713,plain,
% 1.24/1.45 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[712])).
% 1.24/1.45 tff(714,plain,
% 1.24/1.45 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[710])).
% 1.24/1.45 tff(715,plain,
% 1.24/1.45 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[695, 714, 691, 713])).
% 1.24/1.45 tff(716,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.24/1.45 tff(717,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[716, 715])).
% 1.24/1.45 tff(718,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(719,plain,
% 1.24/1.45 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[718, 709])).
% 1.24/1.45 tff(720,plain,
% 1.24/1.45 (s(s(s(s(elem!1)))) = elem!1),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[719, 702])).
% 1.24/1.45 tff(721,plain,
% 1.24/1.45 ((~![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)))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(722,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[721, 8])).
% 1.24/1.45 tff(723,assumption,(s(elem!1) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.45 tff(724,plain,
% 1.24/1.45 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[723])).
% 1.24/1.45 tff(725,plain,
% 1.24/1.45 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[724])).
% 1.24/1.45 tff(726,plain,
% 1.24/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(727,plain,
% 1.24/1.45 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[726, 8])).
% 1.24/1.45 tff(728,assumption,(s(s(s(s(elem!1)))) = elem!1), introduced(assumption)).
% 1.24/1.45 tff(729,plain,
% 1.24/1.45 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[728])).
% 1.24/1.45 tff(730,plain,
% 1.24/1.45 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[723])).
% 1.24/1.45 tff(731,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.24/1.45 inference(symmetry,[status(thm)],[730])).
% 1.24/1.45 tff(732,plain,
% 1.24/1.45 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[45, 731, 682, 729])).
% 1.24/1.45 tff(733,plain,
% 1.24/1.45 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[732])).
% 1.24/1.45 tff(734,plain,
% 1.24/1.45 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[92, 733, 727, 725])).
% 1.24/1.45 tff(735,plain,
% 1.24/1.45 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[734])).
% 1.24/1.45 tff(736,plain,
% 1.24/1.45 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[16, 735, 722])).
% 1.24/1.45 tff(737,plain,
% 1.24/1.45 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[736])).
% 1.24/1.45 tff(738,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.24/1.45 inference(symmetry,[status(thm)],[737])).
% 1.24/1.45 tff(739,plain,
% 1.24/1.45 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(quant_inst,[status(thm)],[])).
% 1.24/1.45 tff(740,plain,
% 1.24/1.45 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[739, 8])).
% 1.24/1.45 tff(741,plain,
% 1.24/1.45 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[740])).
% 1.24/1.45 tff(742,plain,
% 1.24/1.45 (s(s(s(s(s(z))))) = s(z)),
% 1.24/1.45 inference(transitivity,[status(thm)],[741, 738, 10])).
% 1.24/1.45 tff(743,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[50, 742])).
% 1.24/1.45 tff(744,plain,((~(s(s(s(s(elem!1)))) = elem!1)) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(745,plain,
% 1.24/1.45 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[744, 720])).
% 1.24/1.45 tff(746,plain,
% 1.24/1.45 ((s(elem!1) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.45 inference(commutativity,[status(thm)],[])).
% 1.24/1.45 tff(747,plain,
% 1.24/1.45 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.45 inference(symmetry,[status(thm)],[746])).
% 1.24/1.45 tff(748,assumption,(s(s(s(s(s(z))))) = s(elem!1)), introduced(assumption)).
% 1.24/1.45 tff(749,plain,
% 1.24/1.45 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.24/1.45 inference(modus_ponens,[status(thm)],[748, 747])).
% 1.24/1.45 tff(750,assumption,(~(s(elem!1) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.45 tff(751,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[750, 749])).
% 1.24/1.45 tff(752,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.45 tff(753,plain,
% 1.24/1.45 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[752, 745])).
% 1.24/1.45 tff(754,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(755,plain,
% 1.24/1.45 (((~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)))) <=> ((~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))))),
% 1.24/1.45 inference(rewrite,[status(thm)],[])).
% 1.24/1.45 tff(756,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))),
% 1.24/1.45 inference(monotonicity,[status(thm)],[755])).
% 1.24/1.45 tff(757,plain,
% 1.24/1.45 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 1.24/1.45 inference(transitivity,[status(thm)],[756, 754])).
% 1.24/1.45 tff(758,plain,
% 1.24/1.45 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(759,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[758, 757])).
% 1.24/1.46 tff(760,plain,
% 1.24/1.46 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[759, 77, 668, 66])).
% 1.24/1.46 tff(761,plain,
% 1.24/1.46 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[597, 760, 753])).
% 1.24/1.46 tff(762,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(763,plain,
% 1.24/1.46 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(764,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[763])).
% 1.24/1.46 tff(765,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[764, 762])).
% 1.24/1.46 tff(766,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(767,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[766, 765])).
% 1.24/1.46 tff(768,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[767, 77, 668, 67])).
% 1.24/1.46 tff(769,assumption,(~(s(s(s(s(z)))) = s(elem!1))), introduced(assumption)).
% 1.24/1.46 tff(770,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(771,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(772,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[771, 770])).
% 1.24/1.46 tff(773,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[772, 60, 769, 768])).
% 1.24/1.46 tff(774,plain,
% 1.24/1.46 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.24/1.46 inference(commutativity,[status(thm)],[])).
% 1.24/1.46 tff(775,plain,
% 1.24/1.46 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(z))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[774])).
% 1.24/1.46 tff(776,plain,
% 1.24/1.46 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[769, 775])).
% 1.24/1.46 tff(777,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(778,plain,
% 1.24/1.46 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(779,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[778])).
% 1.24/1.46 tff(780,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[779, 777])).
% 1.24/1.46 tff(781,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(782,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.24/1.46 tff(783,plain,
% 1.24/1.46 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[782, 77, 668, 67])).
% 1.24/1.46 tff(784,plain,
% 1.24/1.46 (b(s(elem!1), s(s(s(s(z)))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[535, 783, 776])).
% 1.24/1.46 tff(785,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(786,plain,
% 1.24/1.46 (((~b(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(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), 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(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(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(787,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[786])).
% 1.24/1.46 tff(788,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[787, 785])).
% 1.24/1.46 tff(789,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), 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)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(790,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[789, 788])).
% 1.24/1.46 tff(791,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[790, 192, 182, 784, 582, 156, 773])).
% 1.24/1.46 tff(792,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(s(s(s(z)))) = s(elem!1)) | (~r(s(elem!1), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(793,plain,
% 1.24/1.46 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[792, 761, 700, 668, 39])).
% 1.24/1.46 tff(794,plain,
% 1.24/1.46 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[217, 793])).
% 1.24/1.46 tff(795,assumption,(r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(796,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(797,plain,
% 1.24/1.46 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(798,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[797])).
% 1.24/1.46 tff(799,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[798, 796])).
% 1.24/1.46 tff(800,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(801,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.24/1.46 tff(802,plain,
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% 1.24/1.46 inference(unit_resolution,[status(thm)],[801, 77, 668, 795, 118])).
% 1.24/1.46 tff(803,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(804,plain,
% 1.24/1.46 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[803, 668, 66])).
% 1.24/1.46 tff(805,assumption,(~b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(806,assumption,(~r(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(807,plain,
% 1.24/1.46 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(808,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(809,plain,
% 1.24/1.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.24/1.46 tff(810,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[809, 60, 806, 805, 750])).
% 1.24/1.46 tff(811,plain,(b(s(elem!1), s(s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(812,plain,
% 1.24/1.46 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[811, 745, 804])).
% 1.24/1.46 tff(813,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(814,assumption,(b(s(elem!1), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.24/1.46 tff(815,assumption,(~(s(s(s(s(s(z))))) = s(elem!1))), introduced(assumption)).
% 1.24/1.46 tff(816,plain,
% 1.24/1.46 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[759, 77, 668, 118])).
% 1.24/1.46 tff(817,plain,
% 1.24/1.46 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[597, 816, 815])).
% 1.24/1.46 tff(818,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(819,plain,
% 1.24/1.46 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(820,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[819])).
% 1.24/1.46 tff(821,plain,
% 1.24/1.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[820, 818])).
% 1.24/1.46 tff(822,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(823,plain,
% 1.24/1.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[822, 821])).
% 1.24/1.46 tff(824,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[823, 192, 584, 817, 814, 813])).
% 1.24/1.46 tff(825,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(826,plain,
% 1.24/1.46 (~b(z, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[825, 812, 584, 753, 668, 66])).
% 1.24/1.46 tff(827,plain,
% 1.24/1.46 (r(z, s(s(s(s(s(z))))))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[491, 60, 826, 486])).
% 1.24/1.46 tff(828,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(829,plain,
% 1.24/1.46 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(rewrite,[status(thm)],[])).
% 1.24/1.46 tff(830,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[829])).
% 1.24/1.46 tff(831,plain,
% 1.24/1.46 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[830, 828])).
% 1.24/1.46 tff(832,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 1.24/1.46 inference(quant_inst,[status(thm)],[])).
% 1.24/1.46 tff(833,plain,
% 1.24/1.46 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.24/1.46 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.24/1.46 tff(834,plain,
% 1.24/1.46 ($false),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[833, 77, 37, 118, 462])).
% 1.24/1.46 tff(835,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.46 tff(836,plain,
% 1.24/1.46 (~r(z, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[835, 827, 66])).
% 1.24/1.46 tff(837,plain,
% 1.24/1.46 (b(z, s(z))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[292, 836])).
% 1.24/1.46 tff(838,plain,
% 1.24/1.46 (~b(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[521, 192, 515, 837, 794])).
% 1.24/1.46 tff(839,plain,
% 1.24/1.46 (r(s(s(s(s(z)))), z)),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[306, 60, 48, 838])).
% 1.24/1.46 tff(840,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.24/1.46 tff(841,plain,
% 1.24/1.46 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.24/1.46 inference(monotonicity,[status(thm)],[840])).
% 1.24/1.46 tff(842,plain,
% 1.24/1.46 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.46 inference(symmetry,[status(thm)],[841])).
% 1.24/1.46 tff(843,plain,
% 1.24/1.46 (elem!1 = s(s(s(s(z))))),
% 1.24/1.46 inference(transitivity,[status(thm)],[695, 694, 691, 842])).
% 1.24/1.46 tff(844,plain,
% 1.24/1.46 (s(elem!1) = s(s(s(elem!1)))),
% 1.24/1.46 inference(unit_resolution,[status(thm)],[708, 692])).
% 1.24/1.47 tff(845,plain,
% 1.24/1.47 (elem!1 = s(s(s(s(elem!1))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[718, 844])).
% 1.24/1.47 tff(846,plain,
% 1.24/1.47 (s(s(s(s(elem!1)))) = elem!1),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[845, 702])).
% 1.24/1.47 tff(847,plain,
% 1.24/1.47 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[744, 846])).
% 1.24/1.47 tff(848,plain,
% 1.24/1.47 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[752, 847])).
% 1.24/1.47 tff(849,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 1.24/1.47 tff(850,plain,
% 1.24/1.47 (s(s(s(s(z)))) = elem!1),
% 1.24/1.47 inference(symmetry,[status(thm)],[849])).
% 1.24/1.47 tff(851,plain,
% 1.24/1.47 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.24/1.47 inference(monotonicity,[status(thm)],[850])).
% 1.24/1.47 tff(852,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[815, 851])).
% 1.24/1.47 tff(853,plain,((~(elem!1 = s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(854,plain,
% 1.24/1.47 (~(elem!1 = s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[853, 848])).
% 1.24/1.47 tff(855,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[854, 843])).
% 1.24/1.47 tff(856,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(857,plain,
% 1.24/1.47 (~(s(s(s(z))) = s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[856, 680])).
% 1.24/1.47 tff(858,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(859,plain,
% 1.24/1.47 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(860,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[859])).
% 1.24/1.47 tff(861,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[860, 858])).
% 1.24/1.47 tff(862,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(863,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[862, 861])).
% 1.24/1.47 tff(864,plain,
% 1.24/1.47 (~b(z, s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[863, 192, 515, 837, 794, 38])).
% 1.24/1.47 tff(865,plain,
% 1.24/1.47 (r(z, s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[339, 864])).
% 1.24/1.47 tff(866,plain,
% 1.24/1.47 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[700, 775])).
% 1.24/1.47 tff(867,plain,
% 1.24/1.47 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[481, 837, 827, 38, 39])).
% 1.24/1.47 tff(868,plain,
% 1.24/1.47 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[181, 867])).
% 1.24/1.47 tff(869,assumption,(b(s(elem!1), s(s(s(s(z)))))), introduced(assumption)).
% 1.24/1.47 tff(870,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(871,plain,
% 1.24/1.47 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(872,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[871])).
% 1.24/1.47 tff(873,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[872, 870])).
% 1.24/1.47 tff(874,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(875,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[874, 873])).
% 1.24/1.47 tff(876,plain,
% 1.24/1.47 (~b(s(s(s(s(s(z))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[875, 192, 584, 396, 869, 582])).
% 1.24/1.47 tff(877,plain,
% 1.24/1.47 (r(s(s(s(s(s(z))))), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[271, 876])).
% 1.24/1.47 tff(878,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(879,plain,
% 1.24/1.47 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(880,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[879])).
% 1.24/1.47 tff(881,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.47 inference(transitivity,[status(thm)],[880, 878])).
% 1.24/1.47 tff(882,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(883,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[882, 881])).
% 1.24/1.47 tff(884,plain,
% 1.24/1.47 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[883, 77, 877, 297])).
% 1.24/1.47 tff(885,plain,
% 1.24/1.47 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[111, 60, 884, 106])).
% 1.24/1.47 tff(886,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(887,plain,
% 1.24/1.47 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(888,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[887])).
% 1.24/1.47 tff(889,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[888, 886])).
% 1.24/1.47 tff(890,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(891,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[890, 889])).
% 1.24/1.47 tff(892,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[891, 192, 396, 869, 814, 885])).
% 1.24/1.47 tff(893,plain,((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(894,plain,
% 1.24/1.47 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[893, 839, 812, 868, 584, 761])).
% 1.24/1.47 tff(895,plain,
% 1.24/1.47 (r(s(elem!1), s(s(s(s(z)))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[535, 894, 866])).
% 1.24/1.47 tff(896,plain,
% 1.24/1.47 (~r(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[553, 895, 865])).
% 1.24/1.47 tff(897,plain,
% 1.24/1.47 (b(s(elem!1), z)),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[560, 896])).
% 1.24/1.47 tff(898,plain,
% 1.24/1.47 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[373, 60, 102, 381])).
% 1.24/1.47 tff(899,plain,
% 1.24/1.47 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(900,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(901,plain,
% 1.24/1.47 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[900, 899])).
% 1.24/1.47 tff(902,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[901, 77, 668, 116])).
% 1.24/1.47 tff(903,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 1.24/1.47 tff(904,plain,
% 1.24/1.47 (((~![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)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(905,plain,
% 1.24/1.47 ((~![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)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(906,plain,
% 1.24/1.47 ((~![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))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[905, 904])).
% 1.24/1.47 tff(907,plain,
% 1.24/1.47 (b(s(s(s(z))), s(elem!1))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[906, 60, 903, 902])).
% 1.24/1.47 tff(908,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(909,plain,
% 1.24/1.47 (((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(910,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.24/1.47 inference(monotonicity,[status(thm)],[909])).
% 1.24/1.47 tff(911,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.24/1.47 inference(transitivity,[status(thm)],[910, 908])).
% 1.24/1.47 tff(912,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(913,plain,
% 1.24/1.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[912, 911])).
% 1.24/1.47 tff(914,plain,
% 1.24/1.47 ($false),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[913, 192, 584, 583, 582, 814, 907, 898])).
% 1.24/1.47 tff(915,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.47 tff(916,plain,
% 1.24/1.47 (~r(s(s(s(z))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[915, 897, 584, 761, 812, 857, 66, 668])).
% 1.24/1.47 tff(917,plain,
% 1.24/1.47 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(918,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.24/1.47 inference(quant_inst,[status(thm)],[])).
% 1.24/1.47 tff(919,plain,
% 1.24/1.47 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.24/1.47 inference(modus_ponens,[status(thm)],[918, 917])).
% 1.24/1.47 tff(920,plain,
% 1.24/1.47 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[919, 60, 34])).
% 1.24/1.47 tff(921,plain,
% 1.24/1.47 (b(s(s(s(z))), s(z))),
% 1.24/1.47 inference(unit_resolution,[status(thm)],[920, 916])).
% 1.24/1.47 tff(922,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(923,plain,
% 1.24/1.47 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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))))),
% 1.24/1.47 inference(rewrite,[status(thm)],[])).
% 1.24/1.47 tff(924,plain,
% 1.24/1.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[923])).
% 1.24/1.48 tff(925,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[924, 922])).
% 1.24/1.48 tff(926,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(927,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(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)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.24/1.48 tff(928,plain,
% 1.24/1.48 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[927, 192, 515, 837, 794, 38, 921])).
% 1.24/1.48 tff(929,plain,
% 1.24/1.48 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[167, 928, 145])).
% 1.24/1.48 tff(930,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(931,plain,
% 1.24/1.48 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(932,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[931])).
% 1.24/1.48 tff(933,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[932, 930])).
% 1.24/1.48 tff(934,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(935,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.24/1.48 tff(936,plain,
% 1.24/1.48 (~b(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[935, 192, 515, 837, 921])).
% 1.24/1.48 tff(937,plain,
% 1.24/1.48 (r(s(s(s(z))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[253, 936])).
% 1.24/1.48 tff(938,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(939,plain,
% 1.24/1.48 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(940,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[939])).
% 1.24/1.48 tff(941,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.48 inference(transitivity,[status(thm)],[940, 938])).
% 1.24/1.48 tff(942,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(943,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[942, 941])).
% 1.24/1.48 tff(944,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[943, 77, 937, 929, 839])).
% 1.24/1.48 tff(945,plain,((~r(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | b(s(s(s(s(s(z))))), s(z)) | b(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(946,plain,
% 1.24/1.48 (~r(s(elem!1), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[945, 667, 38, 640, 39, 633, 515])).
% 1.24/1.48 tff(947,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(948,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(949,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.24/1.48 tff(950,plain,
% 1.24/1.48 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[949, 60])).
% 1.24/1.48 tff(951,plain,
% 1.24/1.48 (b(s(elem!1), s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[950, 946, 115])).
% 1.24/1.48 tff(952,plain,
% 1.24/1.48 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(953,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.24/1.48 tff(954,plain,
% 1.24/1.48 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[723])).
% 1.24/1.48 tff(955,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.24/1.48 inference(symmetry,[status(thm)],[954])).
% 1.24/1.48 tff(956,plain,
% 1.24/1.48 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[955])).
% 1.24/1.48 tff(957,plain,
% 1.24/1.48 (~b(s(elem!1), s(z))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[39, 956])).
% 1.24/1.48 tff(958,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[953, 957])).
% 1.24/1.48 tff(959,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(960,plain,
% 1.24/1.48 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[959, 953, 39])).
% 1.24/1.48 tff(961,plain,
% 1.24/1.48 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[752, 960])).
% 1.24/1.48 tff(962,assumption,(~b(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.24/1.48 tff(963,plain,
% 1.24/1.48 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[597, 962, 961])).
% 1.24/1.48 tff(964,plain,
% 1.24/1.48 (~r(s(z), s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[665, 963, 66])).
% 1.24/1.48 tff(965,plain,
% 1.24/1.48 (b(s(z), s(elem!1))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[658, 964, 651])).
% 1.24/1.48 tff(966,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(967,plain,
% 1.24/1.48 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(968,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[967])).
% 1.24/1.48 tff(969,plain,
% 1.24/1.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[968, 966])).
% 1.24/1.48 tff(970,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(971,plain,
% 1.24/1.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[970, 969])).
% 1.24/1.48 tff(972,plain,
% 1.24/1.48 (~b(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[971, 192, 584, 953, 965])).
% 1.24/1.48 tff(973,plain,
% 1.24/1.48 (r(z, s(z))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[292, 972])).
% 1.24/1.48 tff(974,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.24/1.48 tff(975,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(976,plain,
% 1.24/1.48 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(977,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[976])).
% 1.24/1.48 tff(978,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[977, 975])).
% 1.24/1.48 tff(979,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(980,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[979, 978])).
% 1.24/1.48 tff(981,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[980, 77, 974, 37, 667])).
% 1.24/1.48 tff(982,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(983,plain,
% 1.24/1.48 (~r(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[982, 973, 667])).
% 1.24/1.48 tff(984,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.24/1.48 tff(985,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.24/1.48 tff(986,plain,
% 1.24/1.48 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(987,plain,
% 1.24/1.48 (~(s(s(s(elem!1))) = z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[986, 30])).
% 1.24/1.48 tff(988,plain,
% 1.24/1.48 (((~![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))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(989,plain,
% 1.24/1.48 ((~![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))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(990,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[989, 988])).
% 1.24/1.48 tff(991,plain,
% 1.24/1.48 ($false),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[990, 60, 987, 985, 984])).
% 1.24/1.48 tff(992,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.48 tff(993,plain,
% 1.24/1.48 (b(s(s(s(elem!1))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[992, 983])).
% 1.24/1.48 tff(994,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[278, 77, 973, 66])).
% 1.24/1.48 tff(995,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), z)),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[271, 994])).
% 1.24/1.48 tff(996,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(997,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(998,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[997, 996])).
% 1.24/1.48 tff(999,plain,
% 1.24/1.48 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[998, 77, 118, 667])).
% 1.24/1.48 tff(1000,assumption,(~(s(s(s(s(s(z))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.24/1.48 tff(1001,plain,
% 1.24/1.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(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)))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1002,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(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)))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1003,plain,
% 1.24/1.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(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))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1002, 1001])).
% 1.24/1.48 tff(1004,plain,
% 1.24/1.48 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1003, 60, 1000, 999])).
% 1.24/1.48 tff(1005,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.24/1.48 tff(1006,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1007,plain,
% 1.24/1.48 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, 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))))),
% 1.24/1.48 inference(rewrite,[status(thm)],[])).
% 1.24/1.48 tff(1008,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1007])).
% 1.24/1.48 tff(1009,plain,
% 1.24/1.48 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.24/1.48 inference(transitivity,[status(thm)],[1008, 1006])).
% 1.24/1.48 tff(1010,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.24/1.48 inference(quant_inst,[status(thm)],[])).
% 1.24/1.48 tff(1011,plain,
% 1.24/1.48 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.24/1.48 tff(1012,plain,
% 1.24/1.48 (~r(z, s(s(s(elem!1))))),
% 1.24/1.48 inference(unit_resolution,[status(thm)],[1011, 77, 37, 667])).
% 1.24/1.48 tff(1013,plain,
% 1.24/1.48 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.24/1.48 inference(commutativity,[status(thm)],[])).
% 1.24/1.48 tff(1014,plain,
% 1.24/1.48 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.24/1.48 inference(symmetry,[status(thm)],[1013])).
% 1.24/1.48 tff(1015,plain,
% 1.24/1.48 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.24/1.48 inference(monotonicity,[status(thm)],[1014])).
% 1.24/1.48 tff(1016,plain,
% 1.24/1.48 (~(z = s(s(s(elem!1))))),
% 1.24/1.48 inference(modus_ponens,[status(thm)],[987, 1015])).
% 1.24/1.48 tff(1017,plain,
% 1.24/1.48 (((~![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)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1018,plain,
% 1.24/1.49 ((~![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)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1019,plain,
% 1.24/1.49 ((~![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))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 1.24/1.49 tff(1020,plain,
% 1.24/1.49 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1019, 60])).
% 1.24/1.49 tff(1021,plain,
% 1.24/1.49 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1020, 1016])).
% 1.24/1.49 tff(1022,plain,
% 1.24/1.49 (b(z, s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1021, 1012])).
% 1.24/1.49 tff(1023,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(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))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1024,plain,
% 1.24/1.49 (((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(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))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1025,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1024])).
% 1.24/1.49 tff(1026,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1025, 1023])).
% 1.24/1.49 tff(1027,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1028,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 1.24/1.49 tff(1029,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1028, 192, 1022, 1005, 239, 1004])).
% 1.24/1.49 tff(1030,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1031,plain,
% 1.24/1.49 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1030, 995, 667, 973, 66, 993])).
% 1.24/1.49 tff(1032,plain,
% 1.24/1.49 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1031])).
% 1.24/1.49 tff(1033,plain,
% 1.24/1.49 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1031])).
% 1.24/1.49 tff(1034,plain,
% 1.24/1.49 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1033])).
% 1.24/1.49 tff(1035,plain,
% 1.24/1.49 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[691])).
% 1.24/1.49 tff(1036,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1035, 1034, 44])).
% 1.24/1.49 tff(1037,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1036, 1032])).
% 1.24/1.49 tff(1038,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1037, 952])).
% 1.24/1.49 tff(1039,plain,
% 1.24/1.49 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1038])).
% 1.24/1.49 tff(1040,plain,
% 1.24/1.49 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1039])).
% 1.24/1.49 tff(1041,plain,
% 1.24/1.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[104, 1040])).
% 1.24/1.49 tff(1042,plain,
% 1.24/1.49 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.24/1.49 inference(transitivity,[status(thm)],[45, 1033, 691])).
% 1.24/1.49 tff(1043,plain,
% 1.24/1.49 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1042])).
% 1.24/1.49 tff(1044,plain,
% 1.24/1.49 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1043])).
% 1.24/1.49 tff(1045,plain,
% 1.24/1.49 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1046,plain,
% 1.24/1.49 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1045, 8])).
% 1.24/1.49 tff(1047,plain,
% 1.24/1.49 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1046])).
% 1.24/1.49 tff(1048,plain,
% 1.24/1.49 (s(elem!1) = s(s(s(z)))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1047, 1044, 91])).
% 1.24/1.49 tff(1049,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1036, 1048])).
% 1.24/1.49 tff(1050,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1049])).
% 1.24/1.49 tff(1051,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1036, 1048])).
% 1.24/1.49 tff(1052,plain,
% 1.24/1.49 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1051])).
% 1.24/1.49 tff(1053,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1036])).
% 1.24/1.49 tff(1054,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1053])).
% 1.24/1.49 tff(1055,assumption,(s(s(s(s(s(z))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.24/1.49 tff(1056,plain,
% 1.24/1.49 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1055])).
% 1.24/1.49 tff(1057,plain,
% 1.24/1.49 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1055])).
% 1.24/1.49 tff(1058,plain,
% 1.24/1.49 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1057])).
% 1.24/1.49 tff(1059,plain,
% 1.24/1.49 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1035, 1058, 44])).
% 1.24/1.49 tff(1060,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1059, 1056])).
% 1.24/1.49 tff(1061,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1060, 952])).
% 1.24/1.49 tff(1062,plain,
% 1.24/1.49 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1061])).
% 1.24/1.49 tff(1063,plain,
% 1.24/1.49 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1062])).
% 1.24/1.49 tff(1064,plain,
% 1.24/1.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[104, 1063])).
% 1.24/1.49 tff(1065,plain,
% 1.24/1.49 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1059])).
% 1.24/1.49 tff(1066,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 1.24/1.49 inference(symmetry,[status(thm)],[1065])).
% 1.24/1.49 tff(1067,plain,
% 1.24/1.49 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(elem!1)), z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1066])).
% 1.24/1.49 tff(1068,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1069,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1070,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1069, 1068])).
% 1.24/1.49 tff(1071,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1070, 77, 37, 67, 297])).
% 1.24/1.49 tff(1072,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1073,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1072, 67, 37])).
% 1.24/1.49 tff(1074,plain,
% 1.24/1.49 (~r(s(s(elem!1)), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1073, 1067])).
% 1.24/1.49 tff(1075,plain,
% 1.24/1.49 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1076,plain,
% 1.24/1.49 (~(s(s(elem!1)) = z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1075, 30])).
% 1.24/1.49 tff(1077,plain,
% 1.24/1.49 (((~![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))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1078,plain,
% 1.24/1.49 ((~![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))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1079,plain,
% 1.24/1.49 ((~![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)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 1.24/1.49 tff(1080,plain,
% 1.24/1.49 (b(s(s(elem!1)), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1079, 60, 1076, 1074])).
% 1.24/1.49 tff(1081,plain,
% 1.24/1.49 (~r(s(s(s(elem!1))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[982, 37, 667])).
% 1.24/1.49 tff(1082,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[992, 1081])).
% 1.24/1.49 tff(1083,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1084,plain,
% 1.24/1.49 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1085,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1084])).
% 1.24/1.49 tff(1086,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1085, 1083])).
% 1.24/1.49 tff(1087,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1088,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.24/1.49 tff(1089,plain,
% 1.24/1.49 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1088, 192, 1022, 1082, 1080])).
% 1.24/1.49 tff(1090,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1059])).
% 1.24/1.49 tff(1091,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1090])).
% 1.24/1.49 tff(1092,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[67, 1091])).
% 1.24/1.49 tff(1093,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1094,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1095,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.24/1.49 tff(1096,plain,
% 1.24/1.49 ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1095, 77, 667])).
% 1.24/1.49 tff(1097,plain,
% 1.24/1.49 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1096, 1092])).
% 1.24/1.49 tff(1098,plain,
% 1.24/1.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1099,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1100,plain,
% 1.24/1.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 1.24/1.49 tff(1101,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1100, 60, 1097])).
% 1.24/1.49 tff(1102,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1101, 1089, 1064])).
% 1.24/1.49 tff(1103,plain,((~r(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(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1104,plain,
% 1.24/1.49 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1103, 1031, 667, 973])).
% 1.24/1.49 tff(1105,plain,
% 1.24/1.49 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[217, 1104])).
% 1.24/1.49 tff(1106,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(z))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1105, 1054])).
% 1.24/1.49 tff(1107,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1108,plain,
% 1.24/1.49 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1109,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1108])).
% 1.24/1.49 tff(1110,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1109, 1107])).
% 1.24/1.49 tff(1111,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1112,plain,
% 1.24/1.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 1.24/1.49 tff(1113,plain,
% 1.24/1.49 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1112, 192, 953, 965])).
% 1.24/1.49 tff(1114,plain,
% 1.24/1.49 (~b(s(s(elem!1)), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1113, 1106])).
% 1.24/1.49 tff(1115,plain,
% 1.24/1.49 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1114, 1052])).
% 1.24/1.49 tff(1116,plain,
% 1.24/1.49 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[154, 1115, 146])).
% 1.24/1.49 tff(1117,plain,
% 1.24/1.49 (r(s(s(elem!1)), s(elem!1))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1116, 1050])).
% 1.24/1.49 tff(1118,plain,
% 1.24/1.49 (~b(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[649, 965, 584, 515])).
% 1.24/1.49 tff(1119,plain,
% 1.24/1.49 (r(s(elem!1), z)),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[560, 1118])).
% 1.24/1.49 tff(1120,plain,
% 1.24/1.49 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.24/1.49 inference(monotonicity,[status(thm)],[692])).
% 1.24/1.49 tff(1121,plain,
% 1.24/1.49 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.24/1.49 inference(symmetry,[status(thm)],[1120])).
% 1.24/1.49 tff(1122,plain,
% 1.24/1.49 (r(s(s(s(elem!1))), z)),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[545, 1121])).
% 1.24/1.49 tff(1123,plain,
% 1.24/1.49 ($false),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[985, 1122])).
% 1.24/1.49 tff(1124,plain,((~r(s(elem!1), z)) | r(s(s(s(elem!1))), z) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.49 tff(1125,plain,
% 1.24/1.49 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1124, 983, 1119])).
% 1.24/1.49 tff(1126,plain,
% 1.24/1.49 (r(s(s(s(elem!1))), s(elem!1))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[679, 1125, 633])).
% 1.24/1.49 tff(1127,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1128,plain,
% 1.24/1.49 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1129,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1128])).
% 1.24/1.49 tff(1130,plain,
% 1.24/1.49 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.24/1.49 inference(transitivity,[status(thm)],[1129, 1127])).
% 1.24/1.49 tff(1131,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.24/1.49 inference(quant_inst,[status(thm)],[])).
% 1.24/1.49 tff(1132,plain,
% 1.24/1.49 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.24/1.49 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.24/1.49 tff(1133,plain,
% 1.24/1.49 ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1132, 77, 1126])).
% 1.24/1.49 tff(1134,plain,
% 1.24/1.49 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1133, 1117])).
% 1.24/1.49 tff(1135,plain,
% 1.24/1.49 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1100, 60, 1134])).
% 1.24/1.49 tff(1136,plain,
% 1.24/1.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.24/1.49 inference(unit_resolution,[status(thm)],[1135, 1041])).
% 1.24/1.49 tff(1137,plain,
% 1.24/1.49 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1032, 1036])).
% 1.24/1.49 tff(1138,plain,
% 1.24/1.49 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.24/1.49 inference(symmetry,[status(thm)],[1137])).
% 1.24/1.49 tff(1139,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1140,plain,
% 1.24/1.49 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.49 inference(rewrite,[status(thm)],[])).
% 1.24/1.49 tff(1141,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.49 inference(monotonicity,[status(thm)],[1140])).
% 1.24/1.49 tff(1142,plain,
% 1.24/1.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.34/1.50 tff(1143,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1144,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.34/1.50 tff(1145,plain,
% 1.34/1.50 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1144, 192, 953, 464, 38])).
% 1.34/1.50 tff(1146,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 1.34/1.50 tff(1147,plain,
% 1.34/1.50 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.50 tff(1148,plain,
% 1.34/1.50 (b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[584, 1147])).
% 1.34/1.50 tff(1149,plain,
% 1.34/1.50 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1150,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1149])).
% 1.34/1.50 tff(1151,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1150, 466])).
% 1.34/1.50 tff(1152,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1153,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.34/1.50 tff(1154,plain,
% 1.34/1.50 (~b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1153, 192, 1148, 512, 38])).
% 1.34/1.50 tff(1155,plain,
% 1.34/1.50 (r(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[292, 1154])).
% 1.34/1.50 tff(1156,plain,
% 1.34/1.50 (~r(s(s(s(elem!1))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[982, 1155, 667])).
% 1.34/1.50 tff(1157,plain,
% 1.34/1.50 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(commutativity,[status(thm)],[])).
% 1.34/1.50 tff(1158,plain,
% 1.34/1.50 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.50 tff(1159,plain,
% 1.34/1.50 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1158])).
% 1.34/1.50 tff(1160,plain,
% 1.34/1.50 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1159])).
% 1.34/1.50 tff(1161,plain,
% 1.34/1.50 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1160])).
% 1.34/1.50 tff(1162,plain,
% 1.34/1.50 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1161, 1157])).
% 1.34/1.50 tff(1163,plain,
% 1.34/1.50 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1162])).
% 1.34/1.50 tff(1164,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.50 tff(1165,plain,
% 1.34/1.50 (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1164])).
% 1.34/1.50 tff(1166,plain,
% 1.34/1.50 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1165])).
% 1.34/1.50 tff(1167,plain,
% 1.34/1.50 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1166])).
% 1.34/1.50 tff(1168,plain,
% 1.34/1.50 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[741, 1167, 44])).
% 1.34/1.50 tff(1169,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[104, 1168])).
% 1.34/1.50 tff(1170,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1171,plain,
% 1.34/1.50 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1170, 1163])).
% 1.34/1.50 tff(1172,plain,
% 1.34/1.50 (~b(s(s(s(elem!1))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1030, 1155, 667, 239, 118, 1171])).
% 1.34/1.50 tff(1173,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[992, 1172, 1156])).
% 1.34/1.50 tff(1174,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1175,plain,
% 1.34/1.50 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1174, 530, 667, 66, 464, 38, 584])).
% 1.34/1.50 tff(1176,plain,
% 1.34/1.50 (r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[535, 1175, 1145])).
% 1.34/1.50 tff(1177,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[541, 77, 170, 1176, 538])).
% 1.34/1.50 tff(1178,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1179,plain,
% 1.34/1.50 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1178, 963, 667, 38, 584, 953, 39])).
% 1.34/1.50 tff(1180,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[181, 1179])).
% 1.34/1.50 tff(1181,plain,
% 1.34/1.50 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1180, 1138])).
% 1.34/1.50 tff(1182,plain,
% 1.34/1.50 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1036])).
% 1.34/1.50 tff(1183,plain,
% 1.34/1.50 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1182])).
% 1.34/1.50 tff(1184,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.50 tff(1185,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1184])).
% 1.34/1.50 tff(1186,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[396, 1185])).
% 1.34/1.50 tff(1187,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[962, 1186])).
% 1.34/1.50 tff(1188,plain,((~(s(elem!1) = s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1189,plain,
% 1.34/1.50 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1188, 1180, 962])).
% 1.34/1.50 tff(1190,plain,
% 1.34/1.50 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1036])).
% 1.34/1.50 tff(1191,plain,
% 1.34/1.50 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1190])).
% 1.34/1.50 tff(1192,plain,
% 1.34/1.50 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1036])).
% 1.34/1.50 tff(1193,plain,
% 1.34/1.50 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1192])).
% 1.34/1.50 tff(1194,plain,
% 1.34/1.50 (b(s(z), s(s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[38, 1193])).
% 1.34/1.50 tff(1195,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1196,plain,
% 1.34/1.50 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1197,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1196])).
% 1.34/1.50 tff(1198,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1197, 1195])).
% 1.34/1.50 tff(1199,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1200,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.34/1.50 tff(1201,plain,
% 1.34/1.50 ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1200, 192, 953])).
% 1.34/1.50 tff(1202,plain,
% 1.34/1.50 (~b(s(elem!1), s(s(elem!1)))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1201, 1194, 1106])).
% 1.34/1.50 tff(1203,plain,
% 1.34/1.50 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1202, 1191])).
% 1.34/1.50 tff(1204,plain,
% 1.34/1.50 (r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[535, 1203, 1189])).
% 1.34/1.50 tff(1205,plain,
% 1.34/1.50 (~r(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[553, 1204, 1119])).
% 1.34/1.50 tff(1206,plain,
% 1.34/1.50 (b(z, s(s(s(s(z)))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[339, 1205])).
% 1.34/1.50 tff(1207,plain,
% 1.34/1.50 (b(z, s(s(elem!1)))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1206, 1183])).
% 1.34/1.50 tff(1208,plain,
% 1.34/1.50 (~r(z, s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1011, 77, 973, 667])).
% 1.34/1.50 tff(1209,plain,
% 1.34/1.50 (b(z, s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1021, 1208])).
% 1.34/1.50 tff(1210,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(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))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1211,plain,
% 1.34/1.50 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, 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))))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1212,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1211])).
% 1.34/1.50 tff(1213,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~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))))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1212, 1210])).
% 1.34/1.50 tff(1214,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1215,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 1.34/1.50 tff(1216,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1215, 192, 1209, 1207, 1181, 1136])).
% 1.34/1.50 tff(1217,plain,(b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (s(z) = s(elem!1)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1218,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1217, 951, 38, 667, 633, 640, 515, 639, 39])).
% 1.34/1.50 tff(1219,plain,
% 1.34/1.50 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1055])).
% 1.34/1.50 tff(1220,plain,
% 1.34/1.50 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.50 inference(symmetry,[status(thm)],[1219])).
% 1.34/1.50 tff(1221,plain,
% 1.34/1.50 ((~b(s(s(s(elem!1))), s(elem!1))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1220])).
% 1.34/1.50 tff(1222,plain,
% 1.34/1.50 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.50 inference(modus_ponens,[status(thm)],[633, 1221])).
% 1.34/1.50 tff(1223,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[582, 1222])).
% 1.34/1.50 tff(1224,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1225,plain,
% 1.34/1.50 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1224, 1218, 633])).
% 1.34/1.50 tff(1226,plain,
% 1.34/1.50 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1030, 1082, 667, 1000, 118, 37])).
% 1.34/1.50 tff(1227,plain,
% 1.34/1.50 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[271, 1226])).
% 1.34/1.50 tff(1228,plain,
% 1.34/1.50 ($false),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[278, 77, 37, 1227, 118])).
% 1.34/1.50 tff(1229,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.50 tff(1230,plain,
% 1.34/1.50 (~r(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[1229, 667, 66, 1225])).
% 1.34/1.50 tff(1231,plain,
% 1.34/1.50 (b(z, s(z))),
% 1.34/1.50 inference(unit_resolution,[status(thm)],[292, 1230])).
% 1.34/1.50 tff(1232,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1233,plain,
% 1.34/1.50 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.50 inference(rewrite,[status(thm)],[])).
% 1.34/1.50 tff(1234,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 1.34/1.50 inference(monotonicity,[status(thm)],[1233])).
% 1.34/1.50 tff(1235,plain,
% 1.34/1.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.34/1.50 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.34/1.50 tff(1236,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 1.34/1.50 inference(quant_inst,[status(thm)],[])).
% 1.34/1.50 tff(1237,plain,
% 1.34/1.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.34/1.51 tff(1238,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1237, 192, 515, 583, 953, 465])).
% 1.34/1.51 tff(1239,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1240,plain,
% 1.34/1.51 (~b(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1239, 465, 515, 953])).
% 1.34/1.51 tff(1241,plain,
% 1.34/1.51 (r(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[560, 1240])).
% 1.34/1.51 tff(1242,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.51 tff(1243,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1244,plain,
% 1.34/1.51 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1245,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1244])).
% 1.34/1.51 tff(1246,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1245, 1243])).
% 1.34/1.51 tff(1247,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(elem!1))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1248,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.34/1.51 tff(1249,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1248, 192, 584, 953, 1242, 465, 38])).
% 1.34/1.51 tff(1250,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1251,plain,
% 1.34/1.51 (~b(z, s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1250, 465, 953, 640, 38])).
% 1.34/1.51 tff(1252,plain,
% 1.34/1.51 (r(z, s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[339, 1251])).
% 1.34/1.51 tff(1253,plain,
% 1.34/1.51 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[553, 1252, 1241])).
% 1.34/1.51 tff(1254,plain,
% 1.34/1.51 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[535, 1253, 531])).
% 1.34/1.51 tff(1255,plain,
% 1.34/1.51 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1254])).
% 1.34/1.51 tff(1256,plain,
% 1.34/1.51 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1255])).
% 1.34/1.51 tff(1257,plain,
% 1.34/1.51 (r(z, s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1252, 1256])).
% 1.34/1.51 tff(1258,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[634, 1257])).
% 1.34/1.51 tff(1259,plain,((~b(z, s(z))) | r(z, s(elem!1)) | b(s(elem!1), s(s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1260,plain,
% 1.34/1.51 (b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1259, 1231, 634, 951, 38, 515])).
% 1.34/1.51 tff(1261,plain,
% 1.34/1.51 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1262,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1261])).
% 1.34/1.51 tff(1263,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1262, 1139])).
% 1.34/1.51 tff(1264,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1265,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 1.34/1.51 tff(1266,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1265, 192, 869, 953, 512, 38])).
% 1.34/1.51 tff(1267,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1268,plain,
% 1.34/1.51 (~b(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1267, 1260, 951, 38])).
% 1.34/1.51 tff(1269,plain,
% 1.34/1.51 (r(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[217, 1268])).
% 1.34/1.51 tff(1270,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[83, 77, 1269, 66])).
% 1.34/1.51 tff(1271,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[111, 60, 1270, 106])).
% 1.34/1.51 tff(1272,plain,
% 1.34/1.51 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[959, 951, 39])).
% 1.34/1.51 tff(1273,plain,
% 1.34/1.51 (~b(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1239, 1231, 515, 951])).
% 1.34/1.51 tff(1274,plain,
% 1.34/1.51 (r(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[560, 1273])).
% 1.34/1.51 tff(1275,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1276,plain,
% 1.34/1.51 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1277,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1276])).
% 1.34/1.51 tff(1278,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1277, 1275])).
% 1.34/1.51 tff(1279,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1280,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 1.34/1.51 tff(1281,plain,
% 1.34/1.51 (~b(z, s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1280, 192, 640, 951, 1231, 1218])).
% 1.34/1.51 tff(1282,plain,
% 1.34/1.51 (r(z, s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[491, 60, 1281, 486])).
% 1.34/1.51 tff(1283,plain,
% 1.34/1.51 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[481, 1282, 1231, 38, 39])).
% 1.34/1.51 tff(1284,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[181, 1283])).
% 1.34/1.51 tff(1285,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[875, 192, 640, 1284, 1260, 1218])).
% 1.34/1.51 tff(1286,plain,
% 1.34/1.51 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[271, 1285])).
% 1.34/1.51 tff(1287,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1288,plain,
% 1.34/1.51 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1289,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1288])).
% 1.34/1.51 tff(1290,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1289, 1287])).
% 1.34/1.51 tff(1291,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1292,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 1.34/1.51 tff(1293,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1292, 77, 545, 795, 296])).
% 1.34/1.51 tff(1294,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1295,plain,
% 1.34/1.51 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1294, 1286, 1274])).
% 1.34/1.51 tff(1296,plain,
% 1.34/1.51 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[811, 1295, 1272])).
% 1.34/1.51 tff(1297,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[891, 192, 1284, 1260, 1296, 1271])).
% 1.34/1.51 tff(1298,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | r(z, s(elem!1)) | (~b(s(z), z)) | b(s(s(s(elem!1))), s(elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1299,plain,
% 1.34/1.51 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1298, 115, 39, 634, 515, 633, 38])).
% 1.34/1.51 tff(1300,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1301,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.34/1.51 tff(1302,plain,
% 1.34/1.51 (s(z) = s(s(s(elem!1)))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1301])).
% 1.34/1.51 tff(1303,plain,
% 1.34/1.51 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1302])).
% 1.34/1.51 tff(1304,plain,
% 1.34/1.51 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1303])).
% 1.34/1.51 tff(1305,plain,
% 1.34/1.51 (s(s(elem!1)) = z),
% 1.34/1.51 inference(transitivity,[status(thm)],[1035, 1304, 20])).
% 1.34/1.51 tff(1306,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1076, 1305])).
% 1.34/1.51 tff(1307,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1308,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1309,plain,
% 1.34/1.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1310,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1311,plain,
% 1.34/1.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 1.34/1.51 tff(1312,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1311, 60, 1308, 1307, 1300])).
% 1.34/1.51 tff(1313,plain,(b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1314,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1313, 1299])).
% 1.34/1.51 tff(1315,assumption,(~r(s(s(s(s(s(z))))), s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(1316,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.34/1.51 tff(1317,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[692])).
% 1.34/1.51 tff(1318,plain,
% 1.34/1.51 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 1.34/1.51 inference(symmetry,[status(thm)],[1317])).
% 1.34/1.51 tff(1319,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[583, 1318])).
% 1.34/1.51 tff(1320,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[984, 1319])).
% 1.34/1.51 tff(1321,plain,((~b(s(elem!1), z)) | b(s(s(s(elem!1))), z) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1322,plain,
% 1.34/1.51 (b(s(s(s(elem!1))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1321, 692, 583])).
% 1.34/1.51 tff(1323,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1324,plain,
% 1.34/1.51 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1325,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1324])).
% 1.34/1.51 tff(1326,plain,
% 1.34/1.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.51 inference(transitivity,[status(thm)],[1325, 1323])).
% 1.34/1.51 tff(1327,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1328,plain,
% 1.34/1.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1327, 1326])).
% 1.34/1.51 tff(1329,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1328, 192, 1005, 515, 1316, 465])).
% 1.34/1.51 tff(1330,plain,((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1331,plain,
% 1.34/1.51 (~b(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1330, 1322, 515, 1316])).
% 1.34/1.51 tff(1332,plain,
% 1.34/1.51 (r(z, s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[292, 1331])).
% 1.34/1.51 tff(1333,plain,
% 1.34/1.51 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[278, 77, 1332, 118])).
% 1.34/1.51 tff(1334,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[271, 1333])).
% 1.34/1.51 tff(1335,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[592, 1334, 584, 583])).
% 1.34/1.51 tff(1336,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[597, 1335, 848, 1315])).
% 1.34/1.51 tff(1337,plain,((~(s(s(s(elem!1))) = s(elem!1))) | r(s(s(s(s(s(z))))), s(elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1338,plain,
% 1.34/1.51 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1337, 666, 640, 583, 66, 515, 1314])).
% 1.34/1.51 tff(1339,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[679, 1338, 633])).
% 1.34/1.51 tff(1340,plain,
% 1.34/1.51 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.51 inference(symmetry,[status(thm)],[774])).
% 1.34/1.51 tff(1341,plain,
% 1.34/1.51 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1340])).
% 1.34/1.51 tff(1342,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.51 tff(1343,plain,
% 1.34/1.51 (~b(s(s(s(elem!1))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1330, 465, 515, 1316])).
% 1.34/1.51 tff(1344,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[992, 1343])).
% 1.34/1.51 tff(1345,plain,
% 1.34/1.51 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.51 inference(symmetry,[status(thm)],[1146])).
% 1.34/1.51 tff(1346,plain,
% 1.34/1.51 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1160, 1345])).
% 1.34/1.51 tff(1347,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1346])).
% 1.34/1.51 tff(1348,plain,
% 1.34/1.51 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1342, 1347])).
% 1.34/1.51 tff(1349,plain,
% 1.34/1.51 (r(s(elem!1), z) <=> r(s(s(s(s(z)))), z)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.51 tff(1350,plain,
% 1.34/1.51 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.51 tff(1351,plain,
% 1.34/1.51 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1350])).
% 1.34/1.51 tff(1352,plain,
% 1.34/1.51 (b(s(z), s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[38, 1351])).
% 1.34/1.51 tff(1353,plain,
% 1.34/1.51 (~b(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[649, 1352, 584, 515])).
% 1.34/1.51 tff(1354,plain,
% 1.34/1.51 (r(s(elem!1), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[560, 1353])).
% 1.34/1.51 tff(1355,plain,
% 1.34/1.51 (r(s(s(s(s(z)))), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1354, 1349])).
% 1.34/1.51 tff(1356,plain,
% 1.34/1.51 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1159])).
% 1.34/1.51 tff(1357,plain,
% 1.34/1.51 (r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[974, 1356])).
% 1.34/1.51 tff(1358,plain,
% 1.34/1.51 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.51 inference(rewrite,[status(thm)],[])).
% 1.34/1.51 tff(1359,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.34/1.51 inference(quant_inst,[status(thm)],[])).
% 1.34/1.51 tff(1360,plain,
% 1.34/1.51 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1359, 1358])).
% 1.34/1.51 tff(1361,plain,
% 1.34/1.51 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1360, 77, 1357, 1355])).
% 1.34/1.51 tff(1362,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1361, 1348])).
% 1.34/1.51 tff(1363,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1364,plain,
% 1.34/1.51 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1363, 1344, 640, 515, 1342, 38])).
% 1.34/1.51 tff(1365,plain,
% 1.34/1.51 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[1364, 1341])).
% 1.34/1.51 tff(1366,plain,
% 1.34/1.51 (~b(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1259, 465, 634, 531, 38, 515])).
% 1.34/1.51 tff(1367,plain,
% 1.34/1.51 (r(s(elem!1), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[950, 1366, 115])).
% 1.34/1.51 tff(1368,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[792, 67, 668, 769, 39])).
% 1.34/1.51 tff(1369,plain,
% 1.34/1.51 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[597, 1368, 760])).
% 1.34/1.51 tff(1370,plain,
% 1.34/1.51 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1369])).
% 1.34/1.51 tff(1371,plain,
% 1.34/1.51 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(symmetry,[status(thm)],[1370])).
% 1.34/1.51 tff(1372,plain,
% 1.34/1.51 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.51 inference(monotonicity,[status(thm)],[1371])).
% 1.34/1.51 tff(1373,plain,
% 1.34/1.51 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.51 inference(modus_ponens,[status(thm)],[531, 1372])).
% 1.34/1.51 tff(1374,plain,
% 1.34/1.51 ($false),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[182, 1373])).
% 1.34/1.51 tff(1375,plain,((~r(s(s(s(s(z)))), s(z))) | b(s(elem!1), s(s(s(s(z))))) | (~r(s(elem!1), s(z))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.51 tff(1376,plain,
% 1.34/1.51 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[1375, 1367, 531, 1365, 39])).
% 1.34/1.51 tff(1377,plain,
% 1.34/1.51 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[217, 1376])).
% 1.34/1.51 tff(1378,plain,
% 1.34/1.51 (~b(s(s(s(s(z)))), z)),
% 1.34/1.51 inference(unit_resolution,[status(thm)],[521, 192, 515, 465, 1377])).
% 1.34/1.52 tff(1379,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[306, 60, 48, 1378])).
% 1.34/1.52 tff(1380,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1381,plain,
% 1.34/1.52 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(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)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1382,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1381])).
% 1.34/1.52 tff(1383,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1382, 1380])).
% 1.34/1.52 tff(1384,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1385,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 1.34/1.52 tff(1386,plain,
% 1.34/1.52 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1385, 77, 1344, 1379])).
% 1.34/1.52 tff(1387,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1388,plain,
% 1.34/1.52 (((~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(s(z)))))) | (~b(s(s(s(elem!1))), 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(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1389,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1388])).
% 1.34/1.52 tff(1390,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1389, 1387])).
% 1.34/1.52 tff(1391,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1392,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 1.34/1.52 tff(1393,plain,
% 1.34/1.52 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1392, 192, 1316, 1377, 38])).
% 1.34/1.52 tff(1394,plain,
% 1.34/1.52 (((~![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))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1395,plain,
% 1.34/1.52 ((~![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))))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1396,plain,
% 1.34/1.52 ((~![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)))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.34/1.52 tff(1397,plain,
% 1.34/1.52 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1396, 60, 1393])).
% 1.34/1.52 tff(1398,plain,
% 1.34/1.52 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1397, 1386])).
% 1.34/1.52 tff(1399,plain,
% 1.34/1.52 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1398])).
% 1.34/1.52 tff(1400,plain,
% 1.34/1.52 (s(s(elem!1)) = s(s(s(z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1035, 1399, 91])).
% 1.34/1.52 tff(1401,plain,
% 1.34/1.52 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1400])).
% 1.34/1.52 tff(1402,plain,
% 1.34/1.52 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1401])).
% 1.34/1.52 tff(1403,plain,
% 1.34/1.52 (s(s(z)) = s(elem!1)),
% 1.34/1.52 inference(transitivity,[status(thm)],[16, 1402, 1046])).
% 1.34/1.52 tff(1404,plain,
% 1.34/1.52 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1403])).
% 1.34/1.52 tff(1405,plain,
% 1.34/1.52 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1404])).
% 1.34/1.52 tff(1406,plain,
% 1.34/1.52 (r(s(s(z)), s(z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1367, 1405])).
% 1.34/1.52 tff(1407,plain,
% 1.34/1.52 (r(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[306, 60, 48, 522])).
% 1.34/1.52 tff(1408,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.34/1.52 tff(1409,plain,
% 1.34/1.52 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[927, 192, 515, 465, 512, 38, 1408])).
% 1.34/1.52 tff(1410,plain,
% 1.34/1.52 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[167, 1409, 145])).
% 1.34/1.52 tff(1411,plain,
% 1.34/1.52 (~b(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[935, 192, 515, 465, 1408])).
% 1.34/1.52 tff(1412,plain,
% 1.34/1.52 (r(s(s(s(z))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[253, 1411])).
% 1.34/1.52 tff(1413,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[943, 77, 1412, 1410, 1407])).
% 1.34/1.52 tff(1414,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1415,plain,
% 1.34/1.52 (~b(s(s(s(z))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1414, 465, 515, 1377, 38])).
% 1.34/1.52 tff(1416,plain,
% 1.34/1.52 (r(s(s(s(z))), s(z))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[920, 1415])).
% 1.34/1.52 tff(1417,plain,
% 1.34/1.52 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1418,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1419,plain,
% 1.34/1.52 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.34/1.52 tff(1420,plain,
% 1.34/1.52 ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1419, 77, 1416])).
% 1.34/1.52 tff(1421,plain,
% 1.34/1.52 (~r(s(s(s(z))), s(s(z)))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1420, 1406])).
% 1.34/1.52 tff(1422,plain,
% 1.34/1.52 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[367, 77, 1416, 66])).
% 1.34/1.52 tff(1423,plain,
% 1.34/1.52 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[373, 60, 102, 1422])).
% 1.34/1.52 tff(1424,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1403])).
% 1.34/1.52 tff(1425,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1424])).
% 1.34/1.52 tff(1426,plain,
% 1.34/1.52 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[759, 77, 1367, 66])).
% 1.34/1.52 tff(1427,plain,
% 1.34/1.52 (s(elem!1) = s(s(z))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1047, 1401, 15])).
% 1.34/1.52 tff(1428,plain,
% 1.34/1.52 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1427])).
% 1.34/1.52 tff(1429,plain,
% 1.34/1.52 (elem!1 = s(z)),
% 1.34/1.52 inference(transitivity,[status(thm)],[695, 1428, 10])).
% 1.34/1.52 tff(1430,plain,
% 1.34/1.52 (b(elem!1, z) <=> b(s(z), z)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1429])).
% 1.34/1.52 tff(1431,plain,
% 1.34/1.52 (b(s(z), z) <=> b(elem!1, z)),
% 1.34/1.52 inference(symmetry,[status(thm)],[1430])).
% 1.34/1.52 tff(1432,plain,
% 1.34/1.52 (b(elem!1, z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[515, 1431])).
% 1.34/1.52 tff(1433,plain,
% 1.34/1.52 (elem!1 = s(s(s(s(z))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[695, 730, 44])).
% 1.34/1.52 tff(1434,plain,
% 1.34/1.52 (b(elem!1, z) <=> b(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1433])).
% 1.34/1.52 tff(1435,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.34/1.52 tff(1436,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 1.34/1.52 tff(1437,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[524, 1436])).
% 1.34/1.52 tff(1438,plain,((~b(elem!1, z)) | b(s(s(s(s(z)))), z) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1439,plain,
% 1.34/1.52 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1438, 1432, 1378])).
% 1.34/1.52 tff(1440,plain,
% 1.34/1.52 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[752, 1439])).
% 1.34/1.52 tff(1441,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[597, 1440, 1426])).
% 1.34/1.52 tff(1442,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1441, 1425])).
% 1.34/1.52 tff(1443,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1403])).
% 1.34/1.52 tff(1444,plain,
% 1.34/1.52 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1443])).
% 1.34/1.52 tff(1445,plain,
% 1.34/1.52 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[803, 1367, 66])).
% 1.34/1.52 tff(1446,plain,
% 1.34/1.52 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[811, 1439, 1445])).
% 1.34/1.52 tff(1447,plain,
% 1.34/1.52 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1446, 1444])).
% 1.34/1.52 tff(1448,plain,
% 1.34/1.52 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1427])).
% 1.34/1.52 tff(1449,plain,
% 1.34/1.52 (b(z, s(s(z)))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[640, 1448])).
% 1.34/1.52 tff(1450,plain,
% 1.34/1.52 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1427])).
% 1.34/1.52 tff(1451,plain,
% 1.34/1.52 (r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[535, 1364, 531])).
% 1.34/1.52 tff(1452,plain,
% 1.34/1.52 (~b(z, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[471, 192, 465, 1377, 38])).
% 1.34/1.52 tff(1453,plain,
% 1.34/1.52 (r(z, s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[339, 1452])).
% 1.34/1.52 tff(1454,plain,
% 1.34/1.52 (~r(s(elem!1), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[553, 1453, 1451])).
% 1.34/1.52 tff(1455,plain,
% 1.34/1.52 (b(s(elem!1), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[560, 1454])).
% 1.34/1.52 tff(1456,plain,
% 1.34/1.52 (b(s(s(z)), z)),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1455, 1450])).
% 1.34/1.52 tff(1457,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1458,plain,
% 1.34/1.52 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1459,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1458])).
% 1.34/1.52 tff(1460,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1459, 1457])).
% 1.34/1.52 tff(1461,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1462,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 1.34/1.52 tff(1463,plain,
% 1.34/1.52 ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1462, 192, 1456, 1449])).
% 1.34/1.52 tff(1464,plain,
% 1.34/1.52 (~b(s(s(s(s(s(z))))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1463, 1442])).
% 1.34/1.52 tff(1465,plain,
% 1.34/1.52 (r(s(s(s(s(s(z))))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[271, 1464])).
% 1.34/1.52 tff(1466,plain,
% 1.34/1.52 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[883, 77, 1465, 1379])).
% 1.34/1.52 tff(1467,plain,
% 1.34/1.52 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[111, 60, 1466, 106])).
% 1.34/1.52 tff(1468,plain,
% 1.34/1.52 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 1.34/1.52 inference(commutativity,[status(thm)],[])).
% 1.34/1.52 tff(1469,plain,
% 1.34/1.52 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 1.34/1.52 inference(symmetry,[status(thm)],[1468])).
% 1.34/1.52 tff(1470,plain,
% 1.34/1.52 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1469])).
% 1.34/1.52 tff(1471,plain,
% 1.34/1.52 (~(z = s(s(s(s(s(z))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[266, 1470])).
% 1.34/1.52 tff(1472,plain,
% 1.34/1.52 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[491, 60, 602])).
% 1.34/1.52 tff(1473,plain,
% 1.34/1.52 (b(z, s(s(s(s(s(z))))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1472, 1471])).
% 1.34/1.52 tff(1474,plain,
% 1.34/1.52 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[327, 77, 170, 321])).
% 1.34/1.52 tff(1475,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[269, 60, 266, 1474])).
% 1.34/1.52 tff(1476,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1477,plain,
% 1.34/1.52 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1478,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1477])).
% 1.34/1.52 tff(1479,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.52 inference(transitivity,[status(thm)],[1478, 1476])).
% 1.34/1.52 tff(1480,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(elem!1), z)))),
% 1.34/1.52 inference(quant_inst,[status(thm)],[])).
% 1.34/1.52 tff(1481,plain,
% 1.34/1.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.34/1.52 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 1.34/1.52 tff(1482,plain,
% 1.34/1.52 ($false),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1481, 192, 583, 814, 1475, 1473])).
% 1.34/1.52 tff(1483,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.52 tff(1484,plain,
% 1.34/1.52 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[1483, 1446, 1453, 1455])).
% 1.34/1.52 tff(1485,plain,
% 1.34/1.52 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.52 inference(unit_resolution,[status(thm)],[181, 1484])).
% 1.34/1.52 tff(1486,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1487,plain,
% 1.34/1.52 (((~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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.52 inference(rewrite,[status(thm)],[])).
% 1.34/1.52 tff(1488,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.34/1.52 inference(monotonicity,[status(thm)],[1487])).
% 1.34/1.52 tff(1489,plain,
% 1.34/1.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1488, 1486])).
% 1.34/1.53 tff(1490,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1491,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 1.34/1.53 tff(1492,plain,
% 1.34/1.53 (~b(s(s(s(z))), s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1491, 192, 1485, 1467, 1447, 1442, 1423])).
% 1.34/1.53 tff(1493,plain,
% 1.34/1.53 (b(elem!1, s(z)) <=> b(s(z), s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1429])).
% 1.34/1.53 tff(1494,plain,
% 1.34/1.53 (b(s(z), s(z)) <=> b(elem!1, s(z))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1493])).
% 1.34/1.53 tff(1495,plain,
% 1.34/1.53 ((~b(s(z), s(z))) <=> (~b(elem!1, s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1494])).
% 1.34/1.53 tff(1496,plain,
% 1.34/1.53 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.34/1.53 inference(bind,[status(th)],[])).
% 1.34/1.53 tff(1497,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(quant_intro,[status(thm)],[1496])).
% 1.34/1.53 tff(1498,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1499,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 1.34/1.53 tff(1500,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 1.34/1.53 tff(1501,plain,(
% 1.34/1.53 ![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(skolemize,[status(sab)],[1500])).
% 1.34/1.53 tff(1502,plain,
% 1.34/1.53 (![X: $i] : (~b(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1501, 1497])).
% 1.34/1.53 tff(1503,plain,
% 1.34/1.53 ((~![X: $i] : (~b(X, X))) | (~b(s(z), s(z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1504,plain,
% 1.34/1.53 (~b(s(z), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1503, 1502])).
% 1.34/1.53 tff(1505,plain,
% 1.34/1.53 (~b(elem!1, s(z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1504, 1495])).
% 1.34/1.53 tff(1506,plain,
% 1.34/1.53 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1428])).
% 1.34/1.53 tff(1507,plain,
% 1.34/1.53 (s(z) = inj_0(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[10])).
% 1.34/1.53 tff(1508,plain,
% 1.34/1.53 (s(z) = elem!1),
% 1.34/1.53 inference(transitivity,[status(thm)],[1507, 1506, 682])).
% 1.34/1.53 tff(1509,plain,
% 1.34/1.53 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1508])).
% 1.34/1.53 tff(1510,plain,
% 1.34/1.53 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1509])).
% 1.34/1.53 tff(1511,plain,
% 1.34/1.53 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1510])).
% 1.34/1.53 tff(1512,plain,
% 1.34/1.53 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.34/1.53 inference(bind,[status(th)],[])).
% 1.34/1.53 tff(1513,plain,
% 1.34/1.53 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.34/1.53 inference(quant_intro,[status(thm)],[1512])).
% 1.34/1.53 tff(1514,plain,
% 1.34/1.53 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1515,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 1.34/1.53 tff(1516,plain,
% 1.34/1.53 (![X: $i] : (~r(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.34/1.53 tff(1517,plain,(
% 1.34/1.53 ![X: $i] : (~r(X, X))),
% 1.34/1.53 inference(skolemize,[status(sab)],[1516])).
% 1.34/1.53 tff(1518,plain,
% 1.34/1.53 (![X: $i] : (~r(X, X))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1517, 1513])).
% 1.34/1.53 tff(1519,plain,
% 1.34/1.53 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1520,plain,
% 1.34/1.53 (~r(elem!1, elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1519, 1518])).
% 1.34/1.53 tff(1521,plain,
% 1.34/1.53 (~r(elem!1, s(z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1520, 1511])).
% 1.34/1.53 tff(1522,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.34/1.53 tff(1523,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.34/1.53 tff(1524,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.34/1.53 tff(1525,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1526,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1527,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.34/1.53 tff(1528,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1527, 60, 1524, 1523, 1522])).
% 1.34/1.53 tff(1529,plain,(b(elem!1, s(z)) | (elem!1 = s(z)) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1530,plain,
% 1.34/1.53 (elem!1 = s(z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1529, 1521, 1505])).
% 1.34/1.53 tff(1531,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.34/1.53 tff(1532,plain,
% 1.34/1.53 (s(s(z)) = s(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1531])).
% 1.34/1.53 tff(1533,plain,
% 1.34/1.53 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1532])).
% 1.34/1.53 tff(1534,plain,
% 1.34/1.53 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1533])).
% 1.34/1.53 tff(1535,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.34/1.53 tff(1536,plain,
% 1.34/1.53 (s(elem!1) = s(s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1535])).
% 1.34/1.53 tff(1537,plain,
% 1.34/1.53 (s(elem!1) = s(z)),
% 1.34/1.53 inference(transitivity,[status(thm)],[1536, 16, 1534, 10])).
% 1.34/1.53 tff(1538,plain,
% 1.34/1.53 ((z = elem!1) <=> (z = s(z))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1535])).
% 1.34/1.53 tff(1539,plain,
% 1.34/1.53 ((z = elem!1) <=> (s(z) = z)),
% 1.34/1.53 inference(transitivity,[status(thm)],[1538, 282])).
% 1.34/1.53 tff(1540,plain,
% 1.34/1.53 ((s(z) = z) <=> (z = elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[1539])).
% 1.34/1.53 tff(1541,plain,
% 1.34/1.53 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1540])).
% 1.34/1.53 tff(1542,plain,
% 1.34/1.53 (~(z = elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[286, 1541])).
% 1.34/1.53 tff(1543,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.34/1.53 tff(1544,plain,
% 1.34/1.53 (s(z) = s(elem!1)),
% 1.34/1.53 inference(symmetry,[status(thm)],[1543])).
% 1.34/1.53 tff(1545,plain,
% 1.34/1.53 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1544])).
% 1.34/1.53 tff(1546,plain,
% 1.34/1.53 (z = inj_0(s(z))),
% 1.34/1.53 inference(symmetry,[status(thm)],[20])).
% 1.34/1.53 tff(1547,plain,
% 1.34/1.53 (z = elem!1),
% 1.34/1.53 inference(transitivity,[status(thm)],[1546, 1545, 682])).
% 1.34/1.53 tff(1548,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1549,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1548, 1547])).
% 1.34/1.53 tff(1550,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1551,plain,
% 1.34/1.53 (~(s(elem!1) = s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1550, 1542])).
% 1.34/1.53 tff(1552,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1551, 1537])).
% 1.34/1.53 tff(1553,plain,((~(s(s(s(z))) = s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1554,plain,
% 1.34/1.53 (~(s(s(s(z))) = s(s(z)))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1553, 1530])).
% 1.34/1.53 tff(1555,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1556,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1557,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.34/1.53 tff(1558,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1557, 60, 1554, 1492, 1421])).
% 1.34/1.53 tff(1559,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = s(z)) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1560,plain,
% 1.34/1.53 (~b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1559, 1339, 38, 1314, 531, 39, 515, 115, 634])).
% 1.34/1.53 tff(1561,plain,
% 1.34/1.53 (r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[292, 1560])).
% 1.34/1.53 tff(1562,plain,
% 1.34/1.53 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[278, 77, 37, 66])).
% 1.34/1.53 tff(1563,plain,
% 1.34/1.53 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[271, 1562])).
% 1.34/1.53 tff(1564,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[306, 60, 48, 1073])).
% 1.34/1.53 tff(1565,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1566,plain,
% 1.34/1.53 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1567,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1566])).
% 1.34/1.53 tff(1568,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1567, 1565])).
% 1.34/1.53 tff(1569,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1570,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 1.34/1.53 tff(1571,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1570, 77, 321, 37, 67])).
% 1.34/1.53 tff(1572,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1573,plain,
% 1.34/1.53 (~r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1572, 67, 37])).
% 1.34/1.53 tff(1574,plain,
% 1.34/1.53 (b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[339, 1573])).
% 1.34/1.53 tff(1575,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1576,plain,
% 1.34/1.53 (((~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))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1577,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1576])).
% 1.34/1.53 tff(1578,plain,
% 1.34/1.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1577, 1575])).
% 1.34/1.53 tff(1579,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(s(z)))))) | (~b(s(s(s(s(z)))), 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)))))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1580,plain,
% 1.34/1.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1579, 1578])).
% 1.34/1.53 tff(1581,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1580, 192, 182, 1574, 1564, 156, 1563])).
% 1.34/1.53 tff(1582,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1583,plain,
% 1.34/1.53 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1582, 1561, 39])).
% 1.34/1.53 tff(1584,plain,
% 1.34/1.53 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[217, 1583])).
% 1.34/1.53 tff(1585,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1392, 192, 1314, 1584, 38])).
% 1.34/1.53 tff(1586,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[752, 748])).
% 1.34/1.53 tff(1587,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 1.34/1.53 tff(1588,plain,
% 1.34/1.53 (elem!1 = s(s(s(elem!1)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1587])).
% 1.34/1.53 tff(1589,plain,
% 1.34/1.53 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.34/1.53 inference(transitivity,[status(thm)],[45, 731, 682, 1588])).
% 1.34/1.53 tff(1590,plain,
% 1.34/1.53 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1589])).
% 1.34/1.53 tff(1591,plain,
% 1.34/1.53 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[92, 1590, 691, 724])).
% 1.34/1.53 tff(1592,plain,
% 1.34/1.53 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1591])).
% 1.34/1.53 tff(1593,plain,
% 1.34/1.53 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[16, 1592, 740])).
% 1.34/1.53 tff(1594,plain,
% 1.34/1.53 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1593])).
% 1.34/1.53 tff(1595,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1594])).
% 1.34/1.53 tff(1596,plain,
% 1.34/1.53 (s(s(s(s(z)))) = s(z)),
% 1.34/1.53 inference(transitivity,[status(thm)],[45, 1595, 10])).
% 1.34/1.53 tff(1597,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[212, 1596])).
% 1.34/1.53 tff(1598,plain,((~(s(s(s(elem!1))) = elem!1)) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1599,plain,
% 1.34/1.53 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1598, 1586])).
% 1.34/1.53 tff(1600,plain,
% 1.34/1.53 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[748])).
% 1.34/1.53 tff(1601,plain,
% 1.34/1.53 (s(s(s(s(z)))) = elem!1),
% 1.34/1.53 inference(transitivity,[status(thm)],[45, 1600, 682])).
% 1.34/1.53 tff(1602,plain,
% 1.34/1.53 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1601])).
% 1.34/1.53 tff(1603,plain,
% 1.34/1.53 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1602])).
% 1.34/1.53 tff(1604,assumption,(~b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.53 tff(1605,plain,
% 1.34/1.53 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.34/1.53 tff(1606,plain,
% 1.34/1.53 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), elem!1)),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1601])).
% 1.34/1.53 tff(1607,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.53 tff(1608,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1607])).
% 1.34/1.53 tff(1609,plain,
% 1.34/1.53 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1608, 747])).
% 1.34/1.53 tff(1610,plain,
% 1.34/1.53 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1609])).
% 1.34/1.53 tff(1611,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[104, 1610])).
% 1.34/1.53 tff(1612,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[723, 1611])).
% 1.34/1.53 tff(1613,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1614,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1613, 1586])).
% 1.34/1.53 tff(1615,plain,
% 1.34/1.53 (r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[535, 1614, 531])).
% 1.34/1.53 tff(1616,plain,
% 1.34/1.53 (r(s(elem!1), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1615, 1606])).
% 1.34/1.53 tff(1617,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1618,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.34/1.53 tff(1619,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1620,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1621,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 1.34/1.53 tff(1622,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1621, 77, 1342, 1618, 1617])).
% 1.34/1.53 tff(1623,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1624,plain,
% 1.34/1.53 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1623, 1616, 1342])).
% 1.34/1.53 tff(1625,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1626,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1627,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 1.34/1.53 tff(1628,plain,
% 1.34/1.53 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1627, 60])).
% 1.34/1.53 tff(1629,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1628, 1624, 1605, 1599])).
% 1.34/1.53 tff(1630,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1631,plain,
% 1.34/1.53 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1630, 1585, 1339, 531])).
% 1.34/1.53 tff(1632,plain,
% 1.34/1.53 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[278, 77, 1561, 66])).
% 1.34/1.53 tff(1633,plain,
% 1.34/1.53 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[271, 1632])).
% 1.34/1.53 tff(1634,plain,
% 1.34/1.53 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[592, 1633, 640, 583])).
% 1.34/1.53 tff(1635,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[597, 1634, 1631, 666])).
% 1.34/1.53 tff(1636,plain,((~b(s(elem!1), z)) | b(s(elem!1), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(z), z)) | (s(elem!1) = s(z)) | r(z, s(elem!1)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1637,plain,
% 1.34/1.53 (~b(s(elem!1), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1636, 531, 38, 39, 515, 115, 634, 633])).
% 1.34/1.53 tff(1638,plain,
% 1.34/1.53 (r(s(elem!1), z)),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[560, 1637])).
% 1.34/1.53 tff(1639,plain,
% 1.34/1.53 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[553, 321, 545])).
% 1.34/1.53 tff(1640,plain,
% 1.34/1.53 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[535, 1639, 531])).
% 1.34/1.53 tff(1641,plain,
% 1.34/1.53 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1640])).
% 1.34/1.53 tff(1642,plain,
% 1.34/1.53 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1641])).
% 1.34/1.53 tff(1643,plain,
% 1.34/1.53 (r(z, s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[321, 1642])).
% 1.34/1.53 tff(1644,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[634, 1643])).
% 1.34/1.53 tff(1645,plain,((~r(z, s(s(s(s(z)))))) | r(z, s(elem!1)) | b(s(elem!1), s(s(s(s(z))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1646,plain,
% 1.34/1.53 (~r(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1645, 1638, 531, 634])).
% 1.34/1.53 tff(1647,plain,
% 1.34/1.53 (b(z, s(s(s(s(z)))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[339, 1646])).
% 1.34/1.53 tff(1648,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.53 tff(1649,plain,
% 1.34/1.53 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[710])).
% 1.34/1.53 tff(1650,plain,
% 1.34/1.53 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1649])).
% 1.34/1.53 tff(1651,plain,
% 1.34/1.53 (r(z, s(elem!1))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1648, 1650])).
% 1.34/1.53 tff(1652,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[634, 1651])).
% 1.34/1.53 tff(1653,plain,((~(s(elem!1) = s(s(s(elem!1))))) | r(z, s(elem!1)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1654,plain,
% 1.34/1.53 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1653, 1648, 634])).
% 1.34/1.53 tff(1655,plain,
% 1.34/1.53 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[708, 1654])).
% 1.34/1.53 tff(1656,plain,
% 1.34/1.53 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[679, 1655, 633])).
% 1.34/1.53 tff(1657,plain,
% 1.34/1.53 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 1.34/1.53 inference(commutativity,[status(thm)],[])).
% 1.34/1.53 tff(1658,plain,
% 1.34/1.53 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 1.34/1.53 inference(symmetry,[status(thm)],[1657])).
% 1.34/1.53 tff(1659,plain,
% 1.34/1.53 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1658])).
% 1.34/1.53 tff(1660,plain,
% 1.34/1.53 (~(s(z) = s(s(s(elem!1))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1307, 1659])).
% 1.34/1.53 tff(1661,plain,
% 1.34/1.53 (~b(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1559, 1656, 38, 1314, 531, 39, 515, 115, 634])).
% 1.34/1.53 tff(1662,plain,
% 1.34/1.53 (r(z, s(z))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[292, 1661])).
% 1.34/1.53 tff(1663,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.53 tff(1664,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1665,plain,
% 1.34/1.53 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1666,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.53 inference(monotonicity,[status(thm)],[1665])).
% 1.34/1.53 tff(1667,plain,
% 1.34/1.53 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.53 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.34/1.53 tff(1668,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.53 tff(1669,plain,
% 1.34/1.53 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.53 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.34/1.53 tff(1670,plain,
% 1.34/1.53 ($false),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1669, 77, 1648, 37, 1663])).
% 1.34/1.53 tff(1671,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.53 tff(1672,plain,
% 1.34/1.53 (~r(s(z), s(s(s(elem!1))))),
% 1.34/1.53 inference(unit_resolution,[status(thm)],[1671, 1648, 1662])).
% 1.34/1.53 tff(1673,plain,
% 1.34/1.53 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.34/1.53 inference(rewrite,[status(thm)],[])).
% 1.34/1.53 tff(1674,plain,
% 1.34/1.53 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.34/1.53 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1675,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 1.34/1.54 tff(1676,plain,
% 1.34/1.54 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1675, 60, 1672])).
% 1.34/1.54 tff(1677,plain,
% 1.34/1.54 (b(s(z), s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1676, 1660])).
% 1.34/1.54 tff(1678,plain,
% 1.34/1.54 (~r(z, s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1645, 545, 531, 634])).
% 1.34/1.54 tff(1679,plain,
% 1.34/1.54 (b(z, s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[339, 1678])).
% 1.34/1.54 tff(1680,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.34/1.54 tff(1681,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1682,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1683,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.34/1.54 tff(1684,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1683, 77, 1342, 545, 974])).
% 1.34/1.54 tff(1685,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1686,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1685, 545, 1342])).
% 1.34/1.54 tff(1687,plain,
% 1.34/1.54 (b(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[992, 1686])).
% 1.34/1.54 tff(1688,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1689,plain,
% 1.34/1.54 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1690,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1689])).
% 1.34/1.54 tff(1691,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1690, 1688])).
% 1.34/1.54 tff(1692,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1693,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(s(z))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.34/1.54 tff(1694,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1693, 192, 1687, 515, 1680, 1679, 38])).
% 1.34/1.54 tff(1695,plain,((~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | r(z, s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1696,plain,
% 1.34/1.54 (~r(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1695, 1677, 515, 38, 531, 634, 1656])).
% 1.34/1.54 tff(1697,plain,
% 1.34/1.54 (b(s(elem!1), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[560, 1696])).
% 1.34/1.54 tff(1698,plain,
% 1.34/1.54 (~b(s(z), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[649, 1697, 640, 515])).
% 1.34/1.54 tff(1699,plain,
% 1.34/1.54 (r(s(z), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[658, 1698, 639])).
% 1.34/1.54 tff(1700,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1582, 1662, 39])).
% 1.34/1.54 tff(1701,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[217, 1700])).
% 1.34/1.54 tff(1702,plain,
% 1.34/1.54 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1392, 192, 1314, 1701, 38])).
% 1.34/1.54 tff(1703,plain,
% 1.34/1.54 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1630, 1656, 1702, 531])).
% 1.34/1.54 tff(1704,plain,
% 1.34/1.54 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[278, 77, 1662, 66])).
% 1.34/1.54 tff(1705,plain,
% 1.34/1.54 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[271, 1704])).
% 1.34/1.54 tff(1706,plain,
% 1.34/1.54 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[592, 1697, 640, 1705])).
% 1.34/1.54 tff(1707,plain,
% 1.34/1.54 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[597, 1706, 1703])).
% 1.34/1.54 tff(1708,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[665, 1707, 1699, 66])).
% 1.34/1.54 tff(1709,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | r(z, s(elem!1)) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1710,plain,
% 1.34/1.54 (~r(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1709, 531, 38, 515, 634, 39, 115, 633])).
% 1.34/1.54 tff(1711,plain,
% 1.34/1.54 (b(z, s(s(s(elem!1))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1021, 1710])).
% 1.34/1.54 tff(1712,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1713,plain,
% 1.34/1.54 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1714,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1713])).
% 1.34/1.54 tff(1715,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1714, 1712])).
% 1.34/1.54 tff(1716,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1717,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 1.34/1.54 tff(1718,plain,
% 1.34/1.54 (~b(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1717, 192, 1711, 1314, 1647, 38])).
% 1.34/1.54 tff(1719,plain,
% 1.34/1.54 (r(z, s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[292, 1718])).
% 1.34/1.54 tff(1720,plain,
% 1.34/1.54 (~r(s(s(s(s(z)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1582, 1719, 39])).
% 1.34/1.54 tff(1721,plain,
% 1.34/1.54 (b(s(s(s(s(z)))), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[217, 1720])).
% 1.34/1.54 tff(1722,plain,
% 1.34/1.54 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1392, 192, 1314, 1721, 38])).
% 1.34/1.54 tff(1723,plain,
% 1.34/1.54 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[278, 77, 1719, 66])).
% 1.34/1.54 tff(1724,plain,
% 1.34/1.54 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[271, 1723])).
% 1.34/1.54 tff(1725,plain,
% 1.34/1.54 (~r(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[835, 1719, 66])).
% 1.34/1.54 tff(1726,plain,
% 1.34/1.54 (b(z, s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[491, 60, 1725, 486])).
% 1.34/1.54 tff(1727,plain,
% 1.34/1.54 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[615, 192, 515, 1726, 1724])).
% 1.34/1.54 tff(1728,plain,
% 1.34/1.54 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[438, 60, 1727])).
% 1.34/1.54 tff(1729,plain,
% 1.34/1.54 (r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1728, 609])).
% 1.34/1.54 tff(1730,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1731,plain,
% 1.34/1.54 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1732,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1731])).
% 1.34/1.54 tff(1733,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.34/1.54 tff(1734,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1735,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.34/1.54 tff(1736,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1735, 77, 545, 668, 37])).
% 1.34/1.54 tff(1737,plain,((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1738,plain,
% 1.34/1.54 (~r(s(elem!1), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1737, 1719, 1638])).
% 1.34/1.54 tff(1739,plain,
% 1.34/1.54 (b(s(elem!1), s(z))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[950, 1738, 115])).
% 1.34/1.54 tff(1740,plain,
% 1.34/1.54 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[959, 1739, 39])).
% 1.34/1.54 tff(1741,plain,
% 1.34/1.54 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[752, 1740])).
% 1.34/1.54 tff(1742,plain,
% 1.34/1.54 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[597, 962, 815])).
% 1.34/1.54 tff(1743,plain,
% 1.34/1.54 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[543, 537, 538])).
% 1.34/1.54 tff(1744,plain,
% 1.34/1.54 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[181, 1743])).
% 1.34/1.54 tff(1745,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.34/1.54 tff(1746,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1747,plain,
% 1.34/1.54 (((~b(z, 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(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), 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(z)))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1748,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1747])).
% 1.34/1.54 tff(1749,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1748, 1746])).
% 1.34/1.54 tff(1750,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1751,plain,
% 1.34/1.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 1.34/1.54 tff(1752,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1751, 192, 396, 1242, 1745, 239])).
% 1.34/1.54 tff(1753,plain,((~b(s(s(s(s(z)))), 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))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1754,plain,
% 1.34/1.54 (~b(s(s(s(s(z)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1753, 1744, 1242, 239])).
% 1.34/1.54 tff(1755,plain,
% 1.34/1.54 (r(s(s(s(s(z)))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[526, 1754])).
% 1.34/1.54 tff(1756,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1757,plain,
% 1.34/1.54 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1758,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1757])).
% 1.34/1.54 tff(1759,plain,
% 1.34/1.54 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.34/1.54 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.34/1.54 tff(1760,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1761,plain,
% 1.34/1.54 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.34/1.54 tff(1762,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1761, 77, 545, 537, 1755])).
% 1.34/1.54 tff(1763,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1764,plain,
% 1.34/1.54 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1763, 1742, 1242, 239, 545])).
% 1.34/1.54 tff(1765,plain,
% 1.34/1.54 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[535, 1764, 531])).
% 1.34/1.54 tff(1766,plain,
% 1.34/1.54 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1765])).
% 1.34/1.54 tff(1767,plain,
% 1.34/1.54 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1766])).
% 1.34/1.54 tff(1768,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1767])).
% 1.34/1.54 tff(1769,plain,
% 1.34/1.54 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(monotonicity,[status(thm)],[1768])).
% 1.34/1.54 tff(1770,plain,
% 1.34/1.54 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1146, 1340])).
% 1.34/1.54 tff(1771,plain,
% 1.34/1.54 ($false),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[769, 1770])).
% 1.34/1.54 tff(1772,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.54 tff(1773,plain,
% 1.34/1.54 (s(s(s(s(z)))) = s(elem!1)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1772, 1765])).
% 1.34/1.54 tff(1774,plain,
% 1.34/1.54 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[699, 1773])).
% 1.34/1.54 tff(1775,plain,
% 1.34/1.54 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[679, 1774, 633])).
% 1.34/1.54 tff(1776,plain,
% 1.34/1.54 (~r(s(s(s(elem!1))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1685, 1775, 545])).
% 1.34/1.54 tff(1777,plain,
% 1.34/1.54 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1776, 1769])).
% 1.34/1.54 tff(1778,plain,
% 1.34/1.54 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1779,plain,
% 1.34/1.54 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1778, 30])).
% 1.34/1.54 tff(1780,plain,
% 1.34/1.54 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1781,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 1.34/1.54 inference(quant_inst,[status(thm)],[])).
% 1.34/1.54 tff(1782,plain,
% 1.34/1.54 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 1.34/1.54 tff(1783,plain,
% 1.34/1.54 (b(s(s(s(s(s(s(z)))))), z)),
% 1.34/1.54 inference(unit_resolution,[status(thm)],[1782, 60, 1779, 1777])).
% 1.34/1.54 tff(1784,plain,
% 1.34/1.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1785,plain,
% 1.34/1.54 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.54 inference(rewrite,[status(thm)],[])).
% 1.34/1.54 tff(1786,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1785])).
% 1.34/1.55 tff(1787,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1786, 1784])).
% 1.34/1.55 tff(1788,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1789,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1788, 1787])).
% 1.34/1.55 tff(1790,plain,
% 1.34/1.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1789, 192, 813, 239, 1783])).
% 1.34/1.55 tff(1791,plain,
% 1.34/1.55 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1767])).
% 1.34/1.55 tff(1792,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1791])).
% 1.34/1.55 tff(1793,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1792])).
% 1.34/1.55 tff(1794,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1765])).
% 1.34/1.55 tff(1795,plain,
% 1.34/1.55 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1775, 1794])).
% 1.34/1.55 tff(1796,plain,
% 1.34/1.55 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1795, 1793])).
% 1.34/1.55 tff(1797,plain,
% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1188, 1765, 962])).
% 1.34/1.55 tff(1798,plain,
% 1.34/1.55 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[181, 1797])).
% 1.34/1.55 tff(1799,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1800,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1801,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.34/1.55 tff(1802,plain,
% 1.34/1.55 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1801, 77, 1798])).
% 1.34/1.55 tff(1803,plain,
% 1.34/1.55 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1802, 1796])).
% 1.34/1.55 tff(1804,plain,
% 1.34/1.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1805,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1806,plain,
% 1.34/1.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 1.34/1.55 tff(1807,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1806, 60, 1170, 1803, 1790])).
% 1.34/1.55 tff(1808,plain,(b(s(s(s(s(s(z))))), s(elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | b(s(s(s(elem!1))), s(elem!1)) | b(s(elem!1), s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1809,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1808, 1726, 1724, 1638, 633, 531, 1647, 1741])).
% 1.34/1.55 tff(1810,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[823, 192, 584, 582, 814, 813])).
% 1.34/1.55 tff(1811,plain,((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1812,plain,
% 1.34/1.55 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1811, 1809, 640, 1726])).
% 1.34/1.55 tff(1813,plain,
% 1.34/1.55 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[811, 1812, 1740])).
% 1.34/1.55 tff(1814,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1815,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1816,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1815])).
% 1.34/1.55 tff(1817,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1816, 1814])).
% 1.34/1.55 tff(1818,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1819,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.34/1.55 tff(1820,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1819, 77, 170, 537, 795])).
% 1.34/1.55 tff(1821,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1822,plain,
% 1.34/1.55 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1821, 295, 795])).
% 1.34/1.55 tff(1823,plain,
% 1.34/1.55 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[535, 1822, 531])).
% 1.34/1.55 tff(1824,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1823])).
% 1.34/1.55 tff(1825,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1824])).
% 1.34/1.55 tff(1826,plain,
% 1.34/1.55 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1825])).
% 1.34/1.55 tff(1827,plain,
% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[294, 1826])).
% 1.34/1.55 tff(1828,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[582, 1827])).
% 1.34/1.55 tff(1829,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | b(s(elem!1), s(s(s(s(z))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1830,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1829, 1809, 531, 1813])).
% 1.34/1.55 tff(1831,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1055])).
% 1.34/1.55 tff(1832,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1831])).
% 1.34/1.55 tff(1833,plain,
% 1.34/1.55 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1832])).
% 1.34/1.55 tff(1834,plain,
% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1604, 1833])).
% 1.34/1.55 tff(1835,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[396, 1834])).
% 1.34/1.55 tff(1836,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1837,plain,
% 1.34/1.55 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1836, 396, 1604])).
% 1.34/1.55 tff(1838,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[748])).
% 1.34/1.55 tff(1839,plain,
% 1.34/1.55 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(symmetry,[status(thm)],[1838])).
% 1.34/1.55 tff(1840,plain,
% 1.34/1.55 ((~b(s(elem!1), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1839])).
% 1.34/1.55 tff(1841,plain,
% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[531, 1840])).
% 1.34/1.55 tff(1842,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[396, 1841])).
% 1.34/1.55 tff(1843,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1844,plain,
% 1.34/1.55 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1843, 396, 531])).
% 1.34/1.55 tff(1845,plain,
% 1.34/1.55 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[597, 962, 1844])).
% 1.34/1.55 tff(1846,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1847,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1848,plain,
% 1.34/1.55 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 1.34/1.55 tff(1849,plain,
% 1.34/1.55 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1848, 77, 1342, 1845])).
% 1.34/1.55 tff(1850,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1003, 60, 1000, 1849])).
% 1.34/1.55 tff(1851,plain,
% 1.34/1.55 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1188, 962, 396])).
% 1.34/1.55 tff(1852,plain,
% 1.34/1.55 (r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[535, 1851, 531])).
% 1.34/1.55 tff(1853,plain,
% 1.34/1.55 (~r(s(z), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[665, 1845, 118])).
% 1.34/1.55 tff(1854,plain,
% 1.34/1.55 (b(s(z), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[658, 1853, 651])).
% 1.34/1.55 tff(1855,plain,
% 1.34/1.55 (~b(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[649, 1854, 584, 515])).
% 1.34/1.55 tff(1856,plain,
% 1.34/1.55 (r(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[560, 1855])).
% 1.34/1.55 tff(1857,plain,
% 1.34/1.55 (~r(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[553, 1856, 1852])).
% 1.34/1.55 tff(1858,plain,
% 1.34/1.55 (b(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[339, 1857])).
% 1.34/1.55 tff(1859,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1685, 1856, 1342])).
% 1.34/1.55 tff(1860,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[992, 1859])).
% 1.34/1.55 tff(1861,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1862,plain,
% 1.34/1.55 (((~b(z, 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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1863,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1862])).
% 1.34/1.55 tff(1864,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1863, 1861])).
% 1.34/1.55 tff(1865,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1866,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1865, 1864])).
% 1.34/1.55 tff(1867,plain,
% 1.34/1.55 ($false),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1866, 192, 1860, 396, 1858, 239, 1850])).
% 1.34/1.55 tff(1868,plain,(b(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (s(z) = s(elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | b(s(elem!1), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.55 tff(1869,plain,
% 1.34/1.55 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1868, 396, 239, 1837, 1342, 640, 515, 651, 118, 531])).
% 1.34/1.55 tff(1870,plain,
% 1.34/1.55 (~b(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[592, 1869, 640, 239])).
% 1.34/1.55 tff(1871,plain,
% 1.34/1.55 (r(s(elem!1), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[560, 1870])).
% 1.34/1.55 tff(1872,plain,
% 1.34/1.55 (~r(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1645, 1871, 531, 634])).
% 1.34/1.55 tff(1873,plain,
% 1.34/1.55 (b(z, s(s(s(s(z)))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[339, 1872])).
% 1.34/1.55 tff(1874,plain,
% 1.34/1.55 (~r(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1685, 1871, 1342])).
% 1.34/1.55 tff(1875,plain,
% 1.34/1.55 (b(s(s(s(elem!1))), z)),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[992, 1874])).
% 1.34/1.55 tff(1876,plain,
% 1.34/1.55 (~b(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1693, 192, 1875, 515, 1873, 38])).
% 1.34/1.55 tff(1877,plain,
% 1.34/1.55 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1675, 60, 1876])).
% 1.34/1.55 tff(1878,plain,
% 1.34/1.55 (r(s(z), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1877, 1660])).
% 1.34/1.55 tff(1879,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1880,plain,
% 1.34/1.55 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1881,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.34/1.55 inference(monotonicity,[status(thm)],[1880])).
% 1.34/1.55 tff(1882,plain,
% 1.34/1.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(transitivity,[status(thm)],[1881, 1879])).
% 1.34/1.55 tff(1883,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.34/1.55 inference(quant_inst,[status(thm)],[])).
% 1.34/1.55 tff(1884,plain,
% 1.34/1.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.34/1.55 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 1.34/1.55 tff(1885,plain,
% 1.34/1.55 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1884, 192, 640, 1875, 1869, 239])).
% 1.34/1.55 tff(1886,plain,
% 1.34/1.55 (r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.34/1.55 inference(unit_resolution,[status(thm)],[1003, 60, 1837, 1885])).
% 1.34/1.55 tff(1887,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1888,plain,
% 1.34/1.55 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(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(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.55 inference(rewrite,[status(thm)],[])).
% 1.34/1.55 tff(1889,plain,
% 1.34/1.55 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1888])).
% 1.34/1.56 tff(1890,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1889, 1887])).
% 1.34/1.56 tff(1891,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z), s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1892,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1891, 1890])).
% 1.34/1.56 tff(1893,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1892, 77, 619, 1886, 1878])).
% 1.34/1.56 tff(1894,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | r(z, s(elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | b(s(s(s(elem!1))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1895,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1894, 1830, 515, 38, 531, 634, 1729, 1724, 639, 66, 1722])).
% 1.34/1.56 tff(1896,plain,
% 1.34/1.56 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[679, 1895, 633])).
% 1.34/1.56 tff(1897,plain,
% 1.34/1.56 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[699, 1896])).
% 1.34/1.56 tff(1898,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1899,plain,
% 1.34/1.56 (((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1900,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1899])).
% 1.34/1.56 tff(1901,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1900, 1898])).
% 1.34/1.56 tff(1902,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1903,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.34/1.56 tff(1904,plain,
% 1.34/1.56 (~r(s(z), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1903, 77, 1813, 1729])).
% 1.34/1.56 tff(1905,plain,
% 1.34/1.56 (b(s(z), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[658, 1904, 639])).
% 1.34/1.56 tff(1906,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1907,plain,
% 1.34/1.56 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1908,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1907])).
% 1.34/1.56 tff(1909,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1908, 1906])).
% 1.34/1.56 tff(1910,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1911,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), 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)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.34/1.56 tff(1912,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1911, 192, 1739, 1721, 1905])).
% 1.34/1.56 tff(1913,plain,
% 1.34/1.56 ((s(s(s(s(z)))) = s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[772, 60, 1912])).
% 1.34/1.56 tff(1914,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1913, 1897])).
% 1.34/1.56 tff(1915,plain,
% 1.34/1.56 (~b(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1753, 1830, 1647, 1724])).
% 1.34/1.56 tff(1916,plain,
% 1.34/1.56 (r(s(s(s(s(z)))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[526, 1915])).
% 1.34/1.56 tff(1917,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1918,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1919,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.34/1.56 tff(1920,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1919, 77, 1638, 1916, 1914])).
% 1.34/1.56 tff(1921,plain,(b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(elem!1))), s(elem!1)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | r(z, s(elem!1)) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1922,plain,
% 1.34/1.56 (b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1921, 632, 515, 629, 531, 39, 571])).
% 1.34/1.56 tff(1923,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.56 tff(1924,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1925,plain,
% 1.34/1.56 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1926,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1925])).
% 1.34/1.56 tff(1927,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1926, 1924])).
% 1.34/1.56 tff(1928,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1929,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1928, 1927])).
% 1.34/1.56 tff(1930,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1929, 192, 1923, 584, 1005, 583])).
% 1.34/1.56 tff(1931,plain,((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1932,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1931, 1922, 561, 581])).
% 1.34/1.56 tff(1933,plain,
% 1.34/1.56 (r(s(s(s(elem!1))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[992, 1932])).
% 1.34/1.56 tff(1934,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1935,plain,
% 1.34/1.56 (((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1936,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1935])).
% 1.34/1.56 tff(1937,plain,
% 1.34/1.56 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1936, 1934])).
% 1.34/1.56 tff(1938,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1939,plain,
% 1.34/1.56 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1938, 1937])).
% 1.34/1.56 tff(1940,plain,
% 1.34/1.56 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1939, 77, 1933, 605])).
% 1.34/1.56 tff(1941,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[598])).
% 1.34/1.56 tff(1942,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1941])).
% 1.34/1.56 tff(1943,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1942])).
% 1.34/1.56 tff(1944,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[221, 1943])).
% 1.34/1.56 tff(1945,plain,
% 1.34/1.56 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1941])).
% 1.34/1.56 tff(1946,plain,
% 1.34/1.56 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1945])).
% 1.34/1.56 tff(1947,plain,
% 1.34/1.56 (b(s(s(s(z))), s(elem!1))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[440, 1946])).
% 1.34/1.56 tff(1948,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1949,plain,
% 1.34/1.56 (((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1950,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1949])).
% 1.34/1.56 tff(1951,plain,
% 1.34/1.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1950, 1948])).
% 1.34/1.56 tff(1952,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1953,plain,
% 1.34/1.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.34/1.56 tff(1954,plain,
% 1.34/1.56 ((~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1953, 192, 1922, 581, 561])).
% 1.34/1.56 tff(1955,plain,
% 1.34/1.56 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1954, 1947, 1944])).
% 1.34/1.56 tff(1956,plain,
% 1.34/1.56 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(rewrite,[status(thm)],[])).
% 1.34/1.56 tff(1957,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.34/1.56 inference(quant_inst,[status(thm)],[])).
% 1.34/1.56 tff(1958,plain,
% 1.34/1.56 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 1.34/1.56 tff(1959,plain,
% 1.34/1.56 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1958, 60, 1955, 1940])).
% 1.34/1.56 tff(1960,plain,
% 1.34/1.56 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1959])).
% 1.34/1.56 tff(1961,plain,
% 1.34/1.56 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[1960, 601])).
% 1.34/1.56 tff(1962,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.34/1.56 tff(1963,plain,
% 1.34/1.56 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1962])).
% 1.34/1.56 tff(1964,plain,
% 1.34/1.56 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 1.34/1.56 inference(transitivity,[status(thm)],[16, 1963, 722])).
% 1.34/1.56 tff(1965,plain,
% 1.34/1.56 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1964])).
% 1.34/1.56 tff(1966,plain,
% 1.34/1.56 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1965])).
% 1.34/1.56 tff(1967,plain,
% 1.34/1.56 (s(s(s(s(s(z))))) = s(z)),
% 1.34/1.56 inference(transitivity,[status(thm)],[741, 1966, 10])).
% 1.34/1.56 tff(1968,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[50, 1967])).
% 1.34/1.56 tff(1969,plain,(~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1970,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1969, 1961])).
% 1.34/1.56 tff(1971,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1972,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1971, 536, 531, 39, 221, 440, 530, 515, 170, 321])).
% 1.34/1.56 tff(1973,plain,(b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1974,plain,
% 1.34/1.56 (b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1973, 515, 221, 440, 39, 295, 514, 528])).
% 1.34/1.56 tff(1975,plain,
% 1.34/1.56 (~b(s(elem!1), s(z))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1267, 1974, 512, 38])).
% 1.34/1.56 tff(1976,plain,
% 1.34/1.56 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(1977,plain,
% 1.34/1.56 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1976])).
% 1.34/1.56 tff(1978,plain,
% 1.34/1.56 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.56 inference(commutativity,[status(thm)],[])).
% 1.34/1.56 tff(1979,plain,
% 1.34/1.56 (~r(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[313, 118, 295])).
% 1.34/1.56 tff(1980,plain,
% 1.34/1.56 (b(s(z), s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[319, 1979])).
% 1.34/1.56 tff(1981,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 1.34/1.56 tff(1982,plain,
% 1.34/1.56 (~r(s(s(s(s(s(z))))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[302, 295, 297])).
% 1.34/1.56 tff(1983,plain,
% 1.34/1.56 (b(s(s(s(s(s(z))))), z)),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[271, 1982])).
% 1.34/1.56 tff(1984,plain,
% 1.34/1.56 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1146])).
% 1.34/1.56 tff(1985,plain,
% 1.34/1.56 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.34/1.56 inference(symmetry,[status(thm)],[1984])).
% 1.34/1.56 tff(1986,plain,
% 1.34/1.56 (b(s(elem!1), s(z))),
% 1.34/1.56 inference(modus_ponens,[status(thm)],[512, 1985])).
% 1.34/1.56 tff(1987,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1981, 1986])).
% 1.34/1.56 tff(1988,plain,((~(s(elem!1) = s(s(s(s(z)))))) | b(s(elem!1), s(z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1989,plain,
% 1.34/1.56 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1988, 1981, 512])).
% 1.34/1.56 tff(1990,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.34/1.56 tff(1991,plain,
% 1.34/1.56 (s(elem!1) = s(s(s(s(z))))),
% 1.34/1.56 inference(monotonicity,[status(thm)],[1990])).
% 1.34/1.56 tff(1992,plain,
% 1.34/1.56 ($false),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[528, 1991])).
% 1.34/1.56 tff(1993,plain,((~(elem!1 = s(s(s(z))))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.56 tff(1994,plain,
% 1.34/1.56 (~(elem!1 = s(s(s(z))))),
% 1.34/1.56 inference(unit_resolution,[status(thm)],[1993, 1989])).
% 1.34/1.57 tff(1995,plain,
% 1.34/1.57 (z = elem!1),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1550, 1543])).
% 1.34/1.57 tff(1996,plain,
% 1.34/1.57 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1995])).
% 1.34/1.57 tff(1997,plain,
% 1.34/1.57 (r(elem!1, s(s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[321, 1996])).
% 1.34/1.57 tff(1998,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 1.34/1.57 tff(1999,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1995])).
% 1.34/1.57 tff(2000,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[239, 1999])).
% 1.34/1.57 tff(2001,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2002,plain,
% 1.34/1.57 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(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)))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2003,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2002])).
% 1.34/1.57 tff(2004,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2003, 2001])).
% 1.34/1.57 tff(2005,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(z))))), s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2006,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.34/1.57 tff(2007,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2006, 77, 170, 383, 117])).
% 1.34/1.57 tff(2008,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2009,plain,
% 1.34/1.57 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2008, 383, 170])).
% 1.34/1.57 tff(2010,plain,
% 1.34/1.57 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[133, 2009])).
% 1.34/1.57 tff(2011,plain,
% 1.34/1.57 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.34/1.57 inference(commutativity,[status(thm)],[])).
% 1.34/1.57 tff(2012,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.34/1.57 tff(2013,plain,
% 1.34/1.57 (elem!1 = s(s(s(z)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 1.34/1.57 tff(2014,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1998, 2013])).
% 1.34/1.57 tff(2015,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2016,plain,
% 1.34/1.57 (~(s(s(s(z))) = elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2015, 1998])).
% 1.34/1.57 tff(2017,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.57 tff(2018,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2019,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2020,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2019, 2018])).
% 1.34/1.57 tff(2021,plain,
% 1.34/1.57 (~r(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2020, 77, 2017, 383])).
% 1.34/1.57 tff(2022,plain,
% 1.34/1.57 (((~![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))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2023,plain,
% 1.34/1.57 ((~![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))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2024,plain,
% 1.34/1.57 ((~![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)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 1.34/1.57 tff(2025,plain,
% 1.34/1.57 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2024, 60])).
% 1.34/1.57 tff(2026,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2025, 2021, 2016])).
% 1.34/1.57 tff(2027,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2028,plain,
% 1.34/1.57 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2029,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2028])).
% 1.34/1.57 tff(2030,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.34/1.57 tff(2031,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2032,plain,
% 1.34/1.57 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.34/1.57 tff(2033,plain,
% 1.34/1.57 (~r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2032, 77, 2017, 383])).
% 1.34/1.57 tff(2034,plain,
% 1.34/1.57 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2035,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2036,plain,
% 1.34/1.57 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2035, 2034])).
% 1.34/1.57 tff(2037,plain,
% 1.34/1.57 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2036, 60])).
% 1.34/1.57 tff(2038,plain,
% 1.34/1.57 (b(elem!1, s(s(s(z))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2037, 2033, 1998])).
% 1.34/1.57 tff(2039,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.34/1.57 tff(2040,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2041,plain,
% 1.34/1.57 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2042,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2041])).
% 1.34/1.57 tff(2043,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.34/1.57 tff(2044,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2045,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.34/1.57 tff(2046,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2045, 192, 2039, 2038, 2026, 2010])).
% 1.34/1.57 tff(2047,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2048,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2047, 2000, 1998, 1997, 170])).
% 1.34/1.57 tff(2049,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[390, 2048])).
% 1.34/1.57 tff(2050,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2051,plain,
% 1.34/1.57 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(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))))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2052,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2051])).
% 1.34/1.57 tff(2053,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.34/1.57 tff(2054,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2055,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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)))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.34/1.57 tff(2056,plain,
% 1.34/1.57 (~b(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2055, 192, 512, 320, 2049])).
% 1.34/1.57 tff(2057,plain,
% 1.34/1.57 (r(s(s(s(z))), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[920, 2056])).
% 1.34/1.57 tff(2058,plain,
% 1.34/1.57 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[367, 77, 2057, 118])).
% 1.34/1.57 tff(2059,plain,
% 1.34/1.57 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[375, 2058])).
% 1.34/1.57 tff(2060,plain,
% 1.34/1.57 (s(s(elem!1)) = s(s(z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1543])).
% 1.34/1.57 tff(2061,plain,
% 1.34/1.57 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2060])).
% 1.34/1.57 tff(2062,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2061])).
% 1.34/1.57 tff(2063,plain,
% 1.34/1.57 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1995])).
% 1.34/1.57 tff(2064,plain,
% 1.34/1.57 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2063])).
% 1.34/1.57 tff(2065,plain,
% 1.34/1.57 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[987, 2064])).
% 1.34/1.57 tff(2066,plain,
% 1.34/1.57 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1543])).
% 1.34/1.57 tff(2067,plain,
% 1.34/1.57 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2066])).
% 1.34/1.57 tff(2068,plain,
% 1.34/1.57 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1995])).
% 1.34/1.57 tff(2069,plain,
% 1.34/1.57 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.34/1.57 inference(transitivity,[status(thm)],[2068, 2067])).
% 1.34/1.57 tff(2070,plain,
% 1.34/1.57 (r(s(elem!1), z) <=> r(s(z), z)),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1543])).
% 1.34/1.57 tff(2071,plain,
% 1.34/1.57 (r(s(z), z) <=> r(s(elem!1), z)),
% 1.34/1.57 inference(symmetry,[status(thm)],[2070])).
% 1.34/1.57 tff(2072,plain,
% 1.34/1.57 ((~r(s(z), z)) <=> (~r(s(elem!1), z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2071])).
% 1.34/1.57 tff(2073,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.34/1.57 tff(2074,plain,
% 1.34/1.57 (~r(s(elem!1), z)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.34/1.57 tff(2075,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[545, 2074])).
% 1.34/1.57 tff(2076,plain,((~(s(elem!1) = s(z))) | (~r(s(elem!1), z)) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2077,plain,
% 1.34/1.57 (r(s(z), z)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2076, 1543, 545])).
% 1.34/1.57 tff(2078,plain,
% 1.34/1.57 (r(s(elem!1), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2077, 2069])).
% 1.34/1.57 tff(2079,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1543])).
% 1.34/1.57 tff(2080,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2079])).
% 1.34/1.57 tff(2081,plain,
% 1.34/1.57 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.34/1.57 inference(symmetry,[status(thm)],[2061])).
% 1.34/1.57 tff(2082,plain,
% 1.34/1.57 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2081])).
% 1.34/1.57 tff(2083,plain,
% 1.34/1.57 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2082, 2080])).
% 1.34/1.57 tff(2084,plain,
% 1.34/1.57 (r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2057, 2083])).
% 1.34/1.57 tff(2085,plain,
% 1.34/1.57 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1623, 2084, 2078])).
% 1.34/1.57 tff(2086,plain,
% 1.34/1.57 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1628, 2085, 2065])).
% 1.34/1.57 tff(2087,plain,
% 1.34/1.57 (b(s(s(s(z))), elem!1)),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2086, 2062])).
% 1.34/1.57 tff(2088,plain,
% 1.34/1.57 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[1995])).
% 1.34/1.57 tff(2089,plain,
% 1.34/1.57 (b(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[603, 2088])).
% 1.34/1.57 tff(2090,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2091,plain,
% 1.34/1.57 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2092,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 1.34/1.57 inference(monotonicity,[status(thm)],[2091])).
% 1.34/1.57 tff(2093,plain,
% 1.34/1.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(transitivity,[status(thm)],[2092, 2090])).
% 1.34/1.57 tff(2094,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))),
% 1.34/1.57 inference(quant_inst,[status(thm)],[])).
% 1.34/1.57 tff(2095,plain,
% 1.34/1.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 1.34/1.57 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.34/1.57 tff(2096,plain,
% 1.34/1.57 ($false),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2095, 192, 2089, 2000, 2087, 2059])).
% 1.34/1.57 tff(2097,plain,((~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.57 tff(2098,plain,
% 1.34/1.57 (~(s(elem!1) = s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[2097, 1994, 512, 118, 295, 1983, 321, 545])).
% 1.34/1.57 tff(2099,plain,
% 1.34/1.57 (r(s(elem!1), s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[950, 2098, 1981])).
% 1.34/1.57 tff(2100,plain,
% 1.34/1.57 (~r(z, s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[1737, 2099, 545])).
% 1.34/1.57 tff(2101,plain,
% 1.34/1.57 (b(z, s(z))),
% 1.34/1.57 inference(unit_resolution,[status(thm)],[292, 2100])).
% 1.34/1.57 tff(2102,plain,
% 1.34/1.57 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.34/1.57 inference(rewrite,[status(thm)],[])).
% 1.34/1.57 tff(2103,plain,
% 1.34/1.57 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2104,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2103])).
% 1.34/1.58 tff(2105,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2104, 2102])).
% 1.34/1.58 tff(2106,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2107,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 1.34/1.58 tff(2108,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2107, 77, 545, 504, 668])).
% 1.34/1.58 tff(2109,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2110,plain,
% 1.34/1.58 (~r(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2109, 2099, 545])).
% 1.34/1.58 tff(2111,plain,
% 1.34/1.58 (b(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[351, 2110])).
% 1.34/1.58 tff(2112,plain,
% 1.34/1.58 (~b(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1414, 2111, 512, 2101, 1980])).
% 1.34/1.58 tff(2113,plain,
% 1.34/1.58 (r(s(s(s(z))), s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[920, 2112])).
% 1.34/1.58 tff(2114,plain,
% 1.34/1.58 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[367, 77, 2113, 118])).
% 1.34/1.58 tff(2115,plain,
% 1.34/1.58 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[375, 2114])).
% 1.34/1.58 tff(2116,plain,
% 1.34/1.58 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[121, 77, 2113, 118])).
% 1.34/1.58 tff(2117,plain,
% 1.34/1.58 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[133, 2116])).
% 1.34/1.58 tff(2118,plain,
% 1.34/1.58 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[553, 545, 321])).
% 1.34/1.58 tff(2119,plain,
% 1.34/1.58 (b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[535, 1989, 2118])).
% 1.34/1.58 tff(2120,plain,
% 1.34/1.58 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[723])).
% 1.34/1.58 tff(2121,plain,
% 1.34/1.58 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2120])).
% 1.34/1.58 tff(2122,plain,
% 1.34/1.58 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2121])).
% 1.34/1.58 tff(2123,plain,
% 1.34/1.58 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[294, 2122])).
% 1.34/1.58 tff(2124,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[869, 2123])).
% 1.34/1.58 tff(2125,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2126,plain,
% 1.34/1.58 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2125, 2119, 294])).
% 1.34/1.58 tff(2127,plain,
% 1.34/1.58 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[803, 2099, 118])).
% 1.34/1.58 tff(2128,plain,
% 1.34/1.58 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[811, 2127, 2126])).
% 1.34/1.58 tff(2129,plain,
% 1.34/1.58 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[752, 2126])).
% 1.34/1.58 tff(2130,plain,
% 1.34/1.58 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[759, 77, 2099, 118])).
% 1.34/1.58 tff(2131,plain,
% 1.34/1.58 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[597, 2130, 2129])).
% 1.34/1.58 tff(2132,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2133,plain,
% 1.34/1.58 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2134,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2133])).
% 1.34/1.58 tff(2135,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2134, 2132])).
% 1.34/1.58 tff(2136,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2137,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2136, 2135])).
% 1.34/1.58 tff(2138,plain,
% 1.34/1.58 (~b(s(elem!1), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2137, 192, 2131, 2128, 2117, 2115])).
% 1.34/1.58 tff(2139,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2140,plain,
% 1.34/1.58 (((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), 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))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2141,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2140])).
% 1.34/1.58 tff(2142,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2141, 2139])).
% 1.34/1.58 tff(2143,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2144,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2143, 2142])).
% 1.34/1.58 tff(2145,plain,
% 1.34/1.58 (~r(s(elem!1), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2144, 77, 2099, 2113])).
% 1.34/1.58 tff(2146,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2147,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2148,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 1.34/1.58 tff(2149,plain,
% 1.34/1.58 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2148, 60, 2145])).
% 1.34/1.58 tff(2150,plain,
% 1.34/1.58 (s(elem!1) = s(s(s(z)))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2149, 2138])).
% 1.34/1.58 tff(2151,plain,
% 1.34/1.58 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2150])).
% 1.34/1.58 tff(2152,plain,
% 1.34/1.58 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2151])).
% 1.34/1.58 tff(2153,plain,
% 1.34/1.58 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2152])).
% 1.34/1.58 tff(2154,plain,
% 1.34/1.58 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2153, 1978])).
% 1.34/1.58 tff(2155,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.34/1.58 inference(symmetry,[status(thm)],[2154])).
% 1.34/1.58 tff(2156,plain,
% 1.34/1.58 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2150])).
% 1.34/1.58 tff(2157,plain,
% 1.34/1.58 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2156])).
% 1.34/1.58 tff(2158,plain,
% 1.34/1.58 (s(s(z)) = elem!1),
% 1.34/1.58 inference(transitivity,[status(thm)],[16, 2157, 682])).
% 1.34/1.58 tff(2159,plain,
% 1.34/1.58 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2158])).
% 1.34/1.58 tff(2160,plain,
% 1.34/1.58 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2159, 2155, 1977])).
% 1.34/1.58 tff(2161,plain,
% 1.34/1.58 (elem!1 = s(s(z))),
% 1.34/1.58 inference(transitivity,[status(thm)],[695, 2156, 15])).
% 1.34/1.58 tff(2162,plain,
% 1.34/1.58 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2161])).
% 1.34/1.58 tff(2163,plain,
% 1.34/1.58 (~(elem!1 = s(s(s(s(z)))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[853, 2129])).
% 1.34/1.58 tff(2164,plain,
% 1.34/1.58 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2161])).
% 1.34/1.58 tff(2165,plain,
% 1.34/1.58 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2164])).
% 1.34/1.58 tff(2166,plain,
% 1.34/1.58 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2165])).
% 1.34/1.58 tff(2167,assumption,(elem!1 = z), introduced(assumption)).
% 1.34/1.58 tff(2168,plain,
% 1.34/1.58 (s(elem!1) = s(z)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2167])).
% 1.34/1.58 tff(2169,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[115, 2168])).
% 1.34/1.58 tff(2170,plain,((~(elem!1 = z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2171,plain,
% 1.34/1.58 (~(elem!1 = z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2170, 2098])).
% 1.34/1.58 tff(2172,assumption,(s(elem!1) = s(s(s(z)))), introduced(assumption)).
% 1.34/1.58 tff(2173,plain,
% 1.34/1.58 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2172])).
% 1.34/1.58 tff(2174,plain,
% 1.34/1.58 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2173])).
% 1.34/1.58 tff(2175,plain,
% 1.34/1.58 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2172])).
% 1.34/1.58 tff(2176,plain,
% 1.34/1.58 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2175])).
% 1.34/1.58 tff(2177,plain,
% 1.34/1.58 (s(s(z)) = elem!1),
% 1.34/1.58 inference(transitivity,[status(thm)],[16, 2176, 682])).
% 1.34/1.58 tff(2178,plain,
% 1.34/1.58 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2177])).
% 1.34/1.58 tff(2179,plain,
% 1.34/1.58 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2178])).
% 1.34/1.58 tff(2180,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.34/1.58 tff(2181,plain,
% 1.34/1.58 (~b(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 1.34/1.58 tff(2182,plain,
% 1.34/1.58 (r(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2037, 2181, 1998])).
% 1.34/1.58 tff(2183,plain,
% 1.34/1.58 (r(elem!1, s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2182, 2174])).
% 1.34/1.58 tff(2184,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.34/1.58 tff(2185,plain,
% 1.34/1.58 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.34/1.58 inference(commutativity,[status(thm)],[])).
% 1.34/1.58 tff(2186,plain,
% 1.34/1.58 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2185])).
% 1.34/1.58 tff(2187,plain,
% 1.34/1.58 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2177])).
% 1.34/1.58 tff(2188,plain,
% 1.34/1.58 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2187, 2186])).
% 1.34/1.58 tff(2189,plain,
% 1.34/1.58 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2188])).
% 1.34/1.58 tff(2190,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.34/1.58 tff(2191,plain,
% 1.34/1.58 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2190])).
% 1.34/1.58 tff(2192,plain,
% 1.34/1.58 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2191])).
% 1.34/1.58 tff(2193,plain,
% 1.34/1.58 (s(s(z)) = s(z)),
% 1.34/1.58 inference(symmetry,[status(thm)],[2190])).
% 1.34/1.58 tff(2194,plain,
% 1.34/1.58 (s(s(z)) = z),
% 1.34/1.58 inference(transitivity,[status(thm)],[2193, 1507, 2192, 20])).
% 1.34/1.58 tff(2195,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[32, 2194])).
% 1.34/1.58 tff(2196,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2197,plain,
% 1.34/1.58 (~(elem!1 = s(z))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2196, 2189])).
% 1.34/1.58 tff(2198,plain,
% 1.34/1.58 (~r(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2109, 668, 545])).
% 1.34/1.58 tff(2199,plain,
% 1.34/1.58 (b(s(z), z)),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[351, 2198])).
% 1.34/1.58 tff(2200,plain,
% 1.34/1.58 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(z))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2172])).
% 1.34/1.58 tff(2201,plain,
% 1.34/1.58 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2200])).
% 1.34/1.58 tff(2202,plain,
% 1.34/1.58 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2178, 2201])).
% 1.34/1.58 tff(2203,plain,
% 1.34/1.58 ((~b(s(s(z)), s(s(s(z))))) <=> (~b(elem!1, s(elem!1)))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2202])).
% 1.34/1.58 tff(2204,plain,
% 1.34/1.58 (~b(elem!1, s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2180, 2203])).
% 1.34/1.58 tff(2205,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.34/1.58 tff(2206,plain,
% 1.34/1.58 (b(elem!1, s(elem!1)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2205])).
% 1.34/1.58 tff(2207,plain,
% 1.34/1.58 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.34/1.58 inference(symmetry,[status(thm)],[2206])).
% 1.34/1.58 tff(2208,plain,
% 1.34/1.58 (b(elem!1, s(elem!1))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[582, 2207])).
% 1.34/1.58 tff(2209,assumption,(~b(elem!1, s(elem!1))), introduced(assumption)).
% 1.34/1.58 tff(2210,plain,
% 1.34/1.58 ($false),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2209, 2208])).
% 1.34/1.58 tff(2211,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | b(elem!1, s(elem!1)) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.58 tff(2212,plain,
% 1.34/1.58 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2211, 2204, 582])).
% 1.34/1.58 tff(2213,plain,
% 1.34/1.58 (~b(s(z), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[615, 192, 515, 1473, 1475])).
% 1.34/1.58 tff(2214,plain,
% 1.34/1.58 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[438, 60, 2213])).
% 1.34/1.58 tff(2215,plain,
% 1.34/1.58 (r(s(z), s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2214, 609])).
% 1.34/1.58 tff(2216,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.58 tff(2217,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2218,plain,
% 1.34/1.58 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2219,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2218])).
% 1.34/1.58 tff(2220,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2219, 2217])).
% 1.34/1.58 tff(2221,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2222,plain,
% 1.34/1.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2221, 2220])).
% 1.34/1.58 tff(2223,plain,
% 1.34/1.58 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2222, 192, 1435, 1473, 1475])).
% 1.34/1.58 tff(2224,plain,
% 1.34/1.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2225,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2226,plain,
% 1.34/1.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 1.34/1.58 tff(2227,plain,
% 1.34/1.58 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2226, 60])).
% 1.34/1.58 tff(2228,plain,
% 1.34/1.58 (r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2227, 2223, 2216])).
% 1.34/1.58 tff(2229,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2230,plain,
% 1.34/1.58 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(rewrite,[status(thm)],[])).
% 1.34/1.58 tff(2231,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.34/1.58 inference(monotonicity,[status(thm)],[2230])).
% 1.34/1.58 tff(2232,plain,
% 1.34/1.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.34/1.58 inference(transitivity,[status(thm)],[2231, 2229])).
% 1.34/1.58 tff(2233,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))),
% 1.34/1.58 inference(quant_inst,[status(thm)],[])).
% 1.34/1.58 tff(2234,plain,
% 1.34/1.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.34/1.58 inference(modus_ponens,[status(thm)],[2233, 2232])).
% 1.34/1.58 tff(2235,plain,
% 1.34/1.58 (~r(elem!1, s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[2234, 77, 2228, 2215])).
% 1.34/1.58 tff(2236,plain,
% 1.34/1.58 (b(elem!1, s(z))),
% 1.34/1.58 inference(unit_resolution,[status(thm)],[1529, 2235, 1523])).
% 1.34/1.58 tff(2237,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.34/1.58 tff(2238,plain,
% 1.34/1.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2239,plain,
% 1.34/1.59 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2240,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2239])).
% 1.34/1.59 tff(2241,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2240, 2238])).
% 1.34/1.59 tff(2242,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2243,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 1.34/1.59 tff(2244,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2243, 192, 1435, 515, 2237, 465])).
% 1.34/1.59 tff(2245,plain,((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2246,plain,
% 1.34/1.59 (~b(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2245, 2236, 515, 1435])).
% 1.34/1.59 tff(2247,plain,
% 1.34/1.59 (r(z, s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[292, 2246])).
% 1.34/1.59 tff(2248,plain,
% 1.34/1.59 (~r(s(elem!1), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1735, 77, 668, 2247])).
% 1.34/1.59 tff(2249,plain,
% 1.34/1.59 (b(s(elem!1), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[560, 2248])).
% 1.34/1.59 tff(2250,plain,
% 1.34/1.59 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1483, 2249, 170, 321])).
% 1.34/1.59 tff(2251,plain,
% 1.34/1.59 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[811, 2250, 806])).
% 1.34/1.59 tff(2252,plain,
% 1.34/1.59 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2251])).
% 1.34/1.59 tff(2253,plain,
% 1.34/1.59 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2252])).
% 1.34/1.59 tff(2254,plain,
% 1.34/1.59 (s(s(s(s(z)))) = elem!1),
% 1.34/1.59 inference(transitivity,[status(thm)],[45, 2253, 682])).
% 1.34/1.59 tff(2255,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2254])).
% 1.34/1.59 tff(2256,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2255])).
% 1.34/1.59 tff(2257,plain,
% 1.34/1.59 (~(s(s(s(elem!1))) = elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1598, 2251])).
% 1.34/1.59 tff(2258,plain,
% 1.34/1.59 (elem!1 = s(s(s(s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[695, 2252, 44])).
% 1.34/1.59 tff(2259,plain,
% 1.34/1.59 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2258])).
% 1.34/1.59 tff(2260,plain,
% 1.34/1.59 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[2259])).
% 1.34/1.59 tff(2261,plain,
% 1.34/1.59 (b(s(z), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[38, 2260])).
% 1.34/1.59 tff(2262,plain,
% 1.34/1.59 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[2251])).
% 1.34/1.59 tff(2263,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2262])).
% 1.34/1.59 tff(2264,plain,
% 1.34/1.59 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2263])).
% 1.34/1.59 tff(2265,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2254])).
% 1.34/1.59 tff(2266,plain,
% 1.34/1.59 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2265])).
% 1.34/1.59 tff(2267,plain,
% 1.34/1.59 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2228, 2266])).
% 1.34/1.59 tff(2268,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.34/1.59 tff(2269,assumption,(r(s(s(s(elem!1))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.59 tff(2270,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2271,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2272,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.34/1.59 tff(2273,plain,
% 1.34/1.59 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2272, 77, 619])).
% 1.34/1.59 tff(2274,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2273, 2269])).
% 1.34/1.59 tff(2275,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1311, 60, 1307, 2274])).
% 1.34/1.59 tff(2276,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.34/1.59 tff(2277,plain,
% 1.34/1.59 (s(s(s(s(z)))) = elem!1),
% 1.34/1.59 inference(transitivity,[status(thm)],[45, 731, 682])).
% 1.34/1.59 tff(2278,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2277])).
% 1.34/1.59 tff(2279,plain,
% 1.34/1.59 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2278])).
% 1.34/1.59 tff(2280,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.34/1.59 tff(2281,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2282,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2283,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2282, 2281])).
% 1.34/1.59 tff(2284,plain,
% 1.34/1.59 ((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2283, 77, 2280])).
% 1.34/1.59 tff(2285,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2284, 2269])).
% 1.34/1.59 tff(2286,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2285, 2279])).
% 1.34/1.59 tff(2287,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1628, 2286, 2276])).
% 1.34/1.59 tff(2288,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2289,plain,
% 1.34/1.59 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2290,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2289])).
% 1.34/1.59 tff(2291,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2290, 2288])).
% 1.34/1.59 tff(2292,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2293,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 1.34/1.59 tff(2294,plain,
% 1.34/1.59 ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2293, 192])).
% 1.34/1.59 tff(2295,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2294, 2287, 2275, 2237, 2268])).
% 1.34/1.59 tff(2296,plain,((~r(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~(s(elem!1) = s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2297,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2296, 2257, 2261, 2236, 2251, 2215, 2267])).
% 1.34/1.59 tff(2298,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2297, 2264])).
% 1.34/1.59 tff(2299,plain,
% 1.34/1.59 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1056])).
% 1.34/1.59 tff(2300,plain,
% 1.34/1.59 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2299])).
% 1.34/1.59 tff(2301,plain,
% 1.34/1.59 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.34/1.59 inference(symmetry,[status(thm)],[723])).
% 1.34/1.59 tff(2302,plain,
% 1.34/1.59 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2301])).
% 1.34/1.59 tff(2303,plain,
% 1.34/1.59 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2302])).
% 1.34/1.59 tff(2304,plain,
% 1.34/1.59 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[1056])).
% 1.34/1.59 tff(2305,plain,
% 1.34/1.59 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2304])).
% 1.34/1.59 tff(2306,plain,
% 1.34/1.59 (elem!1 = s(s(s(s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[695, 730, 2305, 691, 2303, 2300])).
% 1.34/1.59 tff(2307,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[716, 2306])).
% 1.34/1.59 tff(2308,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2309,plain,
% 1.34/1.59 (elem!1 = s(s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2308, 1055, 723])).
% 1.34/1.59 tff(2310,plain,
% 1.34/1.59 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[45, 731, 682, 2309])).
% 1.34/1.59 tff(2311,plain,
% 1.34/1.59 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2310])).
% 1.34/1.59 tff(2312,plain,
% 1.34/1.59 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[92, 2311, 727, 1056])).
% 1.34/1.59 tff(2313,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[102, 2312])).
% 1.34/1.59 tff(2314,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2315,plain,
% 1.34/1.59 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2314, 2251])).
% 1.34/1.59 tff(2316,plain,
% 1.34/1.59 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2301])).
% 1.34/1.59 tff(2317,plain,
% 1.34/1.59 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2316, 703])).
% 1.34/1.59 tff(2318,plain,
% 1.34/1.59 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.34/1.59 inference(symmetry,[status(thm)],[2317])).
% 1.34/1.59 tff(2319,assumption,(~r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.34/1.59 tff(2320,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2301])).
% 1.34/1.59 tff(2321,plain,
% 1.34/1.59 ((~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2320])).
% 1.34/1.59 tff(2322,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2323,plain,
% 1.34/1.59 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(z))))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2324,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(z))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2323])).
% 1.34/1.59 tff(2325,plain,
% 1.34/1.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(z))))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2324, 2322])).
% 1.34/1.59 tff(2326,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), z)) | (~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(s(s(z))))))) | (~b(s(s(s(elem!1))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2327,plain,
% 1.34/1.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.34/1.59 tff(2328,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2327, 192, 1005, 813, 239])).
% 1.34/1.59 tff(2329,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2328, 2321])).
% 1.34/1.59 tff(2330,plain,
% 1.34/1.59 (s(s(s(elem!1))) = s(elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[679, 2329, 2319])).
% 1.34/1.59 tff(2331,plain,
% 1.34/1.59 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2330, 2318])).
% 1.34/1.59 tff(2332,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1000, 2331])).
% 1.34/1.59 tff(2333,plain,((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~(s(elem!1) = s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2334,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2333, 2315, 2298, 2251, 1473, 1475])).
% 1.34/1.59 tff(2335,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[992, 2334])).
% 1.34/1.59 tff(2336,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[982, 2335, 2247])).
% 1.34/1.59 tff(2337,plain,
% 1.34/1.59 (b(s(s(s(elem!1))), s(z))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1311, 60, 1307, 2336])).
% 1.34/1.59 tff(2338,plain,
% 1.34/1.59 (~b(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2294, 2337, 2236, 2261])).
% 1.34/1.59 tff(2339,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), elem!1)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[1628, 2338, 2257])).
% 1.34/1.59 tff(2340,plain,
% 1.34/1.59 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2339, 2256])).
% 1.34/1.59 tff(2341,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2342,plain,
% 1.34/1.59 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2343,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.34/1.59 inference(monotonicity,[status(thm)],[2342])).
% 1.34/1.59 tff(2344,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.34/1.59 inference(transitivity,[status(thm)],[2343, 2341])).
% 1.34/1.59 tff(2345,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), z)))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2346,plain,
% 1.34/1.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 1.34/1.59 tff(2347,plain,
% 1.34/1.59 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2346, 77, 2335, 321])).
% 1.34/1.59 tff(2348,plain,
% 1.34/1.59 ($false),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2347, 2340])).
% 1.34/1.59 tff(2349,plain,((~b(elem!1, z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | r(s(elem!1), s(s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~b(s(z), z)) | (elem!1 = s(z)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.59 tff(2350,plain,
% 1.34/1.59 (~b(elem!1, z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2349, 2212, 170, 321, 38, 668, 2199, 806, 2197])).
% 1.34/1.59 tff(2351,plain,
% 1.34/1.59 (((~![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))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2352,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.34/1.59 inference(quant_inst,[status(thm)],[])).
% 1.34/1.59 tff(2353,plain,
% 1.34/1.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.34/1.59 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 1.34/1.59 tff(2354,plain,
% 1.34/1.59 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2353, 60])).
% 1.34/1.59 tff(2355,plain,
% 1.34/1.59 (r(elem!1, z)),
% 1.34/1.59 inference(unit_resolution,[status(thm)],[2354, 2350, 2184])).
% 1.34/1.59 tff(2356,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2357,plain,
% 1.34/1.59 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.34/1.59 inference(rewrite,[status(thm)],[])).
% 1.34/1.59 tff(2358,plain,
% 1.34/1.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2357])).
% 1.34/1.60 tff(2359,plain,
% 1.34/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z)))),
% 1.34/1.60 inference(transitivity,[status(thm)],[2358, 2356])).
% 1.34/1.60 tff(2360,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.34/1.60 inference(quant_inst,[status(thm)],[])).
% 1.34/1.60 tff(2361,plain,
% 1.34/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 1.34/1.60 tff(2362,plain,
% 1.34/1.60 ((~r(elem!1, z)) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), z))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2361, 77])).
% 1.34/1.60 tff(2363,plain,
% 1.34/1.60 (~r(elem!1, s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2362, 2355, 545])).
% 1.34/1.60 tff(2364,plain,
% 1.34/1.60 ($false),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2363, 2183])).
% 1.34/1.60 tff(2365,plain,(b(s(s(z)), s(s(s(z)))) | (~(s(elem!1) = s(s(s(z))))) | (~r(s(elem!1), z)) | (elem!1 = z) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | r(s(elem!1), s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.60 tff(2366,plain,
% 1.34/1.60 (b(s(s(z)), s(s(s(z))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[2365, 2150, 545, 2171, 295, 321, 1980, 2099, 2127, 2131, 1994])).
% 1.34/1.60 tff(2367,plain,
% 1.34/1.60 (r(s(s(s(s(z)))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2150])).
% 1.34/1.60 tff(2368,plain,
% 1.34/1.60 ((~r(s(s(s(s(z)))), s(elem!1))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2367])).
% 1.34/1.60 tff(2369,plain,
% 1.34/1.60 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[1919, 77, 545, 297])).
% 1.34/1.60 tff(2370,plain,
% 1.34/1.60 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.34/1.60 tff(2371,plain,
% 1.34/1.60 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.34/1.60 inference(unit_resolution,[status(thm)],[406, 2370])).
% 1.34/1.60 tff(2372,plain,
% 1.34/1.60 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.60 inference(monotonicity,[status(thm)],[2150])).
% 1.34/1.60 tff(2373,plain,
% 1.34/1.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.34/1.60 inference(modus_ponens,[status(thm)],[2119, 2372])).
% 1.34/1.60 tff(2374,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2375,plain,
% 1.34/1.60 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.34/1.60 inference(rewrite,[status(thm)],[])).
% 1.34/1.60 tff(2376,plain,
% 1.34/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2375])).
% 1.44/1.60 tff(2377,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2376, 2374])).
% 1.44/1.60 tff(2378,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2379,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 1.44/1.60 tff(2380,plain,
% 1.44/1.60 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2379, 192, 2373, 2371, 2366])).
% 1.44/1.60 tff(2381,plain,
% 1.44/1.60 (~b(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2380, 2166])).
% 1.44/1.60 tff(2382,plain,
% 1.44/1.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2383,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2384,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 1.44/1.60 tff(2385,plain,
% 1.44/1.60 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2384, 60])).
% 1.44/1.60 tff(2386,plain,
% 1.44/1.60 (r(elem!1, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2385, 2381, 2163])).
% 1.44/1.60 tff(2387,plain,
% 1.44/1.60 (r(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2386, 2162])).
% 1.44/1.60 tff(2388,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2389,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2390,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 1.44/1.60 tff(2391,plain,
% 1.44/1.60 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2390, 77, 295, 2387])).
% 1.44/1.60 tff(2392,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2393,plain,
% 1.44/1.60 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2394,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2393])).
% 1.44/1.60 tff(2395,plain,
% 1.44/1.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2394, 2392])).
% 1.44/1.60 tff(2396,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2397,plain,
% 1.44/1.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 1.44/1.60 tff(2398,plain,
% 1.44/1.60 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2397, 192, 2373, 2371, 2117, 2115, 2366])).
% 1.44/1.60 tff(2399,plain,
% 1.44/1.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2400,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2401,plain,
% 1.44/1.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 1.44/1.60 tff(2402,plain,
% 1.44/1.60 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2401, 60, 2398])).
% 1.44/1.60 tff(2403,plain,
% 1.44/1.60 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2402, 2391])).
% 1.44/1.60 tff(2404,plain,
% 1.44/1.60 (elem!1 = s(s(s(elem!1)))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2403, 2160])).
% 1.44/1.60 tff(2405,plain,
% 1.44/1.60 ((s(elem!1) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.60 inference(commutativity,[status(thm)],[])).
% 1.44/1.60 tff(2406,plain,
% 1.44/1.60 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2152])).
% 1.44/1.60 tff(2407,plain,
% 1.44/1.60 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2406])).
% 1.44/1.60 tff(2408,plain,
% 1.44/1.60 (s(s(s(z))) = s(elem!1)),
% 1.44/1.60 inference(symmetry,[status(thm)],[2150])).
% 1.44/1.60 tff(2409,plain,
% 1.44/1.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2408, 2407])).
% 1.44/1.60 tff(2410,plain,
% 1.44/1.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2409, 2405])).
% 1.44/1.60 tff(2411,plain,
% 1.44/1.60 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2410])).
% 1.44/1.60 tff(2412,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.60 tff(2413,plain,
% 1.44/1.60 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2412])).
% 1.44/1.60 tff(2414,plain,
% 1.44/1.60 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[16, 2413, 740])).
% 1.44/1.60 tff(2415,plain,
% 1.44/1.60 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2414])).
% 1.44/1.60 tff(2416,plain,
% 1.44/1.60 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2415])).
% 1.44/1.60 tff(2417,plain,
% 1.44/1.60 (s(s(s(s(z)))) = s(z)),
% 1.44/1.60 inference(transitivity,[status(thm)],[45, 2416, 10])).
% 1.44/1.60 tff(2418,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[212, 2417])).
% 1.44/1.60 tff(2419,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2420,plain,
% 1.44/1.60 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2419, 2411])).
% 1.44/1.60 tff(2421,plain,
% 1.44/1.60 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1587])).
% 1.44/1.60 tff(2422,assumption,(~(s(s(s(s(elem!1)))) = s(elem!1))), introduced(assumption)).
% 1.44/1.60 tff(2423,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2422, 2421])).
% 1.44/1.60 tff(2424,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2425,plain,
% 1.44/1.60 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2424, 2420])).
% 1.44/1.60 tff(2426,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 1.44/1.60 tff(2427,plain,
% 1.44/1.60 (s(s(s(elem!1))) = elem!1),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2426, 1976])).
% 1.44/1.60 tff(2428,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2276, 2427])).
% 1.44/1.60 tff(2429,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2430,plain,
% 1.44/1.60 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2429, 2425])).
% 1.44/1.60 tff(2431,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2430, 2404])).
% 1.44/1.60 tff(2432,plain,(b(s(elem!1), s(z)) | (~r(s(elem!1), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2433,plain,
% 1.44/1.60 (~r(s(elem!1), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2432, 1975, 294, 514, 66, 512, 527])).
% 1.44/1.60 tff(2434,plain,
% 1.44/1.60 (b(s(elem!1), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[560, 2433])).
% 1.44/1.60 tff(2435,plain,
% 1.44/1.60 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2125, 1974, 294])).
% 1.44/1.60 tff(2436,plain,
% 1.44/1.60 (r(s(elem!1), s(z))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[950, 1975, 115])).
% 1.44/1.60 tff(2437,plain,
% 1.44/1.60 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[803, 2436, 66])).
% 1.44/1.60 tff(2438,plain,
% 1.44/1.60 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[811, 2437, 2435])).
% 1.44/1.60 tff(2439,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[1483, 2438, 2434, 295, 514])).
% 1.44/1.60 tff(2440,plain,((~b(s(z), z)) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2441,plain,
% 1.44/1.60 (s(elem!1) = s(s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2440, 511, 218, 115, 461, 134, 376, 39, 294, 361])).
% 1.44/1.60 tff(2442,plain,
% 1.44/1.60 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2441])).
% 1.44/1.60 tff(2443,plain,
% 1.44/1.60 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.44/1.60 inference(symmetry,[status(thm)],[2442])).
% 1.44/1.60 tff(2444,plain,
% 1.44/1.60 (~b(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[471, 192, 361, 218, 461])).
% 1.44/1.60 tff(2445,plain,
% 1.44/1.60 (r(z, s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[339, 2444])).
% 1.44/1.60 tff(2446,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2447,plain,
% 1.44/1.60 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2448,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2447])).
% 1.44/1.60 tff(2449,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.60 inference(transitivity,[status(thm)],[2448, 2446])).
% 1.44/1.60 tff(2450,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2451,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.44/1.60 tff(2452,plain,
% 1.44/1.60 (~r(z, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2451, 77, 321, 383])).
% 1.44/1.60 tff(2453,plain,
% 1.44/1.60 (b(z, s(s(s(z))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[237, 2452])).
% 1.44/1.60 tff(2454,plain,
% 1.44/1.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.60 inference(rewrite,[status(thm)],[])).
% 1.44/1.60 tff(2455,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.44/1.60 inference(quant_inst,[status(thm)],[])).
% 1.44/1.60 tff(2456,plain,
% 1.44/1.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2455, 2454])).
% 1.44/1.60 tff(2457,plain,
% 1.44/1.60 (~r(s(s(s(z))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2456, 77, 321, 383])).
% 1.44/1.60 tff(2458,plain,
% 1.44/1.60 (b(s(s(s(z))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[253, 2457])).
% 1.44/1.60 tff(2459,plain,
% 1.44/1.60 ($false),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[260, 192, 2458, 239, 2453, 2010])).
% 1.44/1.60 tff(2460,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.60 tff(2461,plain,
% 1.44/1.60 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[2460, 2445, 295, 359])).
% 1.44/1.60 tff(2462,plain,
% 1.44/1.60 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[390, 2461])).
% 1.44/1.60 tff(2463,plain,
% 1.44/1.60 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1146])).
% 1.44/1.60 tff(2464,plain,
% 1.44/1.60 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2463])).
% 1.44/1.60 tff(2465,plain,
% 1.44/1.60 (s(s(s(z))) = elem!1),
% 1.44/1.60 inference(transitivity,[status(thm)],[92, 2464, 682])).
% 1.44/1.60 tff(2466,plain,
% 1.44/1.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1160, 2465])).
% 1.44/1.60 tff(2467,plain,
% 1.44/1.60 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2466])).
% 1.44/1.60 tff(2468,plain,
% 1.44/1.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2465, 1160])).
% 1.44/1.60 tff(2469,plain,
% 1.44/1.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.60 inference(transitivity,[status(thm)],[2468, 1976])).
% 1.44/1.60 tff(2470,plain,
% 1.44/1.60 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2469])).
% 1.44/1.60 tff(2471,plain,
% 1.44/1.60 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.60 inference(modus_ponens,[status(thm)],[2419, 2470])).
% 1.44/1.60 tff(2472,plain,
% 1.44/1.60 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.44/1.60 inference(monotonicity,[status(thm)],[1160, 2465])).
% 1.44/1.60 tff(2473,plain,
% 1.44/1.60 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2472])).
% 1.44/1.60 tff(2474,plain,
% 1.44/1.60 (elem!1 = s(s(s(z)))),
% 1.44/1.60 inference(transitivity,[status(thm)],[695, 2463, 91])).
% 1.44/1.60 tff(2475,plain,
% 1.44/1.60 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.60 inference(monotonicity,[status(thm)],[2474])).
% 1.44/1.60 tff(2476,plain,
% 1.44/1.60 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.44/1.60 inference(symmetry,[status(thm)],[2475])).
% 1.44/1.60 tff(2477,plain,
% 1.44/1.60 (r(s(s(s(s(z)))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[526, 524])).
% 1.44/1.60 tff(2478,plain,
% 1.44/1.60 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[302, 170, 2477])).
% 1.44/1.60 tff(2479,plain,
% 1.44/1.60 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[271, 2478])).
% 1.44/1.60 tff(2480,plain,
% 1.44/1.60 (~b(s(z), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[615, 192, 515, 813, 2479])).
% 1.44/1.60 tff(2481,plain,
% 1.44/1.60 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.60 inference(unit_resolution,[status(thm)],[438, 60, 2480])).
% 1.44/1.61 tff(2482,plain,
% 1.44/1.61 (r(s(z), s(s(s(s(s(z))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2481, 609])).
% 1.44/1.61 tff(2483,plain,
% 1.44/1.61 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[627, 2482, 170])).
% 1.44/1.61 tff(2484,plain,
% 1.44/1.61 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[319, 2483])).
% 1.44/1.61 tff(2485,plain,
% 1.44/1.61 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[302, 170, 297])).
% 1.44/1.61 tff(2486,plain,
% 1.44/1.61 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[271, 2485])).
% 1.44/1.61 tff(2487,plain,
% 1.44/1.61 (b(s(s(s(s(s(z))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[175, 67, 170])).
% 1.44/1.61 tff(2488,plain,
% 1.44/1.61 (~r(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1072, 67, 297])).
% 1.44/1.61 tff(2489,plain,
% 1.44/1.61 (b(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[292, 2488])).
% 1.44/1.61 tff(2490,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.44/1.61 tff(2491,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2492,plain,
% 1.44/1.61 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2493,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2492])).
% 1.44/1.61 tff(2494,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2493, 2491])).
% 1.44/1.61 tff(2495,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2496,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.44/1.61 tff(2497,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2496, 192, 515, 465, 2490, 239])).
% 1.44/1.61 tff(2498,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2499,plain,
% 1.44/1.61 (~b(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2498, 2489, 2487, 2486])).
% 1.44/1.61 tff(2500,plain,
% 1.44/1.61 (r(s(z), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[351, 2499])).
% 1.44/1.61 tff(2501,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2502,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2503,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 1.44/1.61 tff(2504,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2503, 77, 2500, 67, 297])).
% 1.44/1.61 tff(2505,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2506,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2505, 170, 2477])).
% 1.44/1.61 tff(2507,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[217, 2506])).
% 1.44/1.61 tff(2508,plain,
% 1.44/1.61 (~b(s(s(s(z))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2055, 192, 2507, 2484, 395])).
% 1.44/1.61 tff(2509,plain,
% 1.44/1.61 (r(s(s(s(z))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[920, 2508])).
% 1.44/1.61 tff(2510,plain,
% 1.44/1.61 (r(elem!1, s(z))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2509, 2476])).
% 1.44/1.61 tff(2511,plain,
% 1.44/1.61 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2512,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2511])).
% 1.44/1.61 tff(2513,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2512, 255])).
% 1.44/1.61 tff(2514,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2515,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 1.44/1.61 tff(2516,plain,
% 1.44/1.61 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2515, 192, 254, 239, 238])).
% 1.44/1.61 tff(2517,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[133, 2516])).
% 1.44/1.61 tff(2518,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2519,plain,
% 1.44/1.61 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2520,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2519])).
% 1.44/1.61 tff(2521,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2520, 2518])).
% 1.44/1.61 tff(2522,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2523,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.44/1.61 tff(2524,plain,
% 1.44/1.61 (~b(s(z), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2523, 192, 515, 254, 238])).
% 1.44/1.61 tff(2525,plain,
% 1.44/1.61 (r(s(z), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[427, 2524])).
% 1.44/1.61 tff(2526,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2527,plain,
% 1.44/1.61 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2528,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2527])).
% 1.44/1.61 tff(2529,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2528, 2526])).
% 1.44/1.61 tff(2530,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2531,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 1.44/1.61 tff(2532,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2531, 77, 619, 2525, 2517])).
% 1.44/1.61 tff(2533,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2534,plain,
% 1.44/1.61 (~r(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2533, 2482, 2479, 515, 2509])).
% 1.44/1.61 tff(2535,plain,
% 1.44/1.61 (b(z, s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[292, 2534])).
% 1.44/1.61 tff(2536,plain,
% 1.44/1.61 (~b(s(s(s(s(s(z))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2498, 2535, 515, 2479])).
% 1.44/1.61 tff(2537,plain,
% 1.44/1.61 (r(s(s(s(s(s(z))))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[65, 2536])).
% 1.44/1.61 tff(2538,plain,
% 1.44/1.61 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[367, 77, 2509, 2537])).
% 1.44/1.61 tff(2539,plain,
% 1.44/1.61 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[375, 2538])).
% 1.44/1.61 tff(2540,plain,
% 1.44/1.61 (~b(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[500, 192, 813, 2479, 2539])).
% 1.44/1.61 tff(2541,plain,
% 1.44/1.61 (r(s(s(s(z))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[253, 2540])).
% 1.44/1.61 tff(2542,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2543,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2544,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 1.44/1.61 tff(2545,plain,
% 1.44/1.61 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2544, 77, 2541, 2477])).
% 1.44/1.61 tff(2546,plain,
% 1.44/1.61 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[406, 2545])).
% 1.44/1.61 tff(2547,plain,
% 1.44/1.61 (s(s(s(s(z)))) = s(elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1772, 1146])).
% 1.44/1.61 tff(2548,plain,
% 1.44/1.61 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[699, 2547])).
% 1.44/1.61 tff(2549,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1146])).
% 1.44/1.61 tff(2550,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(symmetry,[status(thm)],[2549])).
% 1.44/1.61 tff(2551,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1160])).
% 1.44/1.61 tff(2552,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2551, 2550])).
% 1.44/1.61 tff(2553,plain,
% 1.44/1.61 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2552])).
% 1.44/1.61 tff(2554,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.44/1.61 tff(2555,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[992, 985])).
% 1.44/1.61 tff(2556,plain,
% 1.44/1.61 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1330, 2555, 515, 465])).
% 1.44/1.61 tff(2557,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1313, 2556])).
% 1.44/1.61 tff(2558,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2559,plain,
% 1.44/1.61 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2560,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2559])).
% 1.44/1.61 tff(2561,plain,
% 1.44/1.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2560, 2558])).
% 1.44/1.61 tff(2562,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2563,plain,
% 1.44/1.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2562, 2561])).
% 1.44/1.61 tff(2564,plain,
% 1.44/1.61 ($false),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2563, 77, 1617, 2554, 667])).
% 1.44/1.61 tff(2565,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.61 tff(2566,plain,
% 1.44/1.61 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2565, 2557, 2554])).
% 1.44/1.61 tff(2567,plain,
% 1.44/1.61 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1628, 2566, 2471])).
% 1.44/1.61 tff(2568,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2567, 2467])).
% 1.44/1.61 tff(2569,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2570,plain,
% 1.44/1.61 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.61 inference(rewrite,[status(thm)],[])).
% 1.44/1.61 tff(2571,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[2570])).
% 1.44/1.61 tff(2572,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.61 inference(transitivity,[status(thm)],[2571, 2569])).
% 1.44/1.61 tff(2573,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.61 inference(quant_inst,[status(thm)],[])).
% 1.44/1.61 tff(2574,plain,
% 1.44/1.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 1.44/1.61 tff(2575,plain,
% 1.44/1.61 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2574, 192, 395, 394])).
% 1.44/1.61 tff(2576,plain,
% 1.44/1.61 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[2575, 2568])).
% 1.44/1.61 tff(2577,plain,
% 1.44/1.61 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2576, 2553])).
% 1.44/1.61 tff(2578,plain,
% 1.44/1.61 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[679, 2577, 2548])).
% 1.44/1.61 tff(2579,plain,
% 1.44/1.61 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[2578, 1347])).
% 1.44/1.61 tff(2580,plain,
% 1.44/1.61 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(s(z)))))), z))),
% 1.44/1.61 inference(monotonicity,[status(thm)],[1356])).
% 1.44/1.61 tff(2581,plain,
% 1.44/1.61 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.61 inference(modus_ponens,[status(thm)],[985, 2580])).
% 1.44/1.61 tff(2582,plain,
% 1.44/1.61 (b(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.61 inference(unit_resolution,[status(thm)],[1782, 60, 1779, 2581])).
% 1.44/1.61 tff(2583,plain,
% 1.44/1.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2584,plain,
% 1.44/1.62 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2585,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2584])).
% 1.44/1.62 tff(2586,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2585, 2583])).
% 1.44/1.62 tff(2587,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2588,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2587, 2586])).
% 1.44/1.62 tff(2589,plain,
% 1.44/1.62 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2588, 192, 515, 465, 813, 239, 2582])).
% 1.44/1.62 tff(2590,plain,
% 1.44/1.62 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1806, 60, 1170, 2589])).
% 1.44/1.62 tff(2591,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1801, 77, 170, 2590, 2579])).
% 1.44/1.62 tff(2592,plain,(r(s(s(s(elem!1))), z) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2593,plain,
% 1.44/1.62 (r(s(s(s(elem!1))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2592, 1146, 170, 395, 2546, 515, 2535, 813, 2479, 2510])).
% 1.44/1.62 tff(2594,plain,
% 1.44/1.62 (r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2593, 1356])).
% 1.44/1.62 tff(2595,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2596,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2597,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 1.44/1.62 tff(2598,plain,
% 1.44/1.62 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2597, 77, 2541, 2594])).
% 1.44/1.62 tff(2599,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2598, 2473])).
% 1.44/1.62 tff(2600,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1628, 2599, 2471])).
% 1.44/1.62 tff(2601,plain,
% 1.44/1.62 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2600, 2467])).
% 1.44/1.62 tff(2602,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[2551])).
% 1.44/1.62 tff(2603,plain,
% 1.44/1.62 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(monotonicity,[status(thm)],[1146])).
% 1.44/1.62 tff(2604,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.44/1.62 inference(symmetry,[status(thm)],[2603])).
% 1.44/1.62 tff(2605,plain,
% 1.44/1.62 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(elem!1), z))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2604])).
% 1.44/1.62 tff(2606,plain,
% 1.44/1.62 (~b(s(elem!1), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[524, 2605])).
% 1.44/1.62 tff(2607,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[583, 2606])).
% 1.44/1.62 tff(2608,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(elem!1), z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2609,plain,
% 1.44/1.62 (~b(s(elem!1), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2608, 1146, 524])).
% 1.44/1.62 tff(2610,plain,
% 1.44/1.62 (r(s(elem!1), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[560, 2609])).
% 1.44/1.62 tff(2611,plain,
% 1.44/1.62 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1685, 2593, 2610])).
% 1.44/1.62 tff(2612,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[679, 2611, 2548])).
% 1.44/1.62 tff(2613,plain,
% 1.44/1.62 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2612, 2549])).
% 1.44/1.62 tff(2614,plain,
% 1.44/1.62 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2613, 2602])).
% 1.44/1.62 tff(2615,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2616,plain,
% 1.44/1.62 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2617,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2616])).
% 1.44/1.62 tff(2618,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2617, 2615])).
% 1.44/1.62 tff(2619,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2620,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 1.44/1.62 tff(2621,plain,
% 1.44/1.62 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2620, 192, 2507, 2484, 395, 2546])).
% 1.44/1.62 tff(2622,plain,
% 1.44/1.62 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2621, 2614])).
% 1.44/1.62 tff(2623,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2622, 2601])).
% 1.44/1.62 tff(2624,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2625,plain,
% 1.44/1.62 (b(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2624, 2441, 295, 2462, 494, 511])).
% 1.44/1.62 tff(2626,plain,
% 1.44/1.62 (b(s(elem!1), z)),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2625, 2443])).
% 1.44/1.62 tff(2627,plain,
% 1.44/1.62 (b(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1988, 2441, 218])).
% 1.44/1.62 tff(2628,plain,
% 1.44/1.62 (~b(s(elem!1), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1239, 2627, 361, 511])).
% 1.44/1.62 tff(2629,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2628, 2626])).
% 1.44/1.62 tff(2630,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2631,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2630, 116, 39, 115])).
% 1.44/1.62 tff(2632,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[355, 77, 504, 296, 118])).
% 1.44/1.62 tff(2633,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2634,plain,
% 1.44/1.62 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2633, 504, 118])).
% 1.44/1.62 tff(2635,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[271, 2634])).
% 1.44/1.62 tff(2636,plain,
% 1.44/1.62 (~r(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[509, 504, 116])).
% 1.44/1.62 tff(2637,plain,
% 1.44/1.62 (b(s(s(s(z))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[253, 2636])).
% 1.44/1.62 tff(2638,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(2639,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.44/1.62 tff(2640,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[260, 192, 2639, 239, 2638, 221])).
% 1.44/1.62 tff(2641,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2642,plain,
% 1.44/1.62 (~b(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2641, 2637, 2635, 220])).
% 1.44/1.62 tff(2643,plain,
% 1.44/1.62 (r(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[237, 2642])).
% 1.44/1.62 tff(2644,plain,
% 1.44/1.62 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[459, 116, 118])).
% 1.44/1.62 tff(2645,plain,
% 1.44/1.62 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[319, 2644])).
% 1.44/1.62 tff(2646,plain,
% 1.44/1.62 (~r(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[262, 2635, 116, 220])).
% 1.44/1.62 tff(2647,plain,
% 1.44/1.62 (b(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[292, 2646])).
% 1.44/1.62 tff(2648,plain,
% 1.44/1.62 (~b(z, s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[471, 192, 2647, 512, 2645])).
% 1.44/1.62 tff(2649,plain,
% 1.44/1.62 (r(z, s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[339, 2648])).
% 1.44/1.62 tff(2650,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(2651,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2451, 77, 321, 383, 2650])).
% 1.44/1.62 tff(2652,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2653,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2652, 2649, 2643])).
% 1.44/1.62 tff(2654,plain,
% 1.44/1.62 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[390, 2653])).
% 1.44/1.62 tff(2655,plain,
% 1.44/1.62 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[404, 2654, 396, 220])).
% 1.44/1.62 tff(2656,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[406, 2655])).
% 1.44/1.62 tff(2657,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2658,plain,
% 1.44/1.62 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(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(z))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2659,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2658])).
% 1.44/1.62 tff(2660,plain,
% 1.44/1.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2659, 2657])).
% 1.44/1.62 tff(2661,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2662,plain,
% 1.44/1.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2661, 2660])).
% 1.44/1.62 tff(2663,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2662, 77, 2649, 2656, 2643])).
% 1.44/1.62 tff(2664,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2665,plain,
% 1.44/1.62 (~r(s(z), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2664, 2631, 218, 116, 66])).
% 1.44/1.62 tff(2666,plain,
% 1.44/1.62 (b(s(z), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[351, 2665])).
% 1.44/1.62 tff(2667,plain,
% 1.44/1.62 (~b(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[521, 192, 2666, 293, 218])).
% 1.44/1.62 tff(2668,plain,
% 1.44/1.62 (r(s(s(s(s(z)))), z)),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[526, 2667])).
% 1.44/1.62 tff(2669,plain,
% 1.44/1.62 (~b(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1153, 192, 1242, 512, 2645])).
% 1.44/1.62 tff(2670,plain,
% 1.44/1.62 (r(z, s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[292, 2669])).
% 1.44/1.62 tff(2671,plain,
% 1.44/1.62 (~r(z, s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[835, 2670, 118])).
% 1.44/1.62 tff(2672,plain,
% 1.44/1.62 (b(z, s(s(s(s(s(z))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[493, 2671])).
% 1.44/1.62 tff(2673,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2674,plain,
% 1.44/1.62 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(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(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(rewrite,[status(thm)],[])).
% 1.44/1.62 tff(2675,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2674])).
% 1.44/1.62 tff(2676,plain,
% 1.44/1.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.44/1.62 inference(transitivity,[status(thm)],[2675, 2673])).
% 1.44/1.62 tff(2677,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.62 inference(quant_inst,[status(thm)],[])).
% 1.44/1.62 tff(2678,plain,
% 1.44/1.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.44/1.62 tff(2679,plain,
% 1.44/1.62 ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2678, 192, 396, 1242, 382])).
% 1.44/1.62 tff(2680,plain,
% 1.44/1.62 (~b(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2679, 2672])).
% 1.44/1.62 tff(2681,plain,
% 1.44/1.62 (r(z, s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[237, 2680])).
% 1.44/1.62 tff(2682,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[227, 77, 2670, 116, 2681])).
% 1.44/1.62 tff(2683,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2684,plain,
% 1.44/1.62 (~b(z, s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2683, 116, 2631, 66, 218])).
% 1.44/1.62 tff(2685,plain,
% 1.44/1.62 (r(z, s(s(s(s(z)))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[339, 2684])).
% 1.44/1.62 tff(2686,plain,
% 1.44/1.62 (~r(z, s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[570, 536, 2685])).
% 1.44/1.62 tff(2687,plain,
% 1.44/1.62 (~b(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1259, 2686, 2666, 293, 461, 531])).
% 1.44/1.62 tff(2688,plain,
% 1.44/1.62 (r(s(elem!1), s(z))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[950, 2687, 115])).
% 1.44/1.62 tff(2689,plain,
% 1.44/1.62 (~r(s(s(s(z))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[901, 77, 2688, 116])).
% 1.44/1.62 tff(2690,plain,
% 1.44/1.62 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[1843, 531, 2631])).
% 1.44/1.62 tff(2691,plain,
% 1.44/1.62 ($false),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[759, 77, 668, 538, 118])).
% 1.44/1.62 tff(2692,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.62 tff(2693,plain,
% 1.44/1.62 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2692, 2688, 66])).
% 1.44/1.62 tff(2694,plain,
% 1.44/1.62 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[597, 2693, 2690])).
% 1.44/1.62 tff(2695,plain,
% 1.44/1.62 (~r(s(elem!1), s(s(s(z))))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2144, 77, 2688, 116])).
% 1.44/1.62 tff(2696,assumption,(~r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.44/1.62 tff(2697,plain,
% 1.44/1.62 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[906, 60, 2696])).
% 1.44/1.62 tff(2698,plain,
% 1.44/1.62 (b(s(s(s(z))), s(elem!1))),
% 1.44/1.62 inference(unit_resolution,[status(thm)],[2697, 903])).
% 1.44/1.62 tff(2699,plain,
% 1.44/1.62 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 1.44/1.62 inference(commutativity,[status(thm)],[])).
% 1.44/1.62 tff(2700,plain,
% 1.44/1.62 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 1.44/1.62 inference(symmetry,[status(thm)],[2699])).
% 1.44/1.62 tff(2701,plain,
% 1.44/1.62 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.44/1.62 inference(monotonicity,[status(thm)],[2700])).
% 1.44/1.62 tff(2702,plain,
% 1.44/1.62 (~(s(elem!1) = s(s(s(z))))),
% 1.44/1.62 inference(modus_ponens,[status(thm)],[903, 2701])).
% 1.44/1.62 tff(2703,assumption,(~r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 1.44/1.62 tff(2704,plain,
% 1.44/1.62 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2148, 60, 2703])).
% 1.44/1.63 tff(2705,plain,
% 1.44/1.63 (b(s(elem!1), s(s(s(z))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2704, 2702])).
% 1.44/1.63 tff(2706,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2707,plain,
% 1.44/1.63 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2708,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2707])).
% 1.44/1.63 tff(2709,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.44/1.63 tff(2710,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2711,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.44/1.63 tff(2712,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2711, 192, 582, 221, 2705, 2698])).
% 1.44/1.63 tff(2713,plain,((s(s(s(z))) = s(elem!1)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(elem!1), s(s(s(z)))) | r(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2714,plain,
% 1.44/1.63 (s(s(s(z))) = s(elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2713, 2695, 2694, 134, 2689])).
% 1.44/1.63 tff(2715,plain,
% 1.44/1.63 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.63 tff(2716,plain,
% 1.44/1.63 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2715])).
% 1.44/1.63 tff(2717,plain,
% 1.44/1.63 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2716])).
% 1.44/1.63 tff(2718,plain,
% 1.44/1.63 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2715])).
% 1.44/1.63 tff(2719,plain,
% 1.44/1.63 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2718, 2717])).
% 1.44/1.63 tff(2720,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2719])).
% 1.44/1.63 tff(2721,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2716])).
% 1.44/1.63 tff(2722,plain,
% 1.44/1.63 (r(s(s(s(s(z)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2721])).
% 1.44/1.63 tff(2723,plain,
% 1.44/1.63 ((~r(s(s(s(s(z)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2722])).
% 1.44/1.63 tff(2724,plain,
% 1.44/1.63 (b(z, s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[580, 2686])).
% 1.44/1.63 tff(2725,plain,
% 1.44/1.63 (~r(s(elem!1), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[553, 536, 2685])).
% 1.44/1.63 tff(2726,plain,
% 1.44/1.63 (b(s(elem!1), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[560, 2725])).
% 1.44/1.63 tff(2727,plain,
% 1.44/1.63 (b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1921, 115, 515, 38, 634, 39, 633])).
% 1.44/1.63 tff(2728,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2729,plain,
% 1.44/1.63 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2730,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2729])).
% 1.44/1.63 tff(2731,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2730, 2728])).
% 1.44/1.63 tff(2732,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2733,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 1.44/1.63 tff(2734,plain,
% 1.44/1.63 (~b(s(z), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2733, 192, 584, 515, 869, 38])).
% 1.44/1.63 tff(2735,plain,
% 1.44/1.63 (r(s(z), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[658, 2734, 639])).
% 1.44/1.63 tff(2736,plain,
% 1.44/1.63 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[665, 2735, 66])).
% 1.44/1.63 tff(2737,plain,
% 1.44/1.63 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[748])).
% 1.44/1.63 tff(2738,plain,
% 1.44/1.63 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2737])).
% 1.44/1.63 tff(2739,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(s(s(z)))))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2738])).
% 1.44/1.63 tff(2740,plain,
% 1.44/1.63 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2738])).
% 1.44/1.63 tff(2741,plain,
% 1.44/1.63 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2740, 1657])).
% 1.44/1.63 tff(2742,plain,
% 1.44/1.63 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2741])).
% 1.44/1.63 tff(2743,plain,
% 1.44/1.63 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2742])).
% 1.44/1.63 tff(2744,plain,
% 1.44/1.63 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[1307, 2743])).
% 1.44/1.63 tff(2745,plain,
% 1.44/1.63 (r(s(z), s(s(s(s(s(s(s(z)))))))) <=> r(s(z), s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2738])).
% 1.44/1.63 tff(2746,plain,
% 1.44/1.63 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(symmetry,[status(thm)],[2745])).
% 1.44/1.63 tff(2747,plain,
% 1.44/1.63 ((~r(s(z), s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2746])).
% 1.44/1.63 tff(2748,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[748])).
% 1.44/1.63 tff(2749,plain,
% 1.44/1.63 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2748, 703])).
% 1.44/1.63 tff(2750,plain,
% 1.44/1.63 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2749])).
% 1.44/1.63 tff(2751,plain,
% 1.44/1.63 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2314, 1586])).
% 1.44/1.63 tff(2752,plain,
% 1.44/1.63 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 1.44/1.63 tff(2753,plain,
% 1.44/1.63 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[679, 2752, 633])).
% 1.44/1.63 tff(2754,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2755,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2756,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.44/1.63 tff(2757,plain,
% 1.44/1.63 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2756, 77, 2753, 2735])).
% 1.44/1.63 tff(2758,plain,
% 1.44/1.63 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2757, 2747])).
% 1.44/1.63 tff(2759,plain,
% 1.44/1.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2760,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2761,plain,
% 1.44/1.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 1.44/1.63 tff(2762,plain,
% 1.44/1.63 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2761, 60])).
% 1.44/1.63 tff(2763,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2762, 2758, 2744])).
% 1.44/1.63 tff(2764,plain,
% 1.44/1.63 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2763, 2739])).
% 1.44/1.63 tff(2765,plain,
% 1.44/1.63 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1601])).
% 1.44/1.63 tff(2766,plain,
% 1.44/1.63 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(z))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1601])).
% 1.44/1.63 tff(2767,plain,
% 1.44/1.63 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = elem!1)),
% 1.44/1.63 inference(transitivity,[status(thm)],[2766, 2185])).
% 1.44/1.63 tff(2768,plain,
% 1.44/1.63 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(z))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2767, 2186])).
% 1.44/1.63 tff(2769,plain,
% 1.44/1.63 ((~(s(s(s(s(z)))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2768])).
% 1.44/1.63 tff(2770,plain,
% 1.44/1.63 (~(elem!1 = s(z))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[212, 2769])).
% 1.44/1.63 tff(2771,plain,
% 1.44/1.63 (~b(s(elem!1), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[959, 1586, 39])).
% 1.44/1.63 tff(2772,plain,
% 1.44/1.63 (r(s(elem!1), s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[950, 2771, 115])).
% 1.44/1.63 tff(2773,plain,
% 1.44/1.63 (~r(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1737, 545, 668])).
% 1.44/1.63 tff(2774,plain,
% 1.44/1.63 (b(z, s(z))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[292, 2773])).
% 1.44/1.63 tff(2775,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[1330, 1687, 2774, 515, 1316])).
% 1.44/1.63 tff(2776,plain,((~r(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2777,plain,
% 1.44/1.63 (~r(s(elem!1), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2776, 2753, 1316, 515, 2772])).
% 1.44/1.63 tff(2778,plain,
% 1.44/1.63 (b(s(elem!1), z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[560, 2777])).
% 1.44/1.63 tff(2779,plain,
% 1.44/1.63 (~(elem!1 = z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2170, 115])).
% 1.44/1.63 tff(2780,plain,
% 1.44/1.63 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1601])).
% 1.44/1.63 tff(2781,plain,
% 1.44/1.63 (b(s(z), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[38, 2780])).
% 1.44/1.63 tff(2782,plain,
% 1.44/1.63 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[1601])).
% 1.44/1.63 tff(2783,plain,
% 1.44/1.63 (b(s(elem!1), elem!1)),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[869, 2782])).
% 1.44/1.63 tff(2784,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.44/1.63 tff(2785,plain,
% 1.44/1.63 (s(s(elem!1)) = s(elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2784])).
% 1.44/1.63 tff(2786,plain,
% 1.44/1.63 (s(s(elem!1)) = elem!1),
% 1.44/1.63 inference(transitivity,[status(thm)],[2785, 2784])).
% 1.44/1.63 tff(2787,plain,
% 1.44/1.63 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2786])).
% 1.44/1.63 tff(2788,plain,
% 1.44/1.63 (s(s(s(elem!1))) = elem!1),
% 1.44/1.63 inference(transitivity,[status(thm)],[2787, 2784])).
% 1.44/1.63 tff(2789,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2276, 2788])).
% 1.44/1.63 tff(2790,plain,((~(s(elem!1) = elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2791,plain,
% 1.44/1.63 (~(s(elem!1) = elem!1)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2790, 2276])).
% 1.44/1.63 tff(2792,plain,
% 1.44/1.63 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.44/1.63 inference(commutativity,[status(thm)],[])).
% 1.44/1.63 tff(2793,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.44/1.63 tff(2794,plain,
% 1.44/1.63 (s(elem!1) = elem!1),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.44/1.63 tff(2795,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.44/1.63 tff(2796,plain,
% 1.44/1.63 ($false),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2795, 2794])).
% 1.44/1.63 tff(2797,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.63 tff(2798,plain,
% 1.44/1.63 (~(elem!1 = s(elem!1))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2797, 2791])).
% 1.44/1.63 tff(2799,plain,
% 1.44/1.63 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2429, 2276])).
% 1.44/1.63 tff(2800,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2801,plain,
% 1.44/1.63 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), 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(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2802,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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)))))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2801])).
% 1.44/1.63 tff(2803,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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))))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2802, 2800])).
% 1.44/1.63 tff(2804,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2805,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(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)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 1.44/1.63 tff(2806,plain,
% 1.44/1.63 (~b(elem!1, s(s(s(elem!1))))),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2805, 192, 2237, 1316, 1680])).
% 1.44/1.63 tff(2807,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 1.44/1.63 tff(2808,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2809,plain,
% 1.44/1.63 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2810,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 1.44/1.63 inference(monotonicity,[status(thm)],[2809])).
% 1.44/1.63 tff(2811,plain,
% 1.44/1.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 1.44/1.63 inference(transitivity,[status(thm)],[2810, 2808])).
% 1.44/1.63 tff(2812,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2813,plain,
% 1.44/1.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2812, 2811])).
% 1.44/1.63 tff(2814,plain,
% 1.44/1.63 (~b(elem!1, z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2813, 192, 2268, 515, 2237, 465])).
% 1.44/1.63 tff(2815,plain,
% 1.44/1.63 (r(elem!1, z)),
% 1.44/1.63 inference(unit_resolution,[status(thm)],[2354, 2814, 2184])).
% 1.44/1.63 tff(2816,plain,
% 1.44/1.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.44/1.63 inference(rewrite,[status(thm)],[])).
% 1.44/1.63 tff(2817,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.44/1.63 inference(quant_inst,[status(thm)],[])).
% 1.44/1.63 tff(2818,plain,
% 1.44/1.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.63 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 1.44/1.63 tff(2819,plain,
% 1.44/1.63 ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2818, 77])).
% 1.44/1.64 tff(2820,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2819, 2815, 1344])).
% 1.44/1.64 tff(2821,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2822,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2823,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 1.44/1.64 tff(2824,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2823, 60, 2820, 2807, 2806])).
% 1.44/1.64 tff(2825,plain,((~b(elem!1, s(z))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = z) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2826,plain,
% 1.44/1.64 (~b(elem!1, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2825, 465, 2184, 2268, 515, 2799, 1316, 1680])).
% 1.44/1.64 tff(2827,plain,
% 1.44/1.64 (r(elem!1, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1529, 2826, 1523])).
% 1.44/1.64 tff(2828,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2829,plain,
% 1.44/1.64 (((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2830,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2829])).
% 1.44/1.64 tff(2831,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2830, 2828])).
% 1.44/1.64 tff(2832,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2833,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 1.44/1.64 tff(2834,plain,
% 1.44/1.64 (~r(elem!1, s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2833, 77, 668, 2827])).
% 1.44/1.64 tff(2835,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2836,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2837,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2836, 2835])).
% 1.44/1.64 tff(2838,plain,
% 1.44/1.64 (b(elem!1, s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2837, 60, 2834, 2798])).
% 1.44/1.64 tff(2839,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2840,plain,
% 1.44/1.64 (((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2841,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2840])).
% 1.44/1.64 tff(2842,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2841, 2839])).
% 1.44/1.64 tff(2843,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2844,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 1.44/1.64 tff(2845,plain,
% 1.44/1.64 (~b(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2844, 192, 584, 2838, 583])).
% 1.44/1.64 tff(2846,plain,
% 1.44/1.64 (r(elem!1, z)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2354, 2845, 2184])).
% 1.44/1.64 tff(2847,plain,
% 1.44/1.64 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2819, 2846, 1344])).
% 1.44/1.64 tff(2848,plain,
% 1.44/1.64 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2823, 60, 2847, 2799])).
% 1.44/1.64 tff(2849,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2850,plain,
% 1.44/1.64 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2851,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2850])).
% 1.44/1.64 tff(2852,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2851, 2849])).
% 1.44/1.64 tff(2853,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2854,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.44/1.64 tff(2855,plain,
% 1.44/1.64 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2854, 77, 2846, 1344])).
% 1.44/1.64 tff(2856,plain,
% 1.44/1.64 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1628, 2855, 2276])).
% 1.44/1.64 tff(2857,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.44/1.64 tff(2858,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2859,plain,
% 1.44/1.64 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2860,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2859])).
% 1.44/1.64 tff(2861,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2860, 2858])).
% 1.44/1.64 tff(2862,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2863,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.44/1.64 tff(2864,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2863, 192, 2857, 2856, 2848, 2838, 2268, 1680])).
% 1.44/1.64 tff(2865,plain,((~b(z, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (elem!1 = z) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (elem!1 = s(z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2866,plain,
% 1.44/1.64 (~b(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2865, 2783, 2781, 2764, 1599, 2779, 584, 2778, 2772, 2770, 515, 1316])).
% 1.44/1.64 tff(2867,plain,
% 1.44/1.64 (r(z, s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[292, 2866])).
% 1.44/1.64 tff(2868,plain,
% 1.44/1.64 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1582, 2867, 39])).
% 1.44/1.64 tff(2869,plain,
% 1.44/1.64 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[217, 2868])).
% 1.44/1.64 tff(2870,plain,
% 1.44/1.64 (b(elem!1, s(z))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2869, 2765])).
% 1.44/1.64 tff(2871,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2872,plain,
% 1.44/1.64 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2873,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2872])).
% 1.44/1.64 tff(2874,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2873, 2871])).
% 1.44/1.64 tff(2875,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2876,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2875, 2874])).
% 1.44/1.64 tff(2877,plain,
% 1.44/1.64 (~b(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2876, 192, 2781, 2870, 1316, 2764])).
% 1.44/1.64 tff(2878,plain,
% 1.44/1.64 (r(s(s(s(elem!1))), elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[1628, 2877, 1599])).
% 1.44/1.64 tff(2879,plain,
% 1.44/1.64 ((elem!1 = z) <=> (z = elem!1)),
% 1.44/1.64 inference(commutativity,[status(thm)],[])).
% 1.44/1.64 tff(2880,plain,
% 1.44/1.64 ((z = elem!1) <=> (elem!1 = z)),
% 1.44/1.64 inference(symmetry,[status(thm)],[2879])).
% 1.44/1.64 tff(2881,assumption,(z = elem!1), introduced(assumption)).
% 1.44/1.64 tff(2882,plain,
% 1.44/1.64 (elem!1 = z),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2881, 2880])).
% 1.44/1.64 tff(2883,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2184, 2882])).
% 1.44/1.64 tff(2884,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2885,plain,
% 1.44/1.64 (~(z = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2884, 2779])).
% 1.44/1.64 tff(2886,plain,
% 1.44/1.64 (~(s(elem!1) = elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2790, 1599])).
% 1.44/1.64 tff(2887,plain,
% 1.44/1.64 (~(elem!1 = s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2797, 2886])).
% 1.44/1.64 tff(2888,plain,
% 1.44/1.64 (~b(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2805, 192, 2870, 1316, 2764])).
% 1.44/1.64 tff(2889,plain,
% 1.44/1.64 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2429, 1599])).
% 1.44/1.64 tff(2890,plain,
% 1.44/1.64 (r(elem!1, s(s(s(elem!1))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2823, 60, 2889, 2888])).
% 1.44/1.64 tff(2891,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2892,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2893,plain,
% 1.44/1.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 1.44/1.64 tff(2894,plain,
% 1.44/1.64 ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2893, 77])).
% 1.44/1.64 tff(2895,plain,
% 1.44/1.64 (~r(elem!1, s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2894, 2890, 2753])).
% 1.44/1.64 tff(2896,plain,
% 1.44/1.64 (b(elem!1, s(elem!1))),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2837, 60, 2895, 2887])).
% 1.44/1.64 tff(2897,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 1.44/1.64 tff(2898,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.44/1.64 tff(2899,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2900,plain,
% 1.44/1.64 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2901,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.64 inference(monotonicity,[status(thm)],[2900])).
% 1.44/1.64 tff(2902,plain,
% 1.44/1.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.64 inference(transitivity,[status(thm)],[2901, 2899])).
% 1.44/1.64 tff(2903,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(z, elem!1)))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2904,plain,
% 1.44/1.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 1.44/1.64 tff(2905,plain,
% 1.44/1.64 ($false),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2904, 192, 2898, 2857, 584, 2897])).
% 1.44/1.64 tff(2906,plain,((~b(elem!1, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.64 tff(2907,plain,
% 1.44/1.64 (~b(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2906, 2896, 584, 2783])).
% 1.44/1.64 tff(2908,plain,
% 1.44/1.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.44/1.64 inference(rewrite,[status(thm)],[])).
% 1.44/1.64 tff(2909,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.44/1.64 inference(quant_inst,[status(thm)],[])).
% 1.44/1.64 tff(2910,plain,
% 1.44/1.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.44/1.64 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 1.44/1.64 tff(2911,plain,
% 1.44/1.64 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2910, 60])).
% 1.44/1.64 tff(2912,plain,
% 1.44/1.64 (r(z, elem!1)),
% 1.44/1.64 inference(unit_resolution,[status(thm)],[2911, 2907, 2885])).
% 1.44/1.64 tff(2913,plain,
% 1.44/1.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2914,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2915,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2914, 2913])).
% 1.44/1.65 tff(2916,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2915, 77, 2912, 2878])).
% 1.44/1.65 tff(2917,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[992, 2916])).
% 1.44/1.65 tff(2918,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2919,plain,
% 1.44/1.65 (((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2920,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2919])).
% 1.44/1.65 tff(2921,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2920, 2918])).
% 1.44/1.65 tff(2922,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2923,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 1.44/1.65 tff(2924,plain,
% 1.44/1.65 (~r(z, s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2923, 77, 2912, 2878])).
% 1.44/1.65 tff(2925,plain,
% 1.44/1.65 (b(z, s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1021, 2924])).
% 1.44/1.65 tff(2926,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2927,plain,
% 1.44/1.65 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2928,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2927])).
% 1.44/1.65 tff(2929,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2928, 2926])).
% 1.44/1.65 tff(2930,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2931,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2930, 2929])).
% 1.44/1.65 tff(2932,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2931, 192, 2925, 2917, 515, 2764])).
% 1.44/1.65 tff(2933,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(s(z))))), s(z)) | b(s(s(s(elem!1))), s(elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2934,plain,
% 1.44/1.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2933, 1316, 584, 515, 39, 633, 38, 869, 115])).
% 1.44/1.65 tff(2935,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[597, 2934, 2736])).
% 1.44/1.65 tff(2936,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1582, 37, 39])).
% 1.44/1.65 tff(2937,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[217, 2936])).
% 1.44/1.65 tff(2938,plain,
% 1.44/1.65 (~b(s(elem!1), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1267, 2937, 869, 38])).
% 1.44/1.65 tff(2939,plain,
% 1.44/1.65 (r(s(elem!1), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[950, 2938, 115])).
% 1.44/1.65 tff(2940,plain,
% 1.44/1.65 (~r(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1737, 2939, 37])).
% 1.44/1.65 tff(2941,plain,
% 1.44/1.65 (b(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[560, 2940])).
% 1.44/1.65 tff(2942,plain,
% 1.44/1.65 (~b(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[592, 2941, 584, 582])).
% 1.44/1.65 tff(2943,plain,
% 1.44/1.65 (r(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[271, 2942])).
% 1.44/1.65 tff(2944,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[278, 77, 37, 2943, 66])).
% 1.44/1.65 tff(2945,plain,((~r(z, s(z))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2946,plain,
% 1.44/1.65 (~r(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2945, 2935, 584, 115, 869, 38, 39])).
% 1.44/1.65 tff(2947,plain,
% 1.44/1.65 (b(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[292, 2946])).
% 1.44/1.65 tff(2948,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1330, 2947, 515, 1316])).
% 1.44/1.65 tff(2949,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[992, 2948])).
% 1.44/1.65 tff(2950,plain,
% 1.44/1.65 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[747])).
% 1.44/1.65 tff(2951,plain,
% 1.44/1.65 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2934, 2950])).
% 1.44/1.65 tff(2952,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1685, 545, 974])).
% 1.44/1.65 tff(2953,plain,
% 1.44/1.65 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[679, 2952, 633])).
% 1.44/1.65 tff(2954,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2953])).
% 1.44/1.65 tff(2955,plain,
% 1.44/1.65 (b(s(elem!1), s(z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1316, 2954])).
% 1.44/1.65 tff(2956,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1267, 2955, 869, 38])).
% 1.44/1.65 tff(2957,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[217, 2956])).
% 1.44/1.65 tff(2958,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[83, 77, 2957, 118])).
% 1.44/1.65 tff(2959,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[111, 60, 2958, 106])).
% 1.44/1.65 tff(2960,plain,
% 1.44/1.65 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1294, 545, 296])).
% 1.44/1.65 tff(2961,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[811, 2960, 750])).
% 1.44/1.65 tff(2962,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[357, 296, 118])).
% 1.44/1.65 tff(2963,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[181, 2962])).
% 1.44/1.65 tff(2964,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[891, 192, 2963, 869, 2961, 2959])).
% 1.44/1.65 tff(2965,plain,((~r(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2966,plain,
% 1.44/1.65 (~r(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2965, 296, 66, 38, 1316, 2951, 633, 869, 2949])).
% 1.44/1.65 tff(2967,plain,
% 1.44/1.65 (b(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[560, 2966])).
% 1.44/1.65 tff(2968,plain,
% 1.44/1.65 (~b(s(elem!1), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1239, 2967, 515, 2947])).
% 1.44/1.65 tff(2969,plain,
% 1.44/1.65 (r(s(elem!1), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[950, 2968, 115])).
% 1.44/1.65 tff(2970,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[357, 296, 66])).
% 1.44/1.65 tff(2971,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[181, 2970])).
% 1.44/1.65 tff(2972,plain,
% 1.44/1.65 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[803, 2969, 66])).
% 1.44/1.65 tff(2973,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[811, 2972, 2951])).
% 1.44/1.65 tff(2974,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[893, 2973, 869, 2971, 584, 2935])).
% 1.44/1.65 tff(2975,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[526, 2974])).
% 1.44/1.65 tff(2976,plain,
% 1.44/1.65 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1337, 2967, 584, 2736, 66, 515, 1316])).
% 1.44/1.65 tff(2977,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[679, 2976, 633])).
% 1.44/1.65 tff(2978,plain,
% 1.44/1.65 (~r(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2756, 77, 2977, 2735])).
% 1.44/1.65 tff(2979,plain,
% 1.44/1.65 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1675, 60, 2978])).
% 1.44/1.65 tff(2980,plain,
% 1.44/1.65 (b(s(z), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2979, 1660])).
% 1.44/1.65 tff(2981,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2982,plain,
% 1.44/1.65 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(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(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(2983,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2982])).
% 1.44/1.65 tff(2984,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.44/1.65 inference(transitivity,[status(thm)],[2983, 2981])).
% 1.44/1.65 tff(2985,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(2986,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 1.44/1.65 tff(2987,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2986, 192, 515, 1316, 1680, 465, 512, 1745])).
% 1.44/1.65 tff(2988,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), 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(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2989,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2988, 2980, 1316, 515, 2947, 2975])).
% 1.44/1.65 tff(2990,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[217, 2989])).
% 1.44/1.65 tff(2991,plain,
% 1.44/1.65 (s(s(s(s(z)))) = s(elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[792, 2990, 2935, 2969, 39])).
% 1.44/1.65 tff(2992,plain,
% 1.44/1.65 (s(elem!1) = s(s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[2991, 774])).
% 1.44/1.65 tff(2993,plain,
% 1.44/1.65 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1363, 2977, 584, 515, 2949, 38])).
% 1.44/1.65 tff(2994,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2993, 2992])).
% 1.44/1.65 tff(2995,plain,((~r(s(s(s(s(s(z))))), z)) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(2996,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2995, 1314, 39, 515, 2727, 640, 38, 115, 633])).
% 1.44/1.65 tff(2997,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[271, 2996])).
% 1.44/1.65 tff(2998,plain,
% 1.44/1.65 (~b(s(z), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2733, 192, 640, 515, 2727, 38])).
% 1.44/1.65 tff(2999,plain,
% 1.44/1.65 (r(s(z), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[658, 2998, 639])).
% 1.44/1.65 tff(3000,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[665, 2999, 66])).
% 1.44/1.65 tff(3001,plain,
% 1.44/1.65 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2933, 1314, 640, 515, 39, 633, 38, 2727, 115])).
% 1.44/1.65 tff(3002,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[597, 3001, 3000])).
% 1.44/1.65 tff(3003,plain,
% 1.44/1.65 (~r(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2945, 3002, 640, 115, 2727, 38, 39])).
% 1.44/1.65 tff(3004,plain,
% 1.44/1.65 (b(z, s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[292, 3003])).
% 1.44/1.65 tff(3005,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1330, 3004, 515, 1314])).
% 1.44/1.65 tff(3006,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[992, 3005])).
% 1.44/1.65 tff(3007,plain,
% 1.44/1.65 (~b(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[592, 2997, 640, 3002])).
% 1.44/1.65 tff(3008,plain,
% 1.44/1.65 (r(s(elem!1), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[560, 3007])).
% 1.44/1.65 tff(3009,plain,
% 1.44/1.65 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1685, 3008, 3006])).
% 1.44/1.65 tff(3010,plain,
% 1.44/1.65 (s(s(s(elem!1))) = s(elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[679, 3009, 633])).
% 1.44/1.65 tff(3011,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3010])).
% 1.44/1.65 tff(3012,plain,
% 1.44/1.65 (b(s(elem!1), s(z))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[1314, 3011])).
% 1.44/1.65 tff(3013,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1267, 3012, 2727, 38])).
% 1.44/1.65 tff(3014,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(z))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[217, 3013])).
% 1.44/1.65 tff(3015,plain,
% 1.44/1.65 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[175, 3014, 39])).
% 1.44/1.65 tff(3016,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[181, 3015])).
% 1.44/1.65 tff(3017,plain,
% 1.44/1.65 ($false),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[875, 192, 640, 3016, 2727, 3002, 2997])).
% 1.44/1.65 tff(3018,plain,((s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(z), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(elem!1)) | (~b(s(z), z)) | r(z, s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.65 tff(3019,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3018, 2686, 39, 461, 115, 2666])).
% 1.44/1.65 tff(3020,plain,
% 1.44/1.65 (~b(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1931, 3019, 2726, 2724])).
% 1.44/1.65 tff(3021,plain,
% 1.44/1.65 (r(s(s(s(elem!1))), z)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[992, 3020])).
% 1.44/1.65 tff(3022,plain,
% 1.44/1.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3023,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3024,plain,
% 1.44/1.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 1.44/1.65 tff(3025,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3024, 77, 3021, 2668])).
% 1.44/1.65 tff(3026,plain,
% 1.44/1.65 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3025, 2723])).
% 1.44/1.65 tff(3027,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[113, 3026])).
% 1.44/1.65 tff(3028,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3027, 2720])).
% 1.44/1.65 tff(3029,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2715])).
% 1.44/1.65 tff(3030,plain,
% 1.44/1.65 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.44/1.65 inference(commutativity,[status(thm)],[])).
% 1.44/1.65 tff(3031,plain,
% 1.44/1.65 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[3030])).
% 1.44/1.65 tff(3032,plain,
% 1.44/1.65 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3031])).
% 1.44/1.65 tff(3033,plain,
% 1.44/1.65 (~(elem!1 = s(s(s(s(z)))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[853, 2690])).
% 1.44/1.65 tff(3034,plain,
% 1.44/1.65 (~(s(s(s(s(z)))) = elem!1)),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3033, 3032])).
% 1.44/1.65 tff(3035,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.65 tff(3036,plain,
% 1.44/1.65 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(symmetry,[status(thm)],[3035])).
% 1.44/1.65 tff(3037,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2718])).
% 1.44/1.65 tff(3038,plain,
% 1.44/1.65 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3037, 3036])).
% 1.44/1.65 tff(3039,plain,
% 1.44/1.65 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3038])).
% 1.44/1.65 tff(3040,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2716])).
% 1.44/1.65 tff(3041,plain,
% 1.44/1.65 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.65 tff(3042,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[376, 3041])).
% 1.44/1.65 tff(3043,plain,
% 1.44/1.65 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3042, 3040])).
% 1.44/1.65 tff(3044,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3045,plain,
% 1.44/1.65 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(rewrite,[status(thm)],[])).
% 1.44/1.65 tff(3046,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3045])).
% 1.44/1.65 tff(3047,plain,
% 1.44/1.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3046, 3044])).
% 1.44/1.65 tff(3048,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.65 inference(quant_inst,[status(thm)],[])).
% 1.44/1.65 tff(3049,plain,
% 1.44/1.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 1.44/1.65 tff(3050,plain,
% 1.44/1.65 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[3049, 192, 3019, 3043, 3028])).
% 1.44/1.65 tff(3051,plain,
% 1.44/1.65 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(modus_ponens,[status(thm)],[3050, 3039])).
% 1.44/1.65 tff(3052,plain,
% 1.44/1.65 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[406, 3051])).
% 1.44/1.65 tff(3053,plain,
% 1.44/1.65 (~(elem!1 = s(s(s(z))))),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[1993, 528])).
% 1.44/1.65 tff(3054,plain,
% 1.44/1.65 (~(s(s(s(z))) = elem!1)),
% 1.44/1.65 inference(unit_resolution,[status(thm)],[2015, 3053])).
% 1.44/1.65 tff(3055,plain,
% 1.44/1.65 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2716])).
% 1.44/1.65 tff(3056,plain,
% 1.44/1.65 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[3055])).
% 1.44/1.65 tff(3057,plain,
% 1.44/1.65 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2717])).
% 1.44/1.65 tff(3058,plain,
% 1.44/1.65 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3057, 1978])).
% 1.44/1.65 tff(3059,plain,
% 1.44/1.65 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.65 inference(symmetry,[status(thm)],[3058])).
% 1.44/1.65 tff(3060,plain,
% 1.44/1.65 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3059])).
% 1.44/1.65 tff(3061,plain,
% 1.44/1.65 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.65 tff(3062,plain,
% 1.44/1.65 (s(s(z)) = elem!1),
% 1.44/1.65 inference(transitivity,[status(thm)],[16, 3061, 682])).
% 1.44/1.65 tff(3063,plain,
% 1.44/1.65 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3062])).
% 1.44/1.65 tff(3064,plain,
% 1.44/1.65 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.65 inference(transitivity,[status(thm)],[3063, 1978])).
% 1.44/1.65 tff(3065,plain,
% 1.44/1.65 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.44/1.65 inference(monotonicity,[status(thm)],[3064])).
% 1.44/1.65 tff(3066,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.44/1.65 tff(3067,plain,
% 1.44/1.65 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3066])).
% 1.44/1.66 tff(3068,plain,
% 1.44/1.66 (s(s(s(s(z)))) = s(z)),
% 1.44/1.66 inference(transitivity,[status(thm)],[45, 3067, 10])).
% 1.44/1.66 tff(3069,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[212, 3068])).
% 1.44/1.66 tff(3070,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3071,plain,
% 1.44/1.66 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3070, 3065])).
% 1.44/1.66 tff(3072,plain,
% 1.44/1.66 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3071, 3060])).
% 1.44/1.66 tff(3073,plain,
% 1.44/1.66 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2716])).
% 1.44/1.66 tff(3074,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[66, 3073])).
% 1.44/1.66 tff(3075,plain,
% 1.44/1.66 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3062])).
% 1.44/1.66 tff(3076,plain,
% 1.44/1.66 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3075, 2186])).
% 1.44/1.66 tff(3077,plain,
% 1.44/1.66 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3076])).
% 1.44/1.66 tff(3078,plain,
% 1.44/1.66 (~(elem!1 = s(z))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[2196, 3077])).
% 1.44/1.66 tff(3079,plain,
% 1.44/1.66 (~r(elem!1, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2565, 1617, 667])).
% 1.44/1.66 tff(3080,plain,
% 1.44/1.66 (b(elem!1, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1529, 3079, 1523])).
% 1.44/1.66 tff(3081,plain,
% 1.44/1.66 (~b(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2245, 3080, 515, 465])).
% 1.44/1.66 tff(3082,plain,
% 1.44/1.66 (r(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2354, 3081, 2184])).
% 1.44/1.66 tff(3083,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2854, 77, 3082, 974, 1617])).
% 1.44/1.66 tff(3084,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (elem!1 = z) | (~b(s(z), z)) | (~b(z, s(z))) | (elem!1 = s(z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3085,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3084, 3021, 2779, 2666, 293, 3078, 3074])).
% 1.44/1.66 tff(3086,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1628, 3085, 3072])).
% 1.44/1.66 tff(3087,plain,
% 1.44/1.66 (b(s(s(s(s(s(z))))), elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3086, 3056])).
% 1.44/1.66 tff(3088,plain,
% 1.44/1.66 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2717])).
% 1.44/1.66 tff(3089,plain,
% 1.44/1.66 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3088])).
% 1.44/1.66 tff(3090,plain,
% 1.44/1.66 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1321, 3020, 2726])).
% 1.44/1.66 tff(3091,plain,
% 1.44/1.66 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[2714])).
% 1.44/1.66 tff(3092,plain,
% 1.44/1.66 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.44/1.66 inference(transitivity,[status(thm)],[3091, 2792])).
% 1.44/1.66 tff(3093,plain,
% 1.44/1.66 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3092])).
% 1.44/1.66 tff(3094,plain,
% 1.44/1.66 (~(s(elem!1) = elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3053, 3093])).
% 1.44/1.66 tff(3095,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3096,plain,
% 1.44/1.66 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3097,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3096])).
% 1.44/1.66 tff(3098,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3097, 3095])).
% 1.44/1.66 tff(3099,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3100,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3099, 3098])).
% 1.44/1.66 tff(3101,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3100, 77, 1618, 668, 2554])).
% 1.44/1.66 tff(3102,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3103,plain,
% 1.44/1.66 (~r(s(elem!1), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3102, 2554, 668])).
% 1.44/1.66 tff(3104,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.44/1.66 tff(3105,plain,
% 1.44/1.66 (~r(elem!1, s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2833, 77, 668, 2554])).
% 1.44/1.66 tff(3106,plain,
% 1.44/1.66 (b(elem!1, s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2837, 60, 3105, 2798])).
% 1.44/1.66 tff(3107,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2565, 667, 2554])).
% 1.44/1.66 tff(3108,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1628, 3107, 2276])).
% 1.44/1.66 tff(3109,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3110,plain,
% 1.44/1.66 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3111,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3110])).
% 1.44/1.66 tff(3112,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3111, 3109])).
% 1.44/1.66 tff(3113,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3114,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3113, 3112])).
% 1.44/1.66 tff(3115,plain,
% 1.44/1.66 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3114, 192, 2857, 3108, 3106])).
% 1.44/1.66 tff(3116,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[679, 3115, 3104])).
% 1.44/1.66 tff(3117,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[674, 77, 3116, 668, 667])).
% 1.44/1.66 tff(3118,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3119,plain,
% 1.44/1.66 (~b(s(elem!1), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3118, 2554, 3104, 667, 2276, 668])).
% 1.44/1.66 tff(3120,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3121,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3122,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3121, 3120])).
% 1.44/1.66 tff(3123,plain,
% 1.44/1.66 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3122, 60])).
% 1.44/1.66 tff(3124,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3123, 3119, 3103, 2795])).
% 1.44/1.66 tff(3125,plain,((~r(elem!1, s(z))) | (s(elem!1) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3126,plain,
% 1.44/1.66 (~r(elem!1, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3125, 3094, 3090, 3074, 3072, 2688])).
% 1.44/1.66 tff(3127,plain,
% 1.44/1.66 (b(elem!1, s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1529, 3126, 3078])).
% 1.44/1.66 tff(3128,plain,
% 1.44/1.66 (~b(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2245, 3127, 2666, 293])).
% 1.44/1.66 tff(3129,plain,
% 1.44/1.66 (r(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2354, 3128, 2779])).
% 1.44/1.66 tff(3130,plain,
% 1.44/1.66 (~r(elem!1, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2819, 3129, 3021])).
% 1.44/1.66 tff(3131,plain,
% 1.44/1.66 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3130, 3089])).
% 1.44/1.66 tff(3132,plain,
% 1.44/1.66 (b(elem!1, s(s(s(s(s(z))))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2227, 3131, 3071])).
% 1.44/1.66 tff(3133,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.44/1.66 tff(3134,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.44/1.66 tff(3135,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2095, 192, 3134, 2039, 3133, 440])).
% 1.44/1.66 tff(3136,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3137,plain,
% 1.44/1.66 (~b(s(s(s(z))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3136, 3132, 376, 3087])).
% 1.44/1.66 tff(3138,plain,
% 1.44/1.66 (r(s(s(s(z))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2025, 3137, 3054])).
% 1.44/1.66 tff(3139,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.44/1.66 tff(3140,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.44/1.66 tff(3141,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3142,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3143,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 1.44/1.66 tff(3144,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3143, 77, 3140, 3139, 409])).
% 1.44/1.66 tff(3145,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3146,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3145, 3138, 3052])).
% 1.44/1.66 tff(3147,plain,
% 1.44/1.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3148,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3149,plain,
% 1.44/1.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3148, 3147])).
% 1.44/1.66 tff(3150,plain,
% 1.44/1.66 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3149, 60])).
% 1.44/1.66 tff(3151,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3150, 3146, 3034])).
% 1.44/1.66 tff(3152,plain,
% 1.44/1.66 (b(s(s(elem!1)), elem!1)),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3151, 3029])).
% 1.44/1.66 tff(3153,plain,
% 1.44/1.66 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3059, 1977])).
% 1.44/1.66 tff(3154,plain,
% 1.44/1.66 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3153])).
% 1.44/1.66 tff(3155,plain,
% 1.44/1.66 (~(elem!1 = s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3071, 3154])).
% 1.44/1.66 tff(3156,plain,
% 1.44/1.66 (b(elem!1, s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2823, 60, 3130, 3155])).
% 1.44/1.66 tff(3157,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3158,plain,
% 1.44/1.66 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3159,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3158])).
% 1.44/1.66 tff(3160,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3159, 3157])).
% 1.44/1.66 tff(3161,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3162,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3161, 3160])).
% 1.44/1.66 tff(3163,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3162, 192, 3086, 3156, 3152, 3028])).
% 1.44/1.66 tff(3164,plain,(b(s(elem!1), s(s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3165,plain,
% 1.44/1.66 (b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3164, 528, 115, 39, 116])).
% 1.44/1.66 tff(3166,plain,
% 1.44/1.66 (~b(s(elem!1), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1267, 3165, 218, 461])).
% 1.44/1.66 tff(3167,plain,
% 1.44/1.66 (r(s(elem!1), s(z))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[950, 3166, 115])).
% 1.44/1.66 tff(3168,plain,
% 1.44/1.66 (~r(s(s(s(z))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[901, 77, 3167, 116])).
% 1.44/1.66 tff(3169,plain,
% 1.44/1.66 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2692, 3167, 66])).
% 1.44/1.66 tff(3170,plain,
% 1.44/1.66 (s(elem!1) = s(s(s(s(z))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[683, 774])).
% 1.44/1.66 tff(3171,plain,
% 1.44/1.66 ($false),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[528, 3170])).
% 1.44/1.66 tff(3172,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.66 tff(3173,plain,
% 1.44/1.66 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3172, 528])).
% 1.44/1.66 tff(3174,plain,
% 1.44/1.66 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1919, 77, 545, 2477])).
% 1.44/1.66 tff(3175,plain,
% 1.44/1.66 (b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[772, 60, 769, 3174])).
% 1.44/1.66 tff(3176,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3177,plain,
% 1.44/1.66 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3178,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3177])).
% 1.44/1.66 tff(3179,plain,
% 1.44/1.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3178, 3176])).
% 1.44/1.66 tff(3180,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(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(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3181,plain,
% 1.44/1.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3180, 3179])).
% 1.44/1.66 tff(3182,plain,
% 1.44/1.66 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[3181, 192, 396, 869, 3175])).
% 1.44/1.66 tff(3183,plain,
% 1.44/1.66 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[597, 3182, 1315])).
% 1.44/1.66 tff(3184,plain,
% 1.44/1.66 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3183])).
% 1.44/1.66 tff(3185,plain,
% 1.44/1.66 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3184])).
% 1.44/1.66 tff(3186,plain,
% 1.44/1.66 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.44/1.66 inference(symmetry,[status(thm)],[3185])).
% 1.44/1.66 tff(3187,plain,
% 1.44/1.66 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3183])).
% 1.44/1.66 tff(3188,plain,
% 1.44/1.66 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3187, 703])).
% 1.44/1.66 tff(3189,plain,
% 1.44/1.66 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3188, 704])).
% 1.44/1.66 tff(3190,plain,
% 1.44/1.66 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3189])).
% 1.44/1.66 tff(3191,plain,
% 1.44/1.66 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[752, 3183])).
% 1.44/1.66 tff(3192,plain,
% 1.44/1.66 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2314, 3191])).
% 1.44/1.66 tff(3193,plain,
% 1.44/1.66 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3192, 3190])).
% 1.44/1.66 tff(3194,plain,
% 1.44/1.66 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3188])).
% 1.44/1.66 tff(3195,plain,
% 1.44/1.66 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.66 inference(modus_ponens,[status(thm)],[3192, 3194])).
% 1.44/1.66 tff(3196,plain,
% 1.44/1.66 (~b(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1438, 3191, 524])).
% 1.44/1.66 tff(3197,plain,
% 1.44/1.66 (r(elem!1, z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2354, 3196, 2184])).
% 1.44/1.66 tff(3198,plain,
% 1.44/1.66 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1598, 3191])).
% 1.44/1.66 tff(3199,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.44/1.66 tff(3200,plain,
% 1.44/1.66 (~b(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1330, 1316, 515, 465])).
% 1.44/1.66 tff(3201,plain,
% 1.44/1.66 (r(s(s(s(elem!1))), z)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[992, 3200])).
% 1.44/1.66 tff(3202,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2776, 1316, 515, 545, 668])).
% 1.44/1.66 tff(3203,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[679, 3202, 3104])).
% 1.44/1.66 tff(3204,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 1.44/1.66 tff(3205,plain,
% 1.44/1.66 (~r(elem!1, s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2362, 3199, 545])).
% 1.44/1.66 tff(3206,plain,
% 1.44/1.66 (b(elem!1, s(elem!1))),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2837, 60, 3205, 3204])).
% 1.44/1.66 tff(3207,plain,
% 1.44/1.66 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[2854, 77, 3199, 974])).
% 1.44/1.66 tff(3208,plain,
% 1.44/1.66 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.66 inference(unit_resolution,[status(thm)],[1628, 3207, 2276])).
% 1.44/1.66 tff(3209,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3210,plain,
% 1.44/1.66 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.66 inference(rewrite,[status(thm)],[])).
% 1.44/1.66 tff(3211,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))))),
% 1.44/1.66 inference(monotonicity,[status(thm)],[3210])).
% 1.44/1.66 tff(3212,plain,
% 1.44/1.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.44/1.66 inference(transitivity,[status(thm)],[3211, 3209])).
% 1.44/1.66 tff(3213,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.44/1.66 inference(quant_inst,[status(thm)],[])).
% 1.44/1.66 tff(3214,plain,
% 1.44/1.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3213, 3212])).
% 1.44/1.67 tff(3215,plain,
% 1.44/1.67 (~r(s(elem!1), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3214, 77, 3199, 545])).
% 1.44/1.67 tff(3216,plain,
% 1.44/1.67 (b(s(elem!1), elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3123, 3215, 2795])).
% 1.44/1.67 tff(3217,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3114, 192, 1923, 3216, 3208, 3206])).
% 1.44/1.67 tff(3218,plain,((~r(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (s(elem!1) = elem!1) | (elem!1 = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3219,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3218, 3203, 3201, 545, 2276, 2798, 2791, 3199])).
% 1.44/1.67 tff(3220,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, z)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(z), z)) | (~r(s(elem!1), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3221,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3220, 545, 3198, 3197, 3195, 515, 668, 465])).
% 1.44/1.67 tff(3222,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1313, 3221])).
% 1.44/1.67 tff(3223,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3224,plain,
% 1.44/1.67 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3225,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3224])).
% 1.44/1.67 tff(3226,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3225, 3223])).
% 1.44/1.67 tff(3227,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3228,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3227, 3226])).
% 1.44/1.67 tff(3229,plain,
% 1.44/1.67 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3228, 77, 668, 3222])).
% 1.44/1.67 tff(3230,plain,
% 1.44/1.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3231,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3232,plain,
% 1.44/1.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3231, 3230])).
% 1.44/1.67 tff(3233,plain,
% 1.44/1.67 (b(s(elem!1), s(s(s(elem!1))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3232, 60, 3229, 3193])).
% 1.44/1.67 tff(3234,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3183])).
% 1.44/1.67 tff(3235,plain,
% 1.44/1.67 (b(s(s(s(z))), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[440, 3234])).
% 1.44/1.67 tff(3236,plain,
% 1.44/1.67 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3183])).
% 1.44/1.67 tff(3237,plain,
% 1.44/1.67 (b(s(elem!1), s(s(s(z))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[221, 3236])).
% 1.44/1.67 tff(3238,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[674, 77, 668, 3222])).
% 1.44/1.67 tff(3239,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[679, 3238, 3195])).
% 1.44/1.67 tff(3240,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3241,plain,
% 1.44/1.67 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3242,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3241])).
% 1.44/1.67 tff(3243,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3242, 3240])).
% 1.44/1.67 tff(3244,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3245,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3244, 3243])).
% 1.44/1.67 tff(3246,plain,
% 1.44/1.67 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3245, 192, 3239, 3237, 3235, 3233])).
% 1.44/1.67 tff(3247,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3248,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3249,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3248, 3247])).
% 1.44/1.67 tff(3250,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3249, 77, 116, 3222])).
% 1.44/1.67 tff(3251,plain,
% 1.44/1.67 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1958, 60, 3250])).
% 1.44/1.67 tff(3252,plain,
% 1.44/1.67 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3251, 3246])).
% 1.44/1.67 tff(3253,plain,
% 1.44/1.67 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3252])).
% 1.44/1.67 tff(3254,plain,
% 1.44/1.67 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3253, 3186])).
% 1.44/1.67 tff(3255,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[1969, 3254])).
% 1.44/1.67 tff(3256,plain,((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (elem!1 = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(s(z))))), s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3257,plain,
% 1.44/1.67 (~r(s(elem!1), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3256, 3167, 116, 2666, 293, 376, 134, 2779, 2667, 3169, 2631, 3165, 3173])).
% 1.44/1.67 tff(3258,plain,
% 1.44/1.67 (b(s(elem!1), z)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[560, 3257])).
% 1.44/1.67 tff(3259,plain,
% 1.44/1.67 (b(s(s(s(s(s(z))))), z) <=> b(s(elem!1), z)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[748])).
% 1.44/1.67 tff(3260,plain,
% 1.44/1.67 (b(s(elem!1), z) <=> b(s(s(s(s(s(z))))), z)),
% 1.44/1.67 inference(symmetry,[status(thm)],[3259])).
% 1.44/1.67 tff(3261,plain,
% 1.44/1.67 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[583, 3260])).
% 1.44/1.67 tff(3262,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[135, 3261])).
% 1.44/1.67 tff(3263,plain,((~b(s(elem!1), z)) | b(s(s(s(s(s(z))))), z) | (~(s(s(s(s(s(z))))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3264,plain,
% 1.44/1.67 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3263, 3258, 135])).
% 1.44/1.67 tff(3265,plain,
% 1.44/1.67 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[597, 3264, 3169])).
% 1.44/1.67 tff(3266,plain,
% 1.44/1.67 (~r(s(elem!1), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2144, 77, 3167, 116])).
% 1.44/1.67 tff(3267,plain,
% 1.44/1.67 (s(s(s(z))) = s(elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2713, 3265, 3266, 134, 3168])).
% 1.44/1.67 tff(3268,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3267])).
% 1.44/1.67 tff(3269,plain,
% 1.44/1.67 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3268])).
% 1.44/1.67 tff(3270,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3165, 3269])).
% 1.44/1.67 tff(3271,plain,
% 1.44/1.67 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3267])).
% 1.44/1.67 tff(3272,plain,
% 1.44/1.67 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3271])).
% 1.44/1.67 tff(3273,plain,
% 1.44/1.67 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3272])).
% 1.44/1.67 tff(3274,plain,
% 1.44/1.67 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3273])).
% 1.44/1.67 tff(3275,plain,
% 1.44/1.67 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3274])).
% 1.44/1.67 tff(3276,plain,
% 1.44/1.67 ((~r(s(s(s(s(s(z))))), s(elem!1))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3275])).
% 1.44/1.67 tff(3277,plain,
% 1.44/1.67 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3169, 3276])).
% 1.44/1.67 tff(3278,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3279,plain,
% 1.44/1.67 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3280,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3279])).
% 1.44/1.67 tff(3281,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3280, 3278])).
% 1.44/1.67 tff(3282,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3283,plain,
% 1.44/1.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.44/1.67 tff(3284,plain,
% 1.44/1.67 (~b(s(s(s(z))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3283, 192, 869, 582, 395, 440])).
% 1.44/1.67 tff(3285,plain,
% 1.44/1.67 (s(s(s(z))) = s(elem!1)),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[2697, 3284])).
% 1.44/1.67 tff(3286,plain,
% 1.44/1.67 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3285])).
% 1.44/1.67 tff(3287,plain,
% 1.44/1.67 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3286])).
% 1.44/1.67 tff(3288,plain,
% 1.44/1.67 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3287])).
% 1.44/1.67 tff(3289,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3288])).
% 1.44/1.67 tff(3290,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3285])).
% 1.44/1.67 tff(3291,plain,
% 1.44/1.67 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3285])).
% 1.44/1.67 tff(3292,plain,
% 1.44/1.67 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[440, 3291])).
% 1.44/1.67 tff(3293,plain,
% 1.44/1.67 (~b(z, s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[893, 3292, 396, 297, 869, 582])).
% 1.44/1.67 tff(3294,plain,
% 1.44/1.67 (r(z, s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[580, 3293])).
% 1.44/1.67 tff(3295,plain,
% 1.44/1.67 (r(s(s(elem!1)), z) <=> r(s(s(s(s(z)))), z)),
% 1.44/1.67 inference(monotonicity,[status(thm)],[842])).
% 1.44/1.67 tff(3296,plain,
% 1.44/1.67 (r(s(s(s(s(z)))), z) <=> r(s(s(elem!1)), z)),
% 1.44/1.67 inference(symmetry,[status(thm)],[3295])).
% 1.44/1.67 tff(3297,plain,
% 1.44/1.67 (r(s(s(elem!1)), z)),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[297, 3296])).
% 1.44/1.67 tff(3298,plain,
% 1.44/1.67 (s(elem!1) = s(s(s(z)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[840])).
% 1.44/1.67 tff(3299,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[842, 3298])).
% 1.44/1.67 tff(3300,plain,
% 1.44/1.67 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3299])).
% 1.44/1.67 tff(3301,plain,
% 1.44/1.67 (r(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[409, 3300])).
% 1.44/1.67 tff(3302,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3303,plain,
% 1.44/1.67 (((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3304,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3303])).
% 1.44/1.67 tff(3305,plain,
% 1.44/1.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.44/1.67 inference(transitivity,[status(thm)],[3304, 3302])).
% 1.44/1.67 tff(3306,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)))),
% 1.44/1.67 inference(quant_inst,[status(thm)],[])).
% 1.44/1.67 tff(3307,plain,
% 1.44/1.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3306, 3305])).
% 1.44/1.67 tff(3308,plain,
% 1.44/1.67 ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3307, 77, 562])).
% 1.44/1.67 tff(3309,plain,
% 1.44/1.67 ($false),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3308, 3301, 3297])).
% 1.44/1.67 tff(3310,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(elem!1))) | (~(s(s(s(z))) = s(elem!1))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.67 tff(3311,plain,
% 1.44/1.67 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[3310, 3294, 3285, 297])).
% 1.44/1.67 tff(3312,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[406, 3311])).
% 1.44/1.67 tff(3313,plain,
% 1.44/1.67 (b(s(s(s(s(z)))), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3312, 3290])).
% 1.44/1.67 tff(3314,plain,
% 1.44/1.67 (b(s(s(elem!1)), s(elem!1))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3313, 3289])).
% 1.44/1.67 tff(3315,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3287])).
% 1.44/1.67 tff(3316,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3315])).
% 1.44/1.67 tff(3317,plain,
% 1.44/1.67 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3286])).
% 1.44/1.67 tff(3318,plain,
% 1.44/1.67 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3317])).
% 1.44/1.67 tff(3319,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[396, 3318])).
% 1.44/1.67 tff(3320,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[3319, 3316])).
% 1.44/1.67 tff(3321,plain,
% 1.44/1.67 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.67 inference(monotonicity,[status(thm)],[3287])).
% 1.44/1.67 tff(3322,plain,
% 1.44/1.67 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.44/1.67 inference(symmetry,[status(thm)],[3321])).
% 1.44/1.67 tff(3323,plain,
% 1.44/1.67 (b(s(elem!1), s(s(elem!1)))),
% 1.44/1.67 inference(modus_ponens,[status(thm)],[869, 3322])).
% 1.44/1.67 tff(3324,plain,
% 1.44/1.67 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[856, 3285])).
% 1.44/1.67 tff(3325,plain,
% 1.44/1.67 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.67 inference(unit_resolution,[status(thm)],[679, 3324, 2319])).
% 1.44/1.67 tff(3326,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3327,plain,
% 1.44/1.67 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.67 inference(rewrite,[status(thm)],[])).
% 1.44/1.67 tff(3328,plain,
% 1.44/1.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3327])).
% 1.44/1.68 tff(3329,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3328, 3326])).
% 1.44/1.68 tff(3330,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3331,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3330, 3329])).
% 1.44/1.68 tff(3332,plain,
% 1.44/1.68 (~b(s(s(elem!1)), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3331, 192, 3325, 3323, 3320])).
% 1.44/1.68 tff(3333,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3332, 3314])).
% 1.44/1.68 tff(3334,plain,((~b(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | r(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(z))), s(elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3335,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3334, 3277, 3270, 2631, 3165, 376, 3265, 3168, 2668])).
% 1.44/1.68 tff(3336,plain,((s(elem!1) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), z) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3337,plain,
% 1.44/1.68 (s(elem!1) = s(s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3336, 135, 116, 115, 39])).
% 1.44/1.68 tff(3338,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1998, 2474])).
% 1.44/1.68 tff(3339,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3340,plain,
% 1.44/1.68 (elem!1 = s(s(s(z)))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3339, 3337])).
% 1.44/1.68 tff(3341,plain,
% 1.44/1.68 (s(s(s(z))) = elem!1),
% 1.44/1.68 inference(symmetry,[status(thm)],[3340])).
% 1.44/1.68 tff(3342,plain,
% 1.44/1.68 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3337])).
% 1.44/1.68 tff(3343,plain,
% 1.44/1.68 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3342])).
% 1.44/1.68 tff(3344,plain,
% 1.44/1.68 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3343])).
% 1.44/1.68 tff(3345,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3344, 3341])).
% 1.44/1.68 tff(3346,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3345])).
% 1.44/1.68 tff(3347,plain,
% 1.44/1.68 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3341, 3344])).
% 1.44/1.68 tff(3348,plain,
% 1.44/1.68 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.44/1.68 inference(transitivity,[status(thm)],[3347, 1976])).
% 1.44/1.68 tff(3349,plain,
% 1.44/1.68 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3348])).
% 1.44/1.68 tff(3350,plain,
% 1.44/1.68 (~(s(s(s(elem!1))) = elem!1)),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[2419, 3349])).
% 1.44/1.68 tff(3351,plain,
% 1.44/1.68 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3340])).
% 1.44/1.68 tff(3352,plain,
% 1.44/1.68 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3351])).
% 1.44/1.68 tff(3353,plain,
% 1.44/1.68 (r(elem!1, s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[116, 3352])).
% 1.44/1.68 tff(3354,plain,
% 1.44/1.68 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3337])).
% 1.44/1.68 tff(3355,plain,
% 1.44/1.68 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1613, 3337])).
% 1.44/1.68 tff(3356,plain,
% 1.44/1.68 (r(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[271, 135])).
% 1.44/1.68 tff(3357,plain,
% 1.44/1.68 (~b(s(elem!1), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2608, 3337, 2667])).
% 1.44/1.68 tff(3358,plain,
% 1.44/1.68 (r(s(elem!1), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[560, 3357])).
% 1.44/1.68 tff(3359,plain,
% 1.44/1.68 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1294, 3358, 3356])).
% 1.44/1.68 tff(3360,plain,
% 1.44/1.68 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[811, 3359, 3355])).
% 1.44/1.68 tff(3361,plain,
% 1.44/1.68 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3360, 3354])).
% 1.44/1.68 tff(3362,plain,
% 1.44/1.68 (b(s(elem!1), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1988, 1146, 512])).
% 1.44/1.68 tff(3363,plain,
% 1.44/1.68 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1267, 3362, 512, 38])).
% 1.44/1.68 tff(3364,plain,
% 1.44/1.68 (r(z, s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1259, 3362, 515, 465, 38, 3363])).
% 1.44/1.68 tff(3365,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3366,plain,
% 1.44/1.68 (((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3367,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3366])).
% 1.44/1.68 tff(3368,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3367, 3365])).
% 1.44/1.68 tff(3369,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3370,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1)))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 1.44/1.68 tff(3371,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3370, 77, 1342, 562, 974])).
% 1.44/1.68 tff(3372,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3373,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3372, 3201, 3364])).
% 1.44/1.68 tff(3374,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(elem!1))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[679, 3373, 2548])).
% 1.44/1.68 tff(3375,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3374, 2549])).
% 1.44/1.68 tff(3376,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3375, 2602])).
% 1.44/1.68 tff(3377,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[1160])).
% 1.44/1.68 tff(3378,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.68 inference(symmetry,[status(thm)],[3377])).
% 1.44/1.68 tff(3379,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[1316, 3378])).
% 1.44/1.68 tff(3380,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3381,plain,
% 1.44/1.68 (((~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(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3382,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3381])).
% 1.44/1.68 tff(3383,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3382, 3380])).
% 1.44/1.68 tff(3384,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3385,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3384, 3383])).
% 1.44/1.68 tff(3386,plain,
% 1.44/1.68 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3385, 192, 396, 512, 38, 441])).
% 1.44/1.68 tff(3387,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3386, 3379, 3376])).
% 1.44/1.68 tff(3388,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3389,plain,
% 1.44/1.68 (~b(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3388, 3361, 218, 461, 2631, 3337, 2666, 293])).
% 1.44/1.68 tff(3390,plain,
% 1.44/1.68 (r(s(s(s(elem!1))), s(z))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1313, 3389])).
% 1.44/1.68 tff(3391,plain,
% 1.44/1.68 (~r(s(s(s(elem!1))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2565, 3390, 3353])).
% 1.44/1.68 tff(3392,plain,
% 1.44/1.68 (b(s(s(s(elem!1))), elem!1)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1628, 3391, 3350])).
% 1.44/1.68 tff(3393,plain,
% 1.44/1.68 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3392, 3346])).
% 1.44/1.68 tff(3394,plain,
% 1.44/1.68 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[449, 3361, 2631, 376])).
% 1.44/1.68 tff(3395,plain,
% 1.44/1.68 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[390, 3394])).
% 1.44/1.68 tff(3396,plain,
% 1.44/1.68 (~r(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2652, 3395, 2685])).
% 1.44/1.68 tff(3397,plain,
% 1.44/1.68 (b(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[237, 3396])).
% 1.44/1.68 tff(3398,plain,
% 1.44/1.68 (~r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2456, 77, 2685, 3395])).
% 1.44/1.68 tff(3399,plain,
% 1.44/1.68 (b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[253, 3398])).
% 1.44/1.68 tff(3400,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3401,plain,
% 1.44/1.68 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3402,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3401])).
% 1.44/1.68 tff(3403,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3402, 3400])).
% 1.44/1.68 tff(3404,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3405,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 1.44/1.68 tff(3406,plain,
% 1.44/1.68 ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3405, 192, 3399, 3397, 134, 376])).
% 1.44/1.68 tff(3407,plain,
% 1.44/1.68 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3406, 3393])).
% 1.44/1.68 tff(3408,plain,
% 1.44/1.68 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1806, 60, 1170, 3407])).
% 1.44/1.68 tff(3409,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3410,plain,
% 1.44/1.68 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3411,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.44/1.68 inference(monotonicity,[status(thm)],[3410])).
% 1.44/1.68 tff(3412,plain,
% 1.44/1.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.68 inference(transitivity,[status(thm)],[3411, 3409])).
% 1.44/1.68 tff(3413,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3414,plain,
% 1.44/1.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3413, 3412])).
% 1.44/1.68 tff(3415,plain,
% 1.44/1.68 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3414, 192, 3399, 3397])).
% 1.44/1.68 tff(3416,plain,
% 1.44/1.68 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3415, 3393])).
% 1.44/1.68 tff(3417,plain,
% 1.44/1.68 (r(s(s(s(s(s(s(z)))))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[1782, 60, 1779, 3416])).
% 1.44/1.68 tff(3418,plain,
% 1.44/1.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(rewrite,[status(thm)],[])).
% 1.44/1.68 tff(3419,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 1.44/1.68 inference(quant_inst,[status(thm)],[])).
% 1.44/1.68 tff(3420,plain,
% 1.44/1.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.44/1.68 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 1.44/1.68 tff(3421,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3420, 77, 3356, 3417, 3408])).
% 1.44/1.68 tff(3422,plain,(b(s(s(s(s(s(z))))), z) | (~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.68 tff(3423,plain,
% 1.44/1.68 (b(s(s(s(s(s(z))))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[3422, 116, 115, 39])).
% 1.44/1.68 tff(3424,plain,
% 1.44/1.68 (~r(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2652, 383, 321])).
% 1.44/1.68 tff(3425,plain,
% 1.44/1.68 (b(z, s(s(s(z))))),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[237, 3424])).
% 1.44/1.68 tff(3426,plain,
% 1.44/1.68 (~b(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2641, 3425, 239, 221])).
% 1.44/1.68 tff(3427,plain,
% 1.44/1.68 (r(s(s(s(z))), z)),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[253, 3426])).
% 1.44/1.68 tff(3428,plain,
% 1.44/1.68 ($false),
% 1.44/1.68 inference(unit_resolution,[status(thm)],[2456, 77, 321, 3427, 383])).
% 1.44/1.69 tff(3429,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3430,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3429, 2685, 3423, 134])).
% 1.44/1.69 tff(3431,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[390, 3430])).
% 1.44/1.69 tff(3432,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3433,plain,
% 1.44/1.69 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3434,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3433])).
% 1.44/1.69 tff(3435,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3434, 3432])).
% 1.44/1.69 tff(3436,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3437,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3436, 3435])).
% 1.44/1.69 tff(3438,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3437, 192, 396, 465, 38, 395, 239, 2638, 221])).
% 1.44/1.69 tff(3439,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3440,plain,
% 1.44/1.69 (~b(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3439, 2631, 293, 461, 3431, 3423, 134])).
% 1.44/1.69 tff(3441,plain,
% 1.44/1.69 (r(z, s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[237, 3440])).
% 1.44/1.69 tff(3442,plain,
% 1.44/1.69 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[404, 3431, 2631, 134])).
% 1.44/1.69 tff(3443,plain,
% 1.44/1.69 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[406, 3442])).
% 1.44/1.69 tff(3444,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2662, 77, 2685, 3443, 3441])).
% 1.44/1.69 tff(3445,plain,((~r(s(s(s(z))), s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3446,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3445, 115, 39])).
% 1.44/1.69 tff(3447,plain,
% 1.44/1.69 (b(s(s(s(z))), s(z))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[920, 3446])).
% 1.44/1.69 tff(3448,plain,
% 1.44/1.69 (~r(z, s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[835, 37, 66])).
% 1.44/1.69 tff(3449,plain,
% 1.44/1.69 (b(z, s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[493, 3448])).
% 1.44/1.69 tff(3450,plain,
% 1.44/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[313, 295, 66])).
% 1.44/1.69 tff(3451,plain,
% 1.44/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[319, 3450])).
% 1.44/1.69 tff(3452,plain,
% 1.44/1.69 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3453,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3452])).
% 1.44/1.69 tff(3454,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3453, 2050])).
% 1.44/1.69 tff(3455,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3456,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(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)))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3455, 3454])).
% 1.44/1.69 tff(3457,plain,
% 1.44/1.69 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3456, 192, 2937, 3451, 3447])).
% 1.44/1.69 tff(3458,plain,
% 1.44/1.69 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[390, 3457])).
% 1.44/1.69 tff(3459,plain,
% 1.44/1.69 (~r(z, s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2460, 3458, 295, 1563])).
% 1.44/1.69 tff(3460,plain,
% 1.44/1.69 (~r(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[313, 170, 66])).
% 1.44/1.69 tff(3461,plain,
% 1.44/1.69 (b(s(z), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[319, 3460])).
% 1.44/1.69 tff(3462,plain,
% 1.44/1.69 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1267, 953, 2937, 3461])).
% 1.44/1.69 tff(3463,plain,
% 1.44/1.69 (r(s(elem!1), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[535, 3462, 528])).
% 1.44/1.69 tff(3464,plain,
% 1.44/1.69 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[543, 3463, 170])).
% 1.44/1.69 tff(3465,plain,
% 1.44/1.69 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[597, 3464, 961])).
% 1.44/1.69 tff(3466,plain,
% 1.44/1.69 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1821, 3463, 170])).
% 1.44/1.69 tff(3467,plain,
% 1.44/1.69 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[811, 3466, 960])).
% 1.44/1.69 tff(3468,plain,
% 1.44/1.69 (~b(z, s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[1811, 3467, 3449, 3465])).
% 1.44/1.69 tff(3469,plain,
% 1.44/1.69 (r(z, s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[580, 3468])).
% 1.44/1.69 tff(3470,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3471,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3472,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 1.44/1.69 tff(3473,plain,
% 1.44/1.69 ($false),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3472, 77, 562, 504, 660])).
% 1.44/1.69 tff(3474,plain,((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.44/1.69 tff(3475,plain,
% 1.44/1.69 (~r(s(z), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3474, 3469, 504])).
% 1.44/1.69 tff(3476,plain,
% 1.44/1.69 (b(s(z), s(elem!1))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[658, 3475, 651])).
% 1.44/1.69 tff(3477,plain,
% 1.44/1.69 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3456, 192, 2937, 3461, 1408])).
% 1.44/1.69 tff(3478,plain,
% 1.44/1.69 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[390, 3477])).
% 1.44/1.69 tff(3479,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3480,plain,
% 1.44/1.69 (((~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(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3481,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3480])).
% 1.44/1.69 tff(3482,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3481, 3479])).
% 1.44/1.69 tff(3483,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z))), s(s(s(s(s(z))))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3484,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3483, 3482])).
% 1.44/1.69 tff(3485,plain,
% 1.44/1.69 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3484, 77, 170, 3478])).
% 1.44/1.69 tff(3486,plain,
% 1.44/1.69 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[375, 3485])).
% 1.44/1.69 tff(3487,plain,
% 1.44/1.69 (~b(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[500, 192, 3449, 1563, 3486])).
% 1.44/1.69 tff(3488,plain,
% 1.44/1.69 (r(s(s(s(z))), z)),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[253, 3487])).
% 1.44/1.69 tff(3489,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3490,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3491,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3490, 3489])).
% 1.44/1.69 tff(3492,plain,
% 1.44/1.69 (~r(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3491, 77, 504, 3488])).
% 1.44/1.69 tff(3493,plain,
% 1.44/1.69 (b(s(z), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[427, 3492])).
% 1.44/1.69 tff(3494,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3495,plain,
% 1.44/1.69 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3496,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3495])).
% 1.44/1.69 tff(3497,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3496, 3494])).
% 1.44/1.69 tff(3498,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3499,plain,
% 1.44/1.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3498, 3497])).
% 1.44/1.69 tff(3500,plain,
% 1.44/1.69 (~b(s(elem!1), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3499, 192, 953, 1408, 3493, 3476])).
% 1.44/1.69 tff(3501,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3502,plain,
% 1.44/1.69 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3503,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3502])).
% 1.44/1.69 tff(3504,plain,
% 1.44/1.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3503, 3501])).
% 1.44/1.69 tff(3505,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.44/1.69 inference(quant_inst,[status(thm)],[])).
% 1.44/1.69 tff(3506,plain,
% 1.44/1.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 1.44/1.69 tff(3507,plain,
% 1.44/1.69 (~r(s(elem!1), s(s(s(z))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[3506, 77, 3463, 3478])).
% 1.44/1.69 tff(3508,plain,
% 1.44/1.69 (s(elem!1) = s(s(s(z)))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[2148, 60, 3507, 3500])).
% 1.44/1.69 tff(3509,plain,
% 1.44/1.69 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3508])).
% 1.44/1.69 tff(3510,plain,
% 1.44/1.69 (elem!1 = s(s(z))),
% 1.44/1.69 inference(transitivity,[status(thm)],[695, 3509, 15])).
% 1.44/1.69 tff(3511,plain,
% 1.44/1.69 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3510])).
% 1.44/1.69 tff(3512,plain,
% 1.44/1.69 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3511])).
% 1.44/1.69 tff(3513,plain,
% 1.44/1.69 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3512])).
% 1.44/1.69 tff(3514,plain,
% 1.44/1.69 (b(elem!1, z) <=> b(s(s(z)), z)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3510])).
% 1.44/1.69 tff(3515,plain,
% 1.44/1.69 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3509])).
% 1.44/1.69 tff(3516,plain,
% 1.44/1.69 (s(s(z)) = elem!1),
% 1.44/1.69 inference(transitivity,[status(thm)],[16, 3515, 682])).
% 1.44/1.69 tff(3517,plain,
% 1.44/1.69 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3516])).
% 1.44/1.69 tff(3518,plain,
% 1.44/1.69 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 1.44/1.69 inference(transitivity,[status(thm)],[3517, 2186])).
% 1.44/1.69 tff(3519,plain,
% 1.44/1.69 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3518])).
% 1.44/1.69 tff(3520,plain,
% 1.44/1.69 (~(elem!1 = s(z))),
% 1.44/1.69 inference(modus_ponens,[status(thm)],[2196, 3519])).
% 1.44/1.69 tff(3521,plain,
% 1.44/1.69 (~(elem!1 = s(s(s(s(z)))))),
% 1.44/1.69 inference(unit_resolution,[status(thm)],[853, 961])).
% 1.44/1.69 tff(3522,plain,
% 1.44/1.69 (elem!1 = s(s(z))),
% 1.44/1.69 inference(transitivity,[status(thm)],[695, 2175, 15])).
% 1.44/1.69 tff(3523,plain,
% 1.44/1.69 (b(elem!1, s(z)) <=> b(s(s(z)), s(z))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3522])).
% 1.44/1.69 tff(3524,plain,
% 1.44/1.69 (b(s(s(z)), s(z)) <=> b(elem!1, s(z))),
% 1.44/1.69 inference(symmetry,[status(thm)],[3523])).
% 1.44/1.69 tff(3525,plain,
% 1.44/1.69 ((~b(s(s(z)), s(z))) <=> (~b(elem!1, s(z)))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3524])).
% 1.44/1.69 tff(3526,plain,
% 1.44/1.69 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.44/1.69 inference(symmetry,[status(thm)],[2178])).
% 1.44/1.69 tff(3527,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.44/1.69 tff(3528,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 1.44/1.69 tff(3529,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3530,plain,
% 1.44/1.69 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))),
% 1.44/1.69 inference(rewrite,[status(thm)],[])).
% 1.44/1.69 tff(3531,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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)))))))),
% 1.44/1.69 inference(monotonicity,[status(thm)],[3530])).
% 1.44/1.69 tff(3532,plain,
% 1.44/1.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(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))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3531, 3529])).
% 1.54/1.70 tff(3533,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3534,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 1.54/1.70 tff(3535,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3534, 192, 512, 38, 1408, 3527])).
% 1.54/1.70 tff(3536,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[406, 3535])).
% 1.54/1.70 tff(3537,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.54/1.70 tff(3538,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3539,plain,
% 1.54/1.70 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3540,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3539])).
% 1.54/1.70 tff(3541,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3540, 3538])).
% 1.54/1.70 tff(3542,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3543,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 1.54/1.70 tff(3544,plain,
% 1.54/1.70 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3543, 192, 2237, 512, 38])).
% 1.54/1.70 tff(3545,plain,
% 1.54/1.70 (r(elem!1, s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2385, 3544, 3528])).
% 1.54/1.70 tff(3546,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3547,plain,
% 1.54/1.70 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3548,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3547])).
% 1.54/1.70 tff(3549,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3548, 3546])).
% 1.54/1.70 tff(3550,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3551,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3550, 3549])).
% 1.54/1.70 tff(3552,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3551, 77, 3545, 3537, 3536])).
% 1.54/1.70 tff(3553,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(z))))) | (elem!1 = s(s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3554,plain,
% 1.54/1.70 (~r(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3553, 2237, 1408, 512, 38, 3528, 3527])).
% 1.54/1.70 tff(3555,plain,
% 1.54/1.70 (b(elem!1, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2037, 3554, 1998])).
% 1.54/1.70 tff(3556,plain,
% 1.54/1.70 (b(s(s(z)), s(s(s(z))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3555, 3526])).
% 1.54/1.70 tff(3557,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3558,plain,
% 1.54/1.70 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3559,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3558])).
% 1.54/1.70 tff(3560,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3559, 3557])).
% 1.54/1.70 tff(3561,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3562,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 1.54/1.70 tff(3563,plain,
% 1.54/1.70 (~b(s(s(z)), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3562, 192, 1408, 3527, 3556])).
% 1.54/1.70 tff(3564,plain,
% 1.54/1.70 (~b(elem!1, s(z))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3563, 3525])).
% 1.54/1.70 tff(3565,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2237, 3564])).
% 1.54/1.70 tff(3566,plain,((~b(elem!1, s(z))) | (~(s(elem!1) = s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3567,plain,
% 1.54/1.70 (~b(elem!1, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3566, 3508, 1408, 3493, 3053, 2937, 3461, 3521])).
% 1.54/1.70 tff(3568,plain,
% 1.54/1.70 (r(elem!1, s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[1529, 3567, 3520])).
% 1.54/1.70 tff(3569,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3570,plain,
% 1.54/1.70 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3571,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3570])).
% 1.54/1.70 tff(3572,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3571, 3569])).
% 1.54/1.70 tff(3573,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3574,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z)))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3573, 3572])).
% 1.54/1.70 tff(3575,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3574, 77, 3199, 37, 2554])).
% 1.54/1.70 tff(3576,plain,((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3577,plain,
% 1.54/1.70 (~r(elem!1, z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3576, 3568, 37])).
% 1.54/1.70 tff(3578,plain,
% 1.54/1.70 (b(elem!1, z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2354, 3577, 2184])).
% 1.54/1.70 tff(3579,plain,
% 1.54/1.70 (b(s(s(z)), z)),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3578, 3514])).
% 1.54/1.70 tff(3580,plain,
% 1.54/1.70 (~r(s(s(s(z))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[123, 117, 66])).
% 1.54/1.70 tff(3581,plain,
% 1.54/1.70 (b(s(s(s(z))), s(z))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[920, 3580])).
% 1.54/1.70 tff(3582,plain,
% 1.54/1.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2008, 170, 117])).
% 1.54/1.70 tff(3583,plain,
% 1.54/1.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[390, 3582])).
% 1.54/1.70 tff(3584,plain,
% 1.54/1.70 ($false),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[2055, 192, 464, 38, 3583, 3581])).
% 1.54/1.70 tff(3585,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.70 tff(3586,plain,
% 1.54/1.70 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3585, 3461, 170, 39])).
% 1.54/1.70 tff(3587,plain,
% 1.54/1.70 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[133, 3586])).
% 1.54/1.70 tff(3588,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3589,plain,
% 1.54/1.70 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3590,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3589])).
% 1.54/1.70 tff(3591,plain,
% 1.54/1.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3590, 3588])).
% 1.54/1.70 tff(3592,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3593,plain,
% 1.54/1.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3592, 3591])).
% 1.54/1.70 tff(3594,plain,
% 1.54/1.70 (~b(z, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3593, 192, 3449, 3587, 3486])).
% 1.54/1.70 tff(3595,plain,
% 1.54/1.70 (r(z, s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[237, 3594])).
% 1.54/1.70 tff(3596,plain,
% 1.54/1.70 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3534, 192, 2937, 3461, 1408, 3493])).
% 1.54/1.70 tff(3597,plain,
% 1.54/1.70 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[406, 3596])).
% 1.54/1.70 tff(3598,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3599,plain,
% 1.54/1.70 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 1.54/1.70 inference(rewrite,[status(thm)],[])).
% 1.54/1.70 tff(3600,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 1.54/1.70 inference(monotonicity,[status(thm)],[3599])).
% 1.54/1.70 tff(3601,plain,
% 1.54/1.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 1.54/1.70 inference(transitivity,[status(thm)],[3600, 3598])).
% 1.54/1.70 tff(3602,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.70 inference(quant_inst,[status(thm)],[])).
% 1.54/1.70 tff(3603,plain,
% 1.54/1.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))),
% 1.54/1.70 inference(modus_ponens,[status(thm)],[3602, 3601])).
% 1.54/1.70 tff(3604,plain,
% 1.54/1.70 (~r(s(s(s(s(z)))), z)),
% 1.54/1.70 inference(unit_resolution,[status(thm)],[3603, 77, 3597, 3595])).
% 1.54/1.71 tff(3605,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[526, 3604])).
% 1.54/1.71 tff(3606,plain,
% 1.54/1.71 (~r(z, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2460, 3478, 170, 1563])).
% 1.54/1.71 tff(3607,plain,
% 1.54/1.71 (b(z, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[339, 3606])).
% 1.54/1.71 tff(3608,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3609,plain,
% 1.54/1.71 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3610,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3609])).
% 1.54/1.71 tff(3611,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3610, 3608])).
% 1.54/1.71 tff(3612,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3613,plain,
% 1.54/1.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 1.54/1.71 tff(3614,plain,
% 1.54/1.71 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3613, 192, 3607, 3605, 3579])).
% 1.54/1.71 tff(3615,plain,
% 1.54/1.71 (~b(elem!1, s(s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3614, 3513])).
% 1.54/1.71 tff(3616,plain,
% 1.54/1.71 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3508])).
% 1.54/1.71 tff(3617,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3616])).
% 1.54/1.71 tff(3618,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3617])).
% 1.54/1.71 tff(3619,plain,
% 1.54/1.71 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3617, 3510])).
% 1.54/1.71 tff(3620,plain,
% 1.54/1.71 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3619])).
% 1.54/1.71 tff(3621,plain,
% 1.54/1.71 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3620])).
% 1.54/1.71 tff(3622,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3070, 3621])).
% 1.54/1.71 tff(3623,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3617])).
% 1.54/1.71 tff(3624,plain,
% 1.54/1.71 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3623])).
% 1.54/1.71 tff(3625,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[66, 3624])).
% 1.54/1.71 tff(3626,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2565, 3568, 3625])).
% 1.54/1.71 tff(3627,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1628, 3626, 3622])).
% 1.54/1.71 tff(3628,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3627, 3618])).
% 1.54/1.71 tff(3629,plain,
% 1.54/1.71 (~r(elem!1, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2047, 3628, 170, 3053, 3478])).
% 1.54/1.71 tff(3630,plain,
% 1.54/1.71 (b(elem!1, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2385, 3629, 3521])).
% 1.54/1.71 tff(3631,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3630, 3615])).
% 1.54/1.71 tff(3632,plain,((~b(s(elem!1), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (elem!1 = z) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (s(elem!1) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3633,plain,
% 1.54/1.71 (~b(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3632, 528, 2779, 37, 3447, 639, 504, 295, 39])).
% 1.54/1.71 tff(3634,plain,
% 1.54/1.71 (r(s(elem!1), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[950, 3633, 115])).
% 1.54/1.71 tff(3635,plain,
% 1.54/1.71 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2692, 3634, 66])).
% 1.54/1.71 tff(3636,plain,
% 1.54/1.71 (~r(s(elem!1), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1737, 3634, 37])).
% 1.54/1.71 tff(3637,plain,
% 1.54/1.71 (b(s(elem!1), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[560, 3636])).
% 1.54/1.71 tff(3638,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3639,plain,
% 1.54/1.71 (((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3640,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3639])).
% 1.54/1.71 tff(3641,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3640, 3638])).
% 1.54/1.71 tff(3642,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3643,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 1.54/1.71 tff(3644,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3643, 77, 562, 668, 37])).
% 1.54/1.71 tff(3645,plain,((~r(z, s(z))) | (~r(z, s(elem!1))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3646,plain,
% 1.54/1.71 (~r(z, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3645, 3634, 37])).
% 1.54/1.71 tff(3647,plain,
% 1.54/1.71 (b(z, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[580, 3646])).
% 1.54/1.71 tff(3648,plain,
% 1.54/1.71 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[592, 3647, 1563, 3637])).
% 1.54/1.71 tff(3649,plain,
% 1.54/1.71 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[597, 3648, 3635])).
% 1.54/1.71 tff(3650,plain,
% 1.54/1.71 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3649])).
% 1.54/1.71 tff(3651,plain,
% 1.54/1.71 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3650])).
% 1.54/1.71 tff(3652,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(s(z)))))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3651])).
% 1.54/1.71 tff(3653,plain,
% 1.54/1.71 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3649])).
% 1.54/1.71 tff(3654,plain,
% 1.54/1.71 (b(s(elem!1), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3653])).
% 1.54/1.71 tff(3655,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(elem!1), s(s(s(z))))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3654])).
% 1.54/1.71 tff(3656,plain,
% 1.54/1.71 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3585, 3451, 295, 39])).
% 1.54/1.71 tff(3657,plain,
% 1.54/1.71 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[133, 3656])).
% 1.54/1.71 tff(3658,plain,
% 1.54/1.71 (b(s(elem!1), s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3657, 3655])).
% 1.54/1.71 tff(3659,plain,
% 1.54/1.71 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3649])).
% 1.54/1.71 tff(3660,plain,
% 1.54/1.71 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3659, 703])).
% 1.54/1.71 tff(3661,plain,
% 1.54/1.71 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3660, 704])).
% 1.54/1.71 tff(3662,plain,
% 1.54/1.71 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3661])).
% 1.54/1.71 tff(3663,plain,
% 1.54/1.71 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[752, 3649])).
% 1.54/1.71 tff(3664,plain,
% 1.54/1.71 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2314, 3663])).
% 1.54/1.71 tff(3665,plain,
% 1.54/1.71 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3664, 3662])).
% 1.54/1.71 tff(3666,plain,
% 1.54/1.71 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3649])).
% 1.54/1.71 tff(3667,plain,
% 1.54/1.71 (s(s(s(s(z)))) = elem!1),
% 1.54/1.71 inference(transitivity,[status(thm)],[45, 3666, 682])).
% 1.54/1.71 tff(3668,plain,
% 1.54/1.71 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(elem!1), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3667])).
% 1.54/1.71 tff(3669,plain,
% 1.54/1.71 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2125, 3663, 294])).
% 1.54/1.71 tff(3670,plain,
% 1.54/1.71 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[535, 3669, 528])).
% 1.54/1.71 tff(3671,plain,
% 1.54/1.71 (r(s(elem!1), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3670, 3668])).
% 1.54/1.71 tff(3672,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1598, 3663])).
% 1.54/1.71 tff(3673,plain,
% 1.54/1.71 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3667])).
% 1.54/1.71 tff(3674,plain,
% 1.54/1.71 (b(s(z), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3451, 3673])).
% 1.54/1.71 tff(3675,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1229, 3664, 66, 37])).
% 1.54/1.71 tff(3676,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1313, 3675])).
% 1.54/1.71 tff(3677,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3667])).
% 1.54/1.71 tff(3678,plain,
% 1.54/1.71 (b(elem!1, s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2937, 3677])).
% 1.54/1.71 tff(3679,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2294, 3678, 3676, 3674])).
% 1.54/1.71 tff(3680,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1628, 3679, 3672])).
% 1.54/1.71 tff(3681,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.71 tff(3682,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3683,plain,
% 1.54/1.71 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3684,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3683])).
% 1.54/1.71 tff(3685,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3684, 3682])).
% 1.54/1.71 tff(3686,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3687,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3686, 3685])).
% 1.54/1.71 tff(3688,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3687, 77, 1618, 1617, 3681])).
% 1.54/1.71 tff(3689,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3690,plain,
% 1.54/1.71 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3689, 3680, 3671])).
% 1.54/1.71 tff(3691,plain,
% 1.54/1.71 (b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3232, 60, 3690, 3665])).
% 1.54/1.71 tff(3692,plain,
% 1.54/1.71 (b(s(s(s(z))), s(elem!1)) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3653])).
% 1.54/1.71 tff(3693,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3692])).
% 1.54/1.71 tff(3694,plain,
% 1.54/1.71 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3484, 77, 295, 3458])).
% 1.54/1.71 tff(3695,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[375, 3694])).
% 1.54/1.71 tff(3696,plain,
% 1.54/1.71 (b(s(s(s(z))), s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3695, 3693])).
% 1.54/1.71 tff(3697,plain,
% 1.54/1.71 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3660])).
% 1.54/1.71 tff(3698,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3664, 3697])).
% 1.54/1.71 tff(3699,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1623, 3680, 3671])).
% 1.54/1.71 tff(3700,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[679, 3699, 3698])).
% 1.54/1.71 tff(3701,plain,
% 1.54/1.71 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3245, 192, 3700])).
% 1.54/1.71 tff(3702,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3701, 3696, 3691, 3658])).
% 1.54/1.71 tff(3703,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3667])).
% 1.54/1.71 tff(3704,plain,
% 1.54/1.71 (r(s(s(s(z))), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3458, 3703])).
% 1.54/1.71 tff(3705,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3706,plain,
% 1.54/1.71 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3707,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3706])).
% 1.54/1.71 tff(3708,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3707, 3705])).
% 1.54/1.71 tff(3709,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3710,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3709, 3708])).
% 1.54/1.71 tff(3711,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3710, 77, 3680, 3704])).
% 1.54/1.71 tff(3712,plain,
% 1.54/1.71 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1958, 60, 3711])).
% 1.54/1.71 tff(3713,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3712, 3702])).
% 1.54/1.71 tff(3714,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3713])).
% 1.54/1.71 tff(3715,plain,
% 1.54/1.71 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3714, 3652])).
% 1.54/1.71 tff(3716,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1969, 3715])).
% 1.54/1.71 tff(3717,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3718,plain,
% 1.54/1.71 (s(elem!1) = s(s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3717, 504, 294, 115, 37, 39])).
% 1.54/1.71 tff(3719,plain,
% 1.54/1.71 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3718])).
% 1.54/1.71 tff(3720,plain,
% 1.54/1.71 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3719])).
% 1.54/1.71 tff(3721,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3720])).
% 1.54/1.71 tff(3722,plain,
% 1.54/1.71 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3721])).
% 1.54/1.71 tff(3723,plain,
% 1.54/1.71 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3722])).
% 1.54/1.71 tff(3724,plain,
% 1.54/1.71 (elem!1 = s(s(s(z)))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3339, 3718])).
% 1.54/1.71 tff(3725,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3720, 3724])).
% 1.54/1.71 tff(3726,plain,
% 1.54/1.71 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3720])).
% 1.54/1.71 tff(3727,plain,
% 1.54/1.71 (s(s(s(z))) = elem!1),
% 1.54/1.71 inference(symmetry,[status(thm)],[3724])).
% 1.54/1.71 tff(3728,plain,
% 1.54/1.71 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3727, 3726])).
% 1.54/1.71 tff(3729,plain,
% 1.54/1.71 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(transitivity,[status(thm)],[3728, 1976])).
% 1.54/1.71 tff(3730,plain,
% 1.54/1.71 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3729])).
% 1.54/1.71 tff(3731,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[2419, 3730])).
% 1.54/1.71 tff(3732,plain,
% 1.54/1.71 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3724])).
% 1.54/1.71 tff(3733,plain,
% 1.54/1.71 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3732])).
% 1.54/1.71 tff(3734,plain,
% 1.54/1.71 (~b(s(s(s(z))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[500, 192, 3449, 1563, 3695])).
% 1.54/1.71 tff(3735,plain,
% 1.54/1.71 (r(s(s(s(z))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[253, 3734])).
% 1.54/1.71 tff(3736,plain,
% 1.54/1.71 (~r(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3491, 77, 504, 3735])).
% 1.54/1.71 tff(3737,plain,
% 1.54/1.71 (b(s(z), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[427, 3736])).
% 1.54/1.71 tff(3738,plain,
% 1.54/1.71 (b(s(z), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3737, 3733])).
% 1.54/1.71 tff(3739,plain,
% 1.54/1.71 (r(z, s(elem!1)) <=> r(z, s(s(s(s(z)))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[1146])).
% 1.54/1.71 tff(3740,plain,
% 1.54/1.71 (r(z, s(s(s(s(z))))) <=> r(z, s(elem!1))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3739])).
% 1.54/1.71 tff(3741,plain,
% 1.54/1.71 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3740])).
% 1.54/1.71 tff(3742,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.71 tff(3743,plain,
% 1.54/1.71 (~r(z, s(elem!1))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3742, 3741])).
% 1.54/1.71 tff(3744,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[562, 3743])).
% 1.54/1.71 tff(3745,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(z, s(elem!1))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3746,plain,
% 1.54/1.71 (~r(z, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3745, 3718, 3459])).
% 1.54/1.71 tff(3747,plain,
% 1.54/1.71 (b(z, s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[580, 3746])).
% 1.54/1.71 tff(3748,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1174, 3747, 1563, 66, 2937, 3451, 3718])).
% 1.54/1.71 tff(3749,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1313, 3748])).
% 1.54/1.71 tff(3750,plain,
% 1.54/1.71 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3724])).
% 1.54/1.71 tff(3751,plain,
% 1.54/1.71 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.71 inference(symmetry,[status(thm)],[3750])).
% 1.54/1.71 tff(3752,plain,
% 1.54/1.71 (b(elem!1, s(z))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3447, 3751])).
% 1.54/1.71 tff(3753,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2294, 3752, 3749, 3738])).
% 1.54/1.71 tff(3754,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1628, 3753, 3731])).
% 1.54/1.71 tff(3755,plain,
% 1.54/1.71 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3754, 3725])).
% 1.54/1.71 tff(3756,plain,
% 1.54/1.71 (~b(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3593, 192, 3449, 3657, 3695])).
% 1.54/1.71 tff(3757,plain,
% 1.54/1.71 (r(z, s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[237, 3756])).
% 1.54/1.71 tff(3758,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3759,plain,
% 1.54/1.71 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3760,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3759])).
% 1.54/1.71 tff(3761,plain,
% 1.54/1.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.54/1.71 inference(transitivity,[status(thm)],[3760, 3758])).
% 1.54/1.71 tff(3762,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 1.54/1.71 inference(quant_inst,[status(thm)],[])).
% 1.54/1.71 tff(3763,plain,
% 1.54/1.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 1.54/1.71 tff(3764,plain,
% 1.54/1.71 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3763, 77, 3757, 3755])).
% 1.54/1.71 tff(3765,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), z)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3764, 3723])).
% 1.54/1.71 tff(3766,plain,
% 1.54/1.71 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3718])).
% 1.54/1.71 tff(3767,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3766])).
% 1.54/1.71 tff(3768,plain,
% 1.54/1.71 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3534, 192, 2937, 3451, 3447, 3737])).
% 1.54/1.71 tff(3769,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[406, 3768])).
% 1.54/1.71 tff(3770,plain,
% 1.54/1.71 (~r(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3603, 77, 3769, 3757])).
% 1.54/1.71 tff(3771,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[526, 3770])).
% 1.54/1.71 tff(3772,plain,
% 1.54/1.71 (b(s(elem!1), z)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3771, 3767])).
% 1.54/1.71 tff(3773,plain,
% 1.54/1.71 (s(s(s(s(z)))) = s(elem!1)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1772, 3718])).
% 1.54/1.71 tff(3774,plain,
% 1.54/1.71 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[699, 3773])).
% 1.54/1.71 tff(3775,plain,
% 1.54/1.71 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3718])).
% 1.54/1.71 tff(3776,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3775])).
% 1.54/1.71 tff(3777,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3724])).
% 1.54/1.71 tff(3778,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3777])).
% 1.54/1.71 tff(3779,plain,
% 1.54/1.71 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 1.54/1.71 inference(transitivity,[status(thm)],[3778, 3776])).
% 1.54/1.71 tff(3780,plain,
% 1.54/1.71 (r(s(elem!1), elem!1)),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[3769, 3779])).
% 1.54/1.71 tff(3781,plain,
% 1.54/1.71 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1623, 3754, 3780])).
% 1.54/1.71 tff(3782,plain,
% 1.54/1.71 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[679, 3781, 3774])).
% 1.54/1.71 tff(3783,plain,
% 1.54/1.71 (~b(s(s(s(elem!1))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[1931, 3782, 3772, 3747])).
% 1.54/1.71 tff(3784,plain,
% 1.54/1.71 (r(s(s(s(elem!1))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[992, 3783])).
% 1.54/1.71 tff(3785,plain,
% 1.54/1.71 ($false),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3784, 3765])).
% 1.54/1.71 tff(3786,plain,((~r(s(z), z)) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.71 tff(3787,plain,
% 1.54/1.71 (~r(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3786, 294, 115, 37, 39])).
% 1.54/1.71 tff(3788,plain,
% 1.54/1.71 (b(s(z), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[351, 2073])).
% 1.54/1.71 tff(3789,plain,
% 1.54/1.71 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3456, 192, 2937, 3461, 3447])).
% 1.54/1.71 tff(3790,plain,
% 1.54/1.71 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[390, 3789])).
% 1.54/1.71 tff(3791,plain,
% 1.54/1.71 (~r(z, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[2460, 3790, 170, 1563])).
% 1.54/1.71 tff(3792,plain,
% 1.54/1.71 (b(z, s(s(s(s(z)))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[339, 3791])).
% 1.54/1.71 tff(3793,plain,
% 1.54/1.71 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[3484, 77, 170, 3790])).
% 1.54/1.71 tff(3794,plain,
% 1.54/1.71 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[375, 3793])).
% 1.54/1.71 tff(3795,plain,
% 1.54/1.71 (~b(s(s(s(z))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[500, 192, 3449, 1563, 3794])).
% 1.54/1.71 tff(3796,plain,
% 1.54/1.71 (r(s(s(s(z))), z)),
% 1.54/1.71 inference(unit_resolution,[status(thm)],[253, 3795])).
% 1.54/1.71 tff(3797,plain,
% 1.54/1.71 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.71 inference(transitivity,[status(thm)],[45, 1057, 691])).
% 1.54/1.71 tff(3798,plain,
% 1.54/1.71 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3797])).
% 1.54/1.71 tff(3799,plain,
% 1.54/1.71 (b(s(s(elem!1)), z) <=> b(s(s(s(s(z)))), z)),
% 1.54/1.71 inference(symmetry,[status(thm)],[3798])).
% 1.54/1.71 tff(3800,plain,
% 1.54/1.71 ((~b(s(s(elem!1)), z)) <=> (~b(s(s(s(s(z)))), z))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3799])).
% 1.54/1.71 tff(3801,plain,
% 1.54/1.71 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3797])).
% 1.54/1.71 tff(3802,plain,
% 1.54/1.71 (b(z, s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[1242, 3801])).
% 1.54/1.71 tff(3803,plain,
% 1.54/1.71 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3797])).
% 1.54/1.71 tff(3804,plain,
% 1.54/1.71 (b(s(z), s(s(elem!1)))),
% 1.54/1.71 inference(modus_ponens,[status(thm)],[38, 3803])).
% 1.54/1.71 tff(3805,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.54/1.71 tff(3806,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.54/1.71 tff(3807,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.54/1.71 tff(3808,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3809,plain,
% 1.54/1.71 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.71 inference(rewrite,[status(thm)],[])).
% 1.54/1.71 tff(3810,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 1.54/1.71 inference(monotonicity,[status(thm)],[3809])).
% 1.54/1.71 tff(3811,plain,
% 1.54/1.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3810, 3808])).
% 1.54/1.72 tff(3812,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3813,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3812, 3811])).
% 1.54/1.72 tff(3814,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3813, 192, 515, 3807, 3806, 3805])).
% 1.54/1.72 tff(3815,plain,((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3816,plain,
% 1.54/1.72 (~b(s(s(elem!1)), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3815, 3804, 3788, 3802])).
% 1.54/1.72 tff(3817,plain,
% 1.54/1.72 (~b(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3816, 3800])).
% 1.54/1.72 tff(3818,plain,
% 1.54/1.72 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3797])).
% 1.54/1.72 tff(3819,plain,
% 1.54/1.72 (s(s(s(z))) = s(elem!1)),
% 1.54/1.72 inference(transitivity,[status(thm)],[92, 3818, 1046])).
% 1.54/1.72 tff(3820,plain,
% 1.54/1.72 (r(s(s(s(z))), z) <=> r(s(elem!1), z)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.72 tff(3821,plain,
% 1.54/1.72 (r(s(elem!1), z)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[503, 3820])).
% 1.54/1.72 tff(3822,plain,
% 1.54/1.72 (~r(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1737, 545, 37])).
% 1.54/1.72 tff(3823,plain,
% 1.54/1.72 (~(s(elem!1) = s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2076, 545, 2073])).
% 1.54/1.72 tff(3824,plain,
% 1.54/1.72 (b(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[950, 3823, 3822])).
% 1.54/1.72 tff(3825,plain,
% 1.54/1.72 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1267, 3824, 512, 38])).
% 1.54/1.72 tff(3826,plain,
% 1.54/1.72 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[535, 3825, 528])).
% 1.54/1.72 tff(3827,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1761, 77, 545, 3826, 297])).
% 1.54/1.72 tff(3828,plain,((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | r(s(z), z) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3829,plain,
% 1.54/1.72 (~r(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3828, 3821, 37, 512, 38, 2073, 528])).
% 1.54/1.72 tff(3830,plain,
% 1.54/1.72 (b(s(s(s(s(z)))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[526, 3829])).
% 1.54/1.72 tff(3831,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3830, 3817])).
% 1.54/1.72 tff(3832,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | r(s(z), z) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3833,plain,
% 1.54/1.72 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3832, 528, 2937, 3461, 2073, 37, 3796, 3792])).
% 1.54/1.72 tff(3834,plain,
% 1.54/1.72 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1229, 3833, 66, 37])).
% 1.54/1.72 tff(3835,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1313, 3834])).
% 1.54/1.72 tff(3836,plain,
% 1.54/1.72 ((~(s(elem!1) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(elem!1)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2699])).
% 1.54/1.72 tff(3837,plain,
% 1.54/1.72 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[2172])).
% 1.54/1.72 tff(3838,plain,
% 1.54/1.72 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3837])).
% 1.54/1.72 tff(3839,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3838])).
% 1.54/1.72 tff(3840,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.72 inference(symmetry,[status(thm)],[3839])).
% 1.54/1.72 tff(3841,plain,
% 1.54/1.72 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3840])).
% 1.54/1.72 tff(3842,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[39, 3841])).
% 1.54/1.72 tff(3843,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1316, 3842])).
% 1.54/1.72 tff(3844,plain,((~(s(elem!1) = s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3845,plain,
% 1.54/1.72 (~(s(elem!1) = s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3844, 1316, 39])).
% 1.54/1.72 tff(3846,plain,
% 1.54/1.72 (~(s(s(s(z))) = s(elem!1))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3845, 3836])).
% 1.54/1.72 tff(3847,plain,
% 1.54/1.72 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1267, 953, 512, 3461])).
% 1.54/1.72 tff(3848,plain,
% 1.54/1.72 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[535, 3847, 528])).
% 1.54/1.72 tff(3849,plain,
% 1.54/1.72 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[543, 3848, 170])).
% 1.54/1.72 tff(3850,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[597, 3849, 961])).
% 1.54/1.72 tff(3851,plain,
% 1.54/1.72 (~r(s(elem!1), s(s(s(z))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3506, 77, 3848, 383])).
% 1.54/1.72 tff(3852,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3853,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3854,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 1.54/1.72 tff(3855,plain,
% 1.54/1.72 (~r(s(s(s(z))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3854, 77, 3848, 383])).
% 1.54/1.72 tff(3856,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2713, 3855, 3851, 903, 3587, 3850])).
% 1.54/1.72 tff(3857,plain,((~b(s(elem!1), s(z))) | (s(s(s(z))) = s(elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(elem!1) = 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,[]))).
% 1.54/1.72 tff(3858,plain,
% 1.54/1.72 (~b(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3857, 3846, 3790, 170, 528, 2937, 39])).
% 1.54/1.72 tff(3859,plain,
% 1.54/1.72 (r(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[950, 3858, 115])).
% 1.54/1.72 tff(3860,plain,
% 1.54/1.72 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2692, 3859, 66])).
% 1.54/1.72 tff(3861,plain,
% 1.54/1.72 (~r(s(elem!1), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1737, 3859, 37])).
% 1.54/1.72 tff(3862,plain,
% 1.54/1.72 (b(s(elem!1), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[560, 3861])).
% 1.54/1.72 tff(3863,plain,
% 1.54/1.72 (~r(z, s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3645, 3859, 37])).
% 1.54/1.72 tff(3864,plain,
% 1.54/1.72 (b(z, s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[580, 3863])).
% 1.54/1.72 tff(3865,plain,
% 1.54/1.72 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[592, 3864, 1563, 3862])).
% 1.54/1.72 tff(3866,plain,
% 1.54/1.72 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[597, 3865, 3860])).
% 1.54/1.72 tff(3867,plain,
% 1.54/1.72 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3866])).
% 1.54/1.72 tff(3868,plain,
% 1.54/1.72 (s(s(s(s(z)))) = elem!1),
% 1.54/1.72 inference(transitivity,[status(thm)],[45, 3867, 682])).
% 1.54/1.72 tff(3869,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3868])).
% 1.54/1.72 tff(3870,plain,
% 1.54/1.72 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3869])).
% 1.54/1.72 tff(3871,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1392, 192, 1316, 2937, 3461])).
% 1.54/1.72 tff(3872,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3871, 3870])).
% 1.54/1.72 tff(3873,plain,
% 1.54/1.72 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1628, 3872, 2276])).
% 1.54/1.72 tff(3874,plain,
% 1.54/1.72 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3018, 3863, 39, 3461, 115, 515])).
% 1.54/1.72 tff(3875,plain,
% 1.54/1.72 (~b(s(s(s(elem!1))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1931, 3874, 3862, 3864])).
% 1.54/1.72 tff(3876,plain,
% 1.54/1.72 (r(s(s(s(elem!1))), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[992, 3875])).
% 1.54/1.72 tff(3877,plain,
% 1.54/1.72 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3868])).
% 1.54/1.72 tff(3878,plain,
% 1.54/1.72 (b(z, elem!1)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3792, 3877])).
% 1.54/1.72 tff(3879,plain,
% 1.54/1.72 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3868])).
% 1.54/1.72 tff(3880,plain,
% 1.54/1.72 (b(s(z), elem!1)),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3461, 3879])).
% 1.54/1.72 tff(3881,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3882,plain,
% 1.54/1.72 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3883,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3882])).
% 1.54/1.72 tff(3884,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3883, 3881])).
% 1.54/1.72 tff(3885,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3886,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 1.54/1.72 tff(3887,plain,
% 1.54/1.72 ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3886, 192])).
% 1.54/1.72 tff(3888,plain,
% 1.54/1.72 (~b(elem!1, z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3887, 3880, 515, 3878])).
% 1.54/1.72 tff(3889,plain,
% 1.54/1.72 (r(elem!1, z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2354, 3888, 2779])).
% 1.54/1.72 tff(3890,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2854, 77, 3889, 3876, 3873])).
% 1.54/1.72 tff(3891,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), z)) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3892,plain,
% 1.54/1.72 (s(s(s(elem!1))) = elem!1),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3891, 3835, 3788, 39, 115, 37, 170, 528])).
% 1.54/1.72 tff(3893,plain,
% 1.54/1.72 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1598, 3892])).
% 1.54/1.72 tff(3894,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3895,plain,
% 1.54/1.72 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3896,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3895])).
% 1.54/1.72 tff(3897,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3896, 3894])).
% 1.54/1.72 tff(3898,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3899,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 1.54/1.72 tff(3900,plain,
% 1.54/1.72 (~b(s(z), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3899, 192, 515, 583, 3792, 3461])).
% 1.54/1.72 tff(3901,plain,
% 1.54/1.72 (r(s(z), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[658, 3900, 639])).
% 1.54/1.72 tff(3902,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3903,plain,
% 1.54/1.72 (((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3904,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3903])).
% 1.54/1.72 tff(3905,plain,
% 1.54/1.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3904, 3902])).
% 1.54/1.72 tff(3906,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3907,plain,
% 1.54/1.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))),
% 1.54/1.72 inference(modus_ponens,[status(thm)],[3906, 3905])).
% 1.54/1.72 tff(3908,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3907, 77, 562, 37, 660])).
% 1.54/1.72 tff(3909,plain,((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3910,plain,
% 1.54/1.72 (~r(z, s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3909, 3901, 37])).
% 1.54/1.72 tff(3911,plain,
% 1.54/1.72 (b(z, s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[580, 3910])).
% 1.54/1.72 tff(3912,plain,
% 1.54/1.72 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[752, 750])).
% 1.54/1.72 tff(3913,plain,
% 1.54/1.72 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[665, 3901, 66])).
% 1.54/1.72 tff(3914,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[597, 3913, 3912])).
% 1.54/1.72 tff(3915,plain,
% 1.54/1.72 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1481, 192, 583, 3449, 1563])).
% 1.54/1.72 tff(3916,plain,
% 1.54/1.72 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[811, 3915, 750])).
% 1.54/1.72 tff(3917,plain,
% 1.54/1.72 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1821, 3916, 170])).
% 1.54/1.72 tff(3918,plain,
% 1.54/1.72 (b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[535, 3917, 528])).
% 1.54/1.72 tff(3919,plain,
% 1.54/1.72 ($false),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[2945, 3918, 3914, 115, 37, 3911, 3461, 39])).
% 1.54/1.72 tff(3920,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.72 tff(3921,plain,
% 1.54/1.72 (~b(s(elem!1), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[3920, 528, 37, 39, 115, 170, 3893, 3788])).
% 1.54/1.72 tff(3922,plain,
% 1.54/1.72 (r(s(elem!1), z)),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[560, 3921])).
% 1.54/1.72 tff(3923,plain,
% 1.54/1.72 (~r(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1737, 3922, 37])).
% 1.54/1.72 tff(3924,plain,
% 1.54/1.72 (b(s(elem!1), s(z))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[950, 3923, 115])).
% 1.54/1.72 tff(3925,plain,
% 1.54/1.72 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1267, 3924, 2937, 3461])).
% 1.54/1.72 tff(3926,plain,
% 1.54/1.72 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[535, 3925, 528])).
% 1.54/1.72 tff(3927,plain,
% 1.54/1.72 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[1821, 3926, 170])).
% 1.54/1.72 tff(3928,plain,
% 1.54/1.72 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[811, 3927, 3893])).
% 1.54/1.72 tff(3929,plain,
% 1.54/1.72 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[752, 3893])).
% 1.54/1.72 tff(3930,plain,
% 1.54/1.72 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[543, 3926, 170])).
% 1.54/1.72 tff(3931,plain,
% 1.54/1.72 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.72 inference(unit_resolution,[status(thm)],[597, 3930, 3929])).
% 1.54/1.72 tff(3932,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3933,plain,
% 1.54/1.72 (((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z)))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.72 inference(rewrite,[status(thm)],[])).
% 1.54/1.72 tff(3934,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.54/1.72 inference(monotonicity,[status(thm)],[3933])).
% 1.54/1.72 tff(3935,plain,
% 1.54/1.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.72 inference(transitivity,[status(thm)],[3934, 3932])).
% 1.54/1.72 tff(3936,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.72 inference(quant_inst,[status(thm)],[])).
% 1.54/1.72 tff(3937,plain,
% 1.54/1.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3936, 3935])).
% 1.54/1.73 tff(3938,plain,
% 1.54/1.73 (~b(s(elem!1), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3937, 192, 3924, 3931, 3928, 3447, 3587])).
% 1.54/1.73 tff(3939,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3940,plain,
% 1.54/1.73 (((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3941,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3940])).
% 1.54/1.73 tff(3942,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3941, 3939])).
% 1.54/1.73 tff(3943,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3944,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3943, 3942])).
% 1.54/1.73 tff(3945,plain,
% 1.54/1.73 (~r(s(elem!1), s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3944, 77, 3922, 3796])).
% 1.54/1.73 tff(3946,plain,
% 1.54/1.73 (~(s(elem!1) = s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3844, 3835, 39])).
% 1.54/1.73 tff(3947,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[2148, 60, 3946, 3945, 3938])).
% 1.54/1.73 tff(3948,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z)) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3949,plain,
% 1.54/1.73 (s(elem!1) = s(s(s(s(z))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3948, 295, 115, 37, 39, 3787])).
% 1.54/1.73 tff(3950,plain,
% 1.54/1.73 (~r(z, s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3745, 3949, 3459])).
% 1.54/1.73 tff(3951,plain,
% 1.54/1.73 (b(z, s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[580, 3950])).
% 1.54/1.73 tff(3952,plain,
% 1.54/1.73 (b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[351, 3787])).
% 1.54/1.73 tff(3953,plain,
% 1.54/1.73 (b(s(elem!1), z) <=> b(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3949])).
% 1.54/1.73 tff(3954,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), z) <=> b(s(elem!1), z)),
% 1.54/1.73 inference(symmetry,[status(thm)],[3953])).
% 1.54/1.73 tff(3955,plain,
% 1.54/1.73 (b(s(elem!1), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1988, 3949, 2937])).
% 1.54/1.73 tff(3956,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3018, 3950, 39, 3451, 115, 3952])).
% 1.54/1.73 tff(3957,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1174, 3951, 1563, 66, 2937, 3451, 3949])).
% 1.54/1.73 tff(3958,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1313, 3957])).
% 1.54/1.73 tff(3959,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3960,plain,
% 1.54/1.73 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3961,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3960])).
% 1.54/1.73 tff(3962,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3961, 3959])).
% 1.54/1.73 tff(3963,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3964,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 1.54/1.73 tff(3965,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3964, 192, 1923, 1005, 515, 1316, 953])).
% 1.54/1.73 tff(3966,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(3967,plain,
% 1.54/1.73 (~b(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3966, 3958, 3952, 3956, 3955])).
% 1.54/1.73 tff(3968,plain,
% 1.54/1.73 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1160, 1345])).
% 1.54/1.73 tff(3969,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[3968])).
% 1.54/1.73 tff(3970,plain,
% 1.54/1.73 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1159])).
% 1.54/1.73 tff(3971,plain,
% 1.54/1.73 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[2474, 3970])).
% 1.54/1.73 tff(3972,plain,
% 1.54/1.73 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(symmetry,[status(thm)],[3971])).
% 1.54/1.73 tff(3973,plain,
% 1.54/1.73 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3972])).
% 1.54/1.73 tff(3974,plain,
% 1.54/1.73 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[1969, 3973])).
% 1.54/1.73 tff(3975,plain,
% 1.54/1.73 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[718, 3974])).
% 1.54/1.73 tff(3976,plain,
% 1.54/1.73 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[708, 3975])).
% 1.54/1.73 tff(3977,plain,
% 1.54/1.73 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1346])).
% 1.54/1.73 tff(3978,plain,
% 1.54/1.73 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(monotonicity,[status(thm)],[1160])).
% 1.54/1.73 tff(3979,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.73 inference(symmetry,[status(thm)],[3978])).
% 1.54/1.73 tff(3980,plain,
% 1.54/1.73 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(s(s(s(z)))))), z))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3979])).
% 1.54/1.73 tff(3981,plain,
% 1.54/1.73 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[984, 3980])).
% 1.54/1.73 tff(3982,plain,
% 1.54/1.73 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1782, 60, 1779])).
% 1.54/1.73 tff(3983,plain,
% 1.54/1.73 (r(s(s(s(s(s(s(z)))))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3982, 3981])).
% 1.54/1.73 tff(3984,plain,
% 1.54/1.73 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1360, 77, 3983, 297])).
% 1.54/1.73 tff(3985,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3984, 3977])).
% 1.54/1.73 tff(3986,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[679, 3985, 3976])).
% 1.54/1.73 tff(3987,plain,
% 1.54/1.73 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3986, 3969])).
% 1.54/1.73 tff(3988,plain,
% 1.54/1.73 (r(s(s(s(elem!1))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[992, 984])).
% 1.54/1.73 tff(3989,plain,
% 1.54/1.73 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[982, 3988, 37])).
% 1.54/1.73 tff(3990,plain,
% 1.54/1.73 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1313, 3989])).
% 1.54/1.73 tff(3991,plain,
% 1.54/1.73 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3990, 3378])).
% 1.54/1.73 tff(3992,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3993,plain,
% 1.54/1.73 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(3994,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3993])).
% 1.54/1.73 tff(3995,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[3994, 3992])).
% 1.54/1.73 tff(3996,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(3997,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3996, 3995])).
% 1.54/1.73 tff(3998,plain,
% 1.54/1.73 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3997, 192, 512, 38, 3991])).
% 1.54/1.73 tff(3999,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[3998, 3987])).
% 1.54/1.73 tff(4000,plain,(b(s(s(s(elem!1))), z) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4001,plain,
% 1.54/1.73 (~r(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4000, 3967, 37, 3451, 2937, 3949])).
% 1.54/1.73 tff(4002,plain,
% 1.54/1.73 (b(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[526, 4001])).
% 1.54/1.73 tff(4003,plain,
% 1.54/1.73 (b(s(elem!1), z)),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4002, 3954])).
% 1.54/1.73 tff(4004,plain,
% 1.54/1.73 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[3949])).
% 1.54/1.73 tff(4005,plain,
% 1.54/1.73 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.54/1.73 inference(symmetry,[status(thm)],[4004])).
% 1.54/1.73 tff(4006,plain,
% 1.54/1.73 (b(s(z), s(elem!1))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[3451, 4005])).
% 1.54/1.73 tff(4007,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[649, 4006, 4003, 3952, 3951])).
% 1.54/1.73 tff(4008,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z))))) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4009,plain,
% 1.54/1.73 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4008, 37, 39, 115])).
% 1.54/1.73 tff(4010,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4011,plain,
% 1.54/1.73 (((~r(z, s(s(s(s(z)))))) | (~r(s(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)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4012,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4011])).
% 1.54/1.73 tff(4013,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4012, 4010])).
% 1.54/1.73 tff(4014,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4015,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4014, 4013])).
% 1.54/1.73 tff(4016,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4015, 77, 504, 321, 308])).
% 1.54/1.73 tff(4017,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4018,plain,
% 1.54/1.73 (~r(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4017, 504, 308])).
% 1.54/1.73 tff(4019,plain,
% 1.54/1.73 (b(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[339, 4018])).
% 1.54/1.73 tff(4020,plain,
% 1.54/1.73 (~b(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[1753, 4019, 239, 396])).
% 1.54/1.73 tff(4021,plain,
% 1.54/1.73 (r(s(s(s(s(z)))), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[526, 4020])).
% 1.54/1.73 tff(4022,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4023,plain,
% 1.54/1.73 (((~r(s(s(s(s(z)))), z)) | (~r(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)))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4024,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4023])).
% 1.54/1.73 tff(4025,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4024, 4022])).
% 1.54/1.73 tff(4026,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4027,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4026, 4025])).
% 1.54/1.73 tff(4028,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4027, 77, 504, 308, 4021])).
% 1.54/1.73 tff(4029,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4030,plain,
% 1.54/1.73 (~r(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4029, 308, 239, 396])).
% 1.54/1.73 tff(4031,plain,
% 1.54/1.73 (b(s(z), z)),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[351, 4030])).
% 1.54/1.73 tff(4032,plain,
% 1.54/1.73 (~b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[615, 192, 4031, 813, 239])).
% 1.54/1.73 tff(4033,plain,
% 1.54/1.73 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[438, 60, 4032, 380])).
% 1.54/1.73 tff(4034,plain,
% 1.54/1.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4035,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.73 tff(4036,plain,
% 1.54/1.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.54/1.73 inference(modus_ponens,[status(thm)],[4035, 4034])).
% 1.54/1.73 tff(4037,plain,
% 1.54/1.73 ($false),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4036, 77, 321, 37, 308])).
% 1.54/1.73 tff(4038,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.73 tff(4039,plain,
% 1.54/1.73 (~r(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[4038, 308, 37])).
% 1.54/1.73 tff(4040,plain,
% 1.54/1.73 (b(z, s(s(s(s(z)))))),
% 1.54/1.73 inference(unit_resolution,[status(thm)],[339, 4039])).
% 1.54/1.73 tff(4041,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4042,plain,
% 1.54/1.73 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(rewrite,[status(thm)],[])).
% 1.54/1.73 tff(4043,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.54/1.73 inference(monotonicity,[status(thm)],[4042])).
% 1.54/1.73 tff(4044,plain,
% 1.54/1.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.73 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.54/1.73 tff(4045,plain,
% 1.54/1.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.73 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4046,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.54/1.74 tff(4047,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4046, 192, 396, 1242, 813, 441])).
% 1.54/1.74 tff(4048,plain,((~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(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4049,plain,
% 1.54/1.74 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4048, 4040, 396, 813])).
% 1.54/1.74 tff(4050,plain,
% 1.54/1.74 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[113, 4049])).
% 1.54/1.74 tff(4051,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[457, 77, 308, 4050, 4033])).
% 1.54/1.74 tff(4052,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4053,plain,
% 1.54/1.74 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4052, 4009, 3449, 37, 1563])).
% 1.54/1.74 tff(4054,plain,
% 1.54/1.74 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[319, 4053])).
% 1.54/1.74 tff(4055,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[3456, 192, 2937, 4054, 3447])).
% 1.54/1.74 tff(4056,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[390, 4055])).
% 1.54/1.74 tff(4057,plain,
% 1.54/1.74 (~r(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2652, 321, 4056])).
% 1.54/1.74 tff(4058,plain,
% 1.54/1.74 (b(z, s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[237, 4057])).
% 1.54/1.74 tff(4059,plain,
% 1.54/1.74 (~r(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2456, 77, 321, 4056])).
% 1.54/1.74 tff(4060,plain,
% 1.54/1.74 (b(s(s(s(z))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[253, 4059])).
% 1.54/1.74 tff(4061,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4062,plain,
% 1.54/1.74 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4063,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4062])).
% 1.54/1.74 tff(4064,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4063, 4061])).
% 1.54/1.74 tff(4065,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4066,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 1.54/1.74 tff(4067,plain,
% 1.54/1.74 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4066, 192, 4060, 3449, 1563, 4058])).
% 1.54/1.74 tff(4068,plain,
% 1.54/1.74 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[375, 4067])).
% 1.54/1.74 tff(4069,plain,
% 1.54/1.74 (b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[535, 2118, 528])).
% 1.54/1.74 tff(4070,plain,
% 1.54/1.74 (~r(s(elem!1), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2109, 545, 504])).
% 1.54/1.74 tff(4071,plain,
% 1.54/1.74 (b(s(elem!1), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[950, 4070, 115])).
% 1.54/1.74 tff(4072,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1267, 4071, 4069, 512, 38])).
% 1.54/1.74 tff(4073,plain,((~r(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4074,plain,
% 1.54/1.74 (~r(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4073, 321, 4054, 115, 2937, 504, 528])).
% 1.54/1.74 tff(4075,plain,
% 1.54/1.74 (b(s(elem!1), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[560, 4074])).
% 1.54/1.74 tff(4076,plain,
% 1.54/1.74 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1481, 192, 4075, 3449, 1563])).
% 1.54/1.74 tff(4077,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.74 tff(4078,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4079,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4080,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4079, 4078])).
% 1.54/1.74 tff(4081,plain,
% 1.54/1.74 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4080, 77, 321, 4077])).
% 1.54/1.74 tff(4082,plain,
% 1.54/1.74 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4083,plain,
% 1.54/1.74 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4082, 30])).
% 1.54/1.74 tff(4084,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4085,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4086,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4085, 4084])).
% 1.54/1.74 tff(4087,plain,
% 1.54/1.74 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4086, 60, 4083, 4081])).
% 1.54/1.74 tff(4088,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4089,plain,
% 1.54/1.74 (((~r(s(s(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(s(s(z)))))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4090,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4089])).
% 1.54/1.74 tff(4091,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4090, 4088])).
% 1.54/1.74 tff(4092,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(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(s(s(z))))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4093,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4092, 4091])).
% 1.54/1.74 tff(4094,plain,
% 1.54/1.74 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4093, 77, 321, 4077])).
% 1.54/1.74 tff(4095,plain,
% 1.54/1.74 ((z = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 1.54/1.74 inference(commutativity,[status(thm)],[])).
% 1.54/1.74 tff(4096,plain,
% 1.54/1.74 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(symmetry,[status(thm)],[4095])).
% 1.54/1.74 tff(4097,plain,
% 1.54/1.74 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4096])).
% 1.54/1.74 tff(4098,plain,
% 1.54/1.74 (~(z = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4083, 4097])).
% 1.54/1.74 tff(4099,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4100,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4101,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4100, 4099])).
% 1.54/1.74 tff(4102,plain,
% 1.54/1.74 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4101, 60])).
% 1.54/1.74 tff(4103,plain,
% 1.54/1.74 (b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4102, 4098])).
% 1.54/1.74 tff(4104,plain,
% 1.54/1.74 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4103, 4094])).
% 1.54/1.74 tff(4105,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4106,plain,
% 1.54/1.74 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4107,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4106])).
% 1.54/1.74 tff(4108,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4107, 4105])).
% 1.54/1.74 tff(4109,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4110,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 1.54/1.74 tff(4111,plain,
% 1.54/1.74 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4110, 77, 383, 4077])).
% 1.54/1.74 tff(4112,plain,
% 1.54/1.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4113,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4114,plain,
% 1.54/1.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 1.54/1.74 tff(4115,plain,
% 1.54/1.74 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4114, 60])).
% 1.54/1.74 tff(4116,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4115, 1969])).
% 1.54/1.74 tff(4117,plain,
% 1.54/1.74 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4116, 4111])).
% 1.54/1.74 tff(4118,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4119,plain,
% 1.54/1.74 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4120,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4119])).
% 1.54/1.74 tff(4121,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.54/1.74 inference(transitivity,[status(thm)],[4120, 4118])).
% 1.54/1.74 tff(4122,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4123,plain,
% 1.54/1.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4122, 4121])).
% 1.54/1.74 tff(4124,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4123, 192, 2458, 4117, 4104, 4087])).
% 1.54/1.74 tff(4125,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4126,plain,
% 1.54/1.74 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4125, 321, 4056])).
% 1.54/1.74 tff(4127,plain,
% 1.54/1.74 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1598, 723])).
% 1.54/1.74 tff(4128,plain,
% 1.54/1.74 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[725, 1433])).
% 1.54/1.74 tff(4129,plain,
% 1.54/1.74 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(symmetry,[status(thm)],[4128])).
% 1.54/1.74 tff(4130,plain,
% 1.54/1.74 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[4129])).
% 1.54/1.74 tff(4131,assumption,(~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.74 tff(4132,plain,
% 1.54/1.74 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4131, 4130])).
% 1.54/1.74 tff(4133,plain,
% 1.54/1.74 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2314, 723])).
% 1.54/1.74 tff(4134,plain,
% 1.54/1.74 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1229, 4133, 118, 37])).
% 1.54/1.74 tff(4135,plain,
% 1.54/1.74 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1313, 4134])).
% 1.54/1.74 tff(4136,plain,
% 1.54/1.74 (b(elem!1, s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1433])).
% 1.54/1.74 tff(4137,plain,
% 1.54/1.74 (b(s(s(s(s(z)))), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.74 inference(symmetry,[status(thm)],[4136])).
% 1.54/1.74 tff(4138,plain,
% 1.54/1.74 (b(elem!1, s(z))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[512, 4137])).
% 1.54/1.74 tff(4139,plain,
% 1.54/1.74 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(z)))))),
% 1.54/1.74 inference(monotonicity,[status(thm)],[1433])).
% 1.54/1.74 tff(4140,plain,
% 1.54/1.74 (b(s(z), s(s(s(s(z))))) <=> b(s(z), elem!1)),
% 1.54/1.74 inference(symmetry,[status(thm)],[4139])).
% 1.54/1.74 tff(4141,plain,
% 1.54/1.74 (b(s(z), elem!1)),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[38, 4140])).
% 1.54/1.74 tff(4142,plain,
% 1.54/1.74 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[2294, 4141, 4138, 4135])).
% 1.54/1.74 tff(4143,plain,
% 1.54/1.74 ($false),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[1628, 4142, 4132, 4127])).
% 1.54/1.74 tff(4144,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.74 tff(4145,plain,
% 1.54/1.74 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4144, 4126, 2937, 4054, 66, 37])).
% 1.54/1.74 tff(4146,plain,
% 1.54/1.74 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[811, 4145, 4076])).
% 1.54/1.74 tff(4147,plain,
% 1.54/1.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(rewrite,[status(thm)],[])).
% 1.54/1.74 tff(4148,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z))))))),
% 1.54/1.74 inference(quant_inst,[status(thm)],[])).
% 1.54/1.74 tff(4149,plain,
% 1.54/1.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(z)))))),
% 1.54/1.74 inference(modus_ponens,[status(thm)],[4148, 4147])).
% 1.54/1.74 tff(4150,plain,
% 1.54/1.74 (~r(s(elem!1), s(s(s(z))))),
% 1.54/1.74 inference(unit_resolution,[status(thm)],[4149, 77, 4146, 4068])).
% 1.54/1.74 tff(4151,plain,
% 1.54/1.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4152,plain,
% 1.54/1.75 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4153,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4152])).
% 1.54/1.75 tff(4154,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4153, 4151])).
% 1.54/1.75 tff(4155,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4156,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4155, 4154])).
% 1.54/1.75 tff(4157,plain,
% 1.54/1.75 (~b(s(elem!1), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4156, 192, 4075, 4060, 4058])).
% 1.54/1.75 tff(4158,plain,
% 1.54/1.75 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2148, 60, 4157])).
% 1.54/1.75 tff(4159,plain,
% 1.54/1.75 (s(elem!1) = s(s(s(z)))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4158, 4150])).
% 1.54/1.75 tff(4160,plain,
% 1.54/1.75 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4159])).
% 1.54/1.75 tff(4161,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.54/1.75 inference(symmetry,[status(thm)],[4160])).
% 1.54/1.75 tff(4162,plain,
% 1.54/1.75 (s(s(z)) = elem!1),
% 1.54/1.75 inference(transitivity,[status(thm)],[16, 4161, 682])).
% 1.54/1.75 tff(4163,plain,
% 1.54/1.75 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4162])).
% 1.54/1.75 tff(4164,plain,
% 1.54/1.75 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[4163])).
% 1.54/1.75 tff(4165,plain,
% 1.54/1.75 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[752, 4145])).
% 1.54/1.75 tff(4166,plain,
% 1.54/1.75 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[853, 4165])).
% 1.54/1.75 tff(4167,plain,
% 1.54/1.75 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3429, 321, 1563, 4056])).
% 1.54/1.75 tff(4168,plain,
% 1.54/1.75 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[133, 4167])).
% 1.54/1.75 tff(4169,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4170,plain,
% 1.54/1.75 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4171,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4170])).
% 1.54/1.75 tff(4172,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4171, 4169])).
% 1.54/1.75 tff(4173,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4174,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4173, 4172])).
% 1.54/1.75 tff(4175,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4174, 77, 118, 408, 117])).
% 1.54/1.75 tff(4176,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4177,plain,
% 1.54/1.75 (~r(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4176, 4168, 66])).
% 1.54/1.75 tff(4178,plain,
% 1.54/1.75 (b(s(z), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[427, 4177])).
% 1.54/1.75 tff(4179,plain,
% 1.54/1.75 (~b(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3566, 4159, 3447, 4178, 3053, 2937, 4054, 4166])).
% 1.54/1.75 tff(4180,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3534, 192, 2937, 4054, 3447, 4178])).
% 1.54/1.75 tff(4181,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[406, 4180])).
% 1.54/1.75 tff(4182,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4183,plain,
% 1.54/1.75 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4184,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4183])).
% 1.54/1.75 tff(4185,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4184, 4182])).
% 1.54/1.75 tff(4186,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4187,plain,
% 1.54/1.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 1.54/1.75 tff(4188,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4187, 77, 4181, 4168])).
% 1.54/1.75 tff(4189,plain,
% 1.54/1.75 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[113, 4188])).
% 1.54/1.75 tff(4190,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4191,plain,
% 1.54/1.75 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), 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))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4192,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4191])).
% 1.54/1.75 tff(4193,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4192, 4190])).
% 1.54/1.75 tff(4194,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4195,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4194, 4193])).
% 1.54/1.75 tff(4196,plain,
% 1.54/1.75 (~b(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4195, 192, 3449, 4189, 1563])).
% 1.54/1.75 tff(4197,plain,
% 1.54/1.75 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3844, 4159, 39])).
% 1.54/1.75 tff(4198,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1313, 4197])).
% 1.54/1.75 tff(4199,plain,
% 1.54/1.75 (~r(s(s(s(elem!1))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[982, 4198, 37])).
% 1.54/1.75 tff(4200,plain,
% 1.54/1.75 (s(s(elem!1)) = s(s(s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[1536])).
% 1.54/1.75 tff(4201,plain,
% 1.54/1.75 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4200])).
% 1.54/1.75 tff(4202,plain,
% 1.54/1.75 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[4201])).
% 1.54/1.75 tff(4203,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4202])).
% 1.54/1.75 tff(4204,plain,
% 1.54/1.75 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(symmetry,[status(thm)],[4203])).
% 1.54/1.75 tff(4205,plain,
% 1.54/1.75 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(z)))), z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4204])).
% 1.54/1.75 tff(4206,plain,
% 1.54/1.75 (~r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[985, 4205])).
% 1.54/1.75 tff(4207,plain,
% 1.54/1.75 (r(s(s(s(s(z)))), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[306, 60, 48, 524])).
% 1.54/1.75 tff(4208,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4207, 4206])).
% 1.54/1.75 tff(4209,plain,(r(s(s(s(elem!1))), z) | (~(elem!1 = s(z))) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4210,plain,
% 1.54/1.75 (~(elem!1 = s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4209, 4199, 4196])).
% 1.54/1.75 tff(4211,plain,
% 1.54/1.75 (r(elem!1, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[1529, 4210, 4179])).
% 1.54/1.75 tff(4212,plain,
% 1.54/1.75 (r(s(s(z)), s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4211, 4164])).
% 1.54/1.75 tff(4213,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(4214,plain,
% 1.54/1.75 (s(s(s(s(s(z))))) = s(s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[4213])).
% 1.54/1.75 tff(4215,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3070, 4214])).
% 1.54/1.75 tff(4216,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(4217,plain,
% 1.54/1.75 (elem!1 = s(s(z))),
% 1.54/1.75 inference(transitivity,[status(thm)],[695, 4160, 15])).
% 1.54/1.75 tff(4218,plain,
% 1.54/1.75 (b(elem!1, z) <=> b(s(s(z)), z)),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4217])).
% 1.54/1.75 tff(4219,plain,
% 1.54/1.75 (~r(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[3576, 4211, 37])).
% 1.54/1.75 tff(4220,plain,
% 1.54/1.75 (b(elem!1, z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2354, 4219, 2779])).
% 1.54/1.75 tff(4221,plain,
% 1.54/1.75 (b(s(s(z)), z)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4220, 4218])).
% 1.54/1.75 tff(4222,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4223,plain,
% 1.54/1.75 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4224,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4223])).
% 1.54/1.75 tff(4225,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4224, 4222])).
% 1.54/1.75 tff(4226,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4227,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4226, 4225])).
% 1.54/1.75 tff(4228,plain,
% 1.54/1.75 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4227, 192, 4060, 3449, 4221, 1563, 4058])).
% 1.54/1.75 tff(4229,plain,
% 1.54/1.75 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[2401, 60, 4228, 4216])).
% 1.54/1.75 tff(4230,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4231,plain,
% 1.54/1.75 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4232,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4231])).
% 1.54/1.75 tff(4233,plain,
% 1.54/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(transitivity,[status(thm)],[4232, 4230])).
% 1.54/1.75 tff(4234,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(4235,plain,
% 1.54/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 1.54/1.75 tff(4236,plain,
% 1.54/1.75 (~b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[4235, 192, 4009, 4054, 4189])).
% 1.54/1.75 tff(4237,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[438, 60, 4236, 380])).
% 1.54/1.75 tff(4238,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4239,plain,
% 1.54/1.75 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(4240,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[4239])).
% 1.54/1.75 tff(4241,plain,
% 1.54/1.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4240, 4238])).
% 1.54/1.76 tff(4242,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(z)), s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4243,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 1.54/1.76 tff(4244,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4243, 77, 4237, 4229, 4212])).
% 1.54/1.76 tff(4245,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (s(elem!1) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4246,plain,
% 1.54/1.76 (~r(z, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4245, 504, 39, 115, 37, 528])).
% 1.54/1.76 tff(4247,plain,
% 1.54/1.76 (b(z, s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[339, 4246])).
% 1.54/1.76 tff(4248,plain,
% 1.54/1.76 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1229, 667, 118, 37])).
% 1.54/1.76 tff(4249,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4248])).
% 1.54/1.76 tff(4250,plain,
% 1.54/1.76 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4249])).
% 1.54/1.76 tff(4251,plain,
% 1.54/1.76 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1035, 4250, 44])).
% 1.54/1.76 tff(4252,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4251])).
% 1.54/1.76 tff(4253,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4252])).
% 1.54/1.76 tff(4254,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1836, 4248, 396])).
% 1.54/1.76 tff(4255,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4254, 4253])).
% 1.54/1.76 tff(4256,plain,
% 1.54/1.76 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[45, 4249, 691])).
% 1.54/1.76 tff(4257,plain,
% 1.54/1.76 (b(z, s(s(s(s(z))))) <=> b(z, s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4256])).
% 1.54/1.76 tff(4258,plain,
% 1.54/1.76 (b(z, s(s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1242, 4257])).
% 1.54/1.76 tff(4259,plain,
% 1.54/1.76 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4256])).
% 1.54/1.76 tff(4260,plain,
% 1.54/1.76 (s(s(s(z))) = s(elem!1)),
% 1.54/1.76 inference(transitivity,[status(thm)],[92, 4259, 1046])).
% 1.54/1.76 tff(4261,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4248, 4260])).
% 1.54/1.76 tff(4262,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4260])).
% 1.54/1.76 tff(4263,plain,
% 1.54/1.76 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[278, 77, 37, 118])).
% 1.54/1.76 tff(4264,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[271, 4263])).
% 1.54/1.76 tff(4265,plain,
% 1.54/1.76 (~r(z, s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[835, 37, 118])).
% 1.54/1.76 tff(4266,plain,
% 1.54/1.76 (b(z, s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[493, 4265])).
% 1.54/1.76 tff(4267,plain,
% 1.54/1.76 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4052, 396, 4266, 37, 4264])).
% 1.54/1.76 tff(4268,plain,
% 1.54/1.76 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[319, 4267])).
% 1.54/1.76 tff(4269,plain,
% 1.54/1.76 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3456, 192, 512, 4268, 1408])).
% 1.54/1.76 tff(4270,plain,
% 1.54/1.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[390, 4269])).
% 1.54/1.76 tff(4271,plain,
% 1.54/1.76 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4270, 4262])).
% 1.54/1.76 tff(4272,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[982, 667, 37])).
% 1.54/1.76 tff(4273,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[992, 4272])).
% 1.54/1.76 tff(4274,plain,
% 1.54/1.76 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4260])).
% 1.54/1.76 tff(4275,plain,
% 1.54/1.76 (b(s(elem!1), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1408, 4274])).
% 1.54/1.76 tff(4276,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4048, 1242, 396, 4266])).
% 1.54/1.76 tff(4277,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[113, 4276])).
% 1.54/1.76 tff(4278,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1059, 1056])).
% 1.54/1.76 tff(4279,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4278])).
% 1.54/1.76 tff(4280,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[2280, 4279])).
% 1.54/1.76 tff(4281,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(4282,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4281, 4280])).
% 1.54/1.76 tff(4283,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4284,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4283, 4248, 4277])).
% 1.54/1.76 tff(4285,plain,
% 1.54/1.76 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[3818])).
% 1.54/1.76 tff(4286,plain,
% 1.54/1.76 (s(elem!1) = s(s(s(z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[1047, 4285, 91])).
% 1.54/1.76 tff(4287,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1059, 4286])).
% 1.54/1.76 tff(4288,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4287])).
% 1.54/1.76 tff(4289,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.76 tff(4290,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4289])).
% 1.54/1.76 tff(4291,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1059])).
% 1.54/1.76 tff(4292,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4291, 4290])).
% 1.54/1.76 tff(4293,plain,
% 1.54/1.76 ((~b(s(s(elem!1)), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4292])).
% 1.54/1.76 tff(4294,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1059])).
% 1.54/1.76 tff(4295,plain,
% 1.54/1.76 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4294])).
% 1.54/1.76 tff(4296,plain,
% 1.54/1.76 (b(s(s(elem!1)), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[512, 4295])).
% 1.54/1.76 tff(4297,plain,
% 1.54/1.76 (b(s(z), s(s(s(z)))) <=> b(s(z), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.76 tff(4298,plain,
% 1.54/1.76 (~r(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4176, 117, 118])).
% 1.54/1.76 tff(4299,plain,
% 1.54/1.76 (b(s(z), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[427, 4298])).
% 1.54/1.76 tff(4300,plain,
% 1.54/1.76 (b(s(z), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4299, 4297])).
% 1.54/1.76 tff(4301,plain,
% 1.54/1.76 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1112, 192, 953, 4300])).
% 1.54/1.76 tff(4302,plain,
% 1.54/1.76 (~b(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4301, 4296])).
% 1.54/1.76 tff(4303,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4302, 4293])).
% 1.54/1.76 tff(4304,plain,
% 1.54/1.76 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[406, 4303])).
% 1.54/1.76 tff(4305,plain,
% 1.54/1.76 (r(s(s(elem!1)), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4304, 4288])).
% 1.54/1.76 tff(4306,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(4307,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1055])).
% 1.54/1.76 tff(4308,plain,
% 1.54/1.76 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.76 inference(symmetry,[status(thm)],[4307])).
% 1.54/1.76 tff(4309,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1055, 3819])).
% 1.54/1.76 tff(4310,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4309, 4308])).
% 1.54/1.76 tff(4311,plain,
% 1.54/1.76 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[117, 4310])).
% 1.54/1.76 tff(4312,plain,
% 1.54/1.76 (~r(s(elem!1), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1763, 4311, 239, 1242, 537])).
% 1.54/1.76 tff(4313,plain,
% 1.54/1.76 (b(s(elem!1), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[560, 4312])).
% 1.54/1.76 tff(4314,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.54/1.76 tff(4315,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4316,plain,
% 1.54/1.76 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4317,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4316])).
% 1.54/1.76 tff(4318,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4317, 4315])).
% 1.54/1.76 tff(4319,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4320,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4319, 4318])).
% 1.54/1.76 tff(4321,plain,
% 1.54/1.76 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4320, 192, 4314, 1005, 4313])).
% 1.54/1.76 tff(4322,plain,
% 1.54/1.76 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1055])).
% 1.54/1.76 tff(4323,plain,
% 1.54/1.76 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4322, 704])).
% 1.54/1.76 tff(4324,plain,
% 1.54/1.76 ((~(s(s(s(s(s(z))))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4323])).
% 1.54/1.76 tff(4325,plain,
% 1.54/1.76 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2314, 1055])).
% 1.54/1.76 tff(4326,plain,
% 1.54/1.76 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[752, 4325])).
% 1.54/1.76 tff(4327,plain,
% 1.54/1.76 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4326, 4324])).
% 1.54/1.76 tff(4328,plain,
% 1.54/1.76 (r(s(elem!1), s(s(s(elem!1))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3232, 60, 4327, 4321])).
% 1.54/1.76 tff(4329,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4330,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4331,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4330, 4329])).
% 1.54/1.76 tff(4332,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4331, 77, 4328, 4306, 4305])).
% 1.54/1.76 tff(4333,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4334,plain,
% 1.54/1.76 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4333, 4284, 4248, 4275, 1022, 4273, 512, 4264, 1242, 4271, 118])).
% 1.54/1.76 tff(4335,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[133, 4334])).
% 1.54/1.76 tff(4336,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4335, 4261])).
% 1.54/1.76 tff(4337,plain,
% 1.54/1.76 (~b(s(s(s(s(z)))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1753, 1242, 4264, 396])).
% 1.54/1.76 tff(4338,plain,
% 1.54/1.76 (~(elem!1 = s(z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4209, 4272, 4337])).
% 1.54/1.76 tff(4339,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4340,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4341,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4340, 4339])).
% 1.54/1.76 tff(4342,plain,
% 1.54/1.76 (~r(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4341, 77, 545, 504])).
% 1.54/1.76 tff(4343,plain,
% 1.54/1.76 (b(s(z), s(elem!1))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[658, 4342, 651])).
% 1.54/1.76 tff(4344,plain,
% 1.54/1.76 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.76 tff(4345,plain,
% 1.54/1.76 (b(s(elem!1), s(z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[1408, 4344])).
% 1.54/1.76 tff(4346,plain,
% 1.54/1.76 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.76 tff(4347,plain,
% 1.54/1.76 (s(s(z)) = elem!1),
% 1.54/1.76 inference(transitivity,[status(thm)],[16, 4346, 682])).
% 1.54/1.76 tff(4348,plain,
% 1.54/1.76 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.76 inference(monotonicity,[status(thm)],[1055, 4347])).
% 1.54/1.76 tff(4349,plain,
% 1.54/1.76 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4348])).
% 1.54/1.76 tff(4350,plain,
% 1.54/1.76 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[3070, 4349])).
% 1.54/1.76 tff(4351,plain,
% 1.54/1.76 (~r(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2565, 2554, 667])).
% 1.54/1.76 tff(4352,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1628, 4351, 2276])).
% 1.54/1.76 tff(4353,plain,
% 1.54/1.76 (~r(elem!1, z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3576, 2554, 37])).
% 1.54/1.76 tff(4354,plain,
% 1.54/1.76 (b(elem!1, z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2354, 4353, 2184])).
% 1.54/1.76 tff(4355,plain,
% 1.54/1.76 (~(z = elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2884, 2184])).
% 1.54/1.76 tff(4356,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.54/1.76 tff(4357,plain,
% 1.54/1.76 (b(s(s(s(elem!1))), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[1628, 2276, 4356])).
% 1.54/1.76 tff(4358,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.54/1.76 tff(4359,plain,
% 1.54/1.76 (b(s(elem!1), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[3123, 2791, 4358])).
% 1.54/1.76 tff(4360,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4361,plain,
% 1.54/1.76 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4362,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4361])).
% 1.54/1.76 tff(4363,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4362, 4360])).
% 1.54/1.76 tff(4364,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4365,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4364, 4363])).
% 1.54/1.76 tff(4366,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4365, 192, 1435, 1923, 4359, 4357, 1005])).
% 1.54/1.76 tff(4367,plain,((s(s(s(elem!1))) = elem!1) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | r(s(elem!1), elem!1) | r(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(4368,plain,
% 1.54/1.76 (r(s(elem!1), elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4367, 4354, 1923, 4273, 4351, 2276])).
% 1.54/1.76 tff(4369,plain,
% 1.54/1.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4370,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4371,plain,
% 1.54/1.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[4370, 4369])).
% 1.54/1.76 tff(4372,plain,
% 1.54/1.76 ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4371, 77])).
% 1.54/1.76 tff(4373,plain,
% 1.54/1.76 (~r(z, elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[4372, 4368, 545])).
% 1.54/1.76 tff(4374,plain,
% 1.54/1.76 (b(z, elem!1)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[2911, 4373, 4355])).
% 1.54/1.76 tff(4375,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4376,plain,
% 1.54/1.76 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(4377,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[4376])).
% 1.54/1.76 tff(4378,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[4377, 4375])).
% 1.54/1.76 tff(4379,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(4380,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4379, 4378])).
% 1.54/1.77 tff(4381,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4380, 192, 4374, 4354, 4352, 4273])).
% 1.54/1.77 tff(4382,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (elem!1 = z) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4383,plain,
% 1.54/1.77 (~r(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4382, 545, 1923, 4350, 2184, 667, 37])).
% 1.54/1.77 tff(4384,plain,
% 1.54/1.77 (b(elem!1, s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1529, 4383, 1523])).
% 1.54/1.77 tff(4385,plain,
% 1.54/1.77 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.77 tff(4386,plain,
% 1.54/1.77 (~(elem!1 = s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[853, 4326])).
% 1.54/1.77 tff(4387,plain,
% 1.54/1.77 (r(s(z), s(s(s(z)))) <=> r(s(z), s(elem!1))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[3819])).
% 1.54/1.77 tff(4388,plain,
% 1.54/1.77 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4387])).
% 1.54/1.77 tff(4389,plain,
% 1.54/1.77 ((~r(s(z), s(elem!1))) <=> (~r(s(z), s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4388])).
% 1.54/1.77 tff(4390,plain,
% 1.54/1.77 (~r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4342, 4389])).
% 1.54/1.77 tff(4391,plain,
% 1.54/1.77 (b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[427, 4390])).
% 1.54/1.77 tff(4392,plain,
% 1.54/1.77 (~r(elem!1, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[3553, 4384, 1408, 512, 38, 4391, 4386])).
% 1.54/1.77 tff(4393,plain,
% 1.54/1.77 (b(elem!1, s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[2037, 4392, 1998])).
% 1.54/1.77 tff(4394,plain,
% 1.54/1.77 (b(elem!1, s(elem!1))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4393, 4385])).
% 1.54/1.77 tff(4395,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4396,plain,
% 1.54/1.77 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4397,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4396])).
% 1.54/1.77 tff(4398,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4397, 4395])).
% 1.54/1.77 tff(4399,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4400,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4399, 4398])).
% 1.54/1.77 tff(4401,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4400, 192, 4394, 4384, 4345, 4343])).
% 1.54/1.77 tff(4402,plain,((~r(s(elem!1), z)) | (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (elem!1 = z) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4403,plain,
% 1.54/1.77 (~r(s(elem!1), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4402, 4248, 1998, 1408, 512, 4268, 4338, 4336, 2184, 667, 37, 651, 504])).
% 1.54/1.77 tff(4404,plain,
% 1.54/1.77 (b(s(elem!1), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[560, 4403])).
% 1.54/1.77 tff(4405,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4406,plain,
% 1.54/1.77 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4407,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4406])).
% 1.54/1.77 tff(4408,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4407, 4405])).
% 1.54/1.77 tff(4409,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4410,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4409, 4408])).
% 1.54/1.77 tff(4411,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4410, 192, 4336, 4273, 4404, 4258, 4255])).
% 1.54/1.77 tff(4412,plain,((~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (elem!1 = z) | (~r(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4413,plain,
% 1.54/1.77 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4412, 504, 3447, 2937, 2779, 37, 639, 3053, 4247, 66, 4009])).
% 1.54/1.77 tff(4414,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[1313, 4413])).
% 1.54/1.77 tff(4415,plain,
% 1.54/1.77 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4048, 4247, 4009, 3449])).
% 1.54/1.77 tff(4416,plain,
% 1.54/1.77 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[113, 4415])).
% 1.54/1.77 tff(4417,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.77 tff(4418,plain,
% 1.54/1.77 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4417])).
% 1.54/1.77 tff(4419,plain,
% 1.54/1.77 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4418])).
% 1.54/1.77 tff(4420,plain,
% 1.54/1.77 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[45, 4419, 722])).
% 1.54/1.77 tff(4421,plain,
% 1.54/1.77 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4420])).
% 1.54/1.77 tff(4422,plain,
% 1.54/1.77 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[92, 4421, 740])).
% 1.54/1.77 tff(4423,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[102, 4422])).
% 1.54/1.77 tff(4424,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4425,plain,
% 1.54/1.77 (s(s(s(s(s(s(s(z))))))) = s(s(s(elem!1)))),
% 1.54/1.77 inference(symmetry,[status(thm)],[725])).
% 1.54/1.77 tff(4426,plain,
% 1.54/1.77 (b(s(s(s(s(s(s(s(z))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4425])).
% 1.54/1.77 tff(4427,plain,
% 1.54/1.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4426])).
% 1.54/1.77 tff(4428,plain,
% 1.54/1.77 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1316, 4427])).
% 1.54/1.77 tff(4429,plain,
% 1.54/1.77 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(4430,plain,
% 1.54/1.77 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.54/1.77 inference(symmetry,[status(thm)],[4429])).
% 1.54/1.77 tff(4431,plain,
% 1.54/1.77 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4430])).
% 1.54/1.77 tff(4432,plain,
% 1.54/1.77 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[1969, 4431])).
% 1.54/1.77 tff(4433,plain,
% 1.54/1.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4144, 723, 512, 4268, 118, 37])).
% 1.54/1.77 tff(4434,plain,
% 1.54/1.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4435,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4436,plain,
% 1.54/1.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 1.54/1.77 tff(4437,plain,
% 1.54/1.77 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4436, 77, 4270, 4433])).
% 1.54/1.77 tff(4438,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4439,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4440,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 1.54/1.77 tff(4441,plain,
% 1.54/1.77 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4440, 60, 4437])).
% 1.54/1.77 tff(4442,plain,
% 1.54/1.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4441, 4432])).
% 1.54/1.77 tff(4443,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 1.54/1.77 tff(4444,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(4445,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4446,plain,
% 1.54/1.77 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(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))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4447,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4446])).
% 1.54/1.77 tff(4448,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4447, 4445])).
% 1.54/1.77 tff(4449,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4450,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4449, 4448])).
% 1.54/1.77 tff(4451,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4450, 192, 512, 38, 1408, 3527, 4444, 4443])).
% 1.54/1.77 tff(4452,plain,((~b(s(z), s(s(s(z))))) | (~b(s(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(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(4453,plain,
% 1.54/1.77 (~b(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4452, 4442, 4268, 1408, 512, 4428])).
% 1.54/1.77 tff(4454,plain,
% 1.54/1.77 (r(s(z), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[427, 4453])).
% 1.54/1.77 tff(4455,plain,
% 1.54/1.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4176, 4454, 118])).
% 1.54/1.77 tff(4456,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[133, 4455])).
% 1.54/1.77 tff(4457,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4458,plain,
% 1.54/1.77 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4459,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[4458])).
% 1.54/1.77 tff(4460,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[4459, 4457])).
% 1.54/1.77 tff(4461,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4462,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4461, 4460])).
% 1.54/1.77 tff(4463,plain,
% 1.54/1.77 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[4462, 192, 396, 512, 1408, 4456, 4442, 4428])).
% 1.54/1.77 tff(4464,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(4465,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(4466,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[4465, 4464])).
% 1.54/1.77 tff(4467,plain,
% 1.54/1.77 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4466, 60, 4463, 4424])).
% 1.54/1.78 tff(4468,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4469,plain,
% 1.54/1.78 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4470,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4469])).
% 1.54/1.78 tff(4471,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4470, 4468])).
% 1.54/1.78 tff(4472,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4473,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 1.54/1.78 tff(4474,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4473, 77, 2280, 4433, 4467])).
% 1.54/1.78 tff(4475,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4476,plain,
% 1.54/1.78 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4475, 4416, 4009, 2937, 3447, 66, 4414, 37])).
% 1.54/1.78 tff(4477,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4048, 1242, 396, 813])).
% 1.54/1.78 tff(4478,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[113, 4477])).
% 1.54/1.78 tff(4479,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1481, 192, 583, 813, 239])).
% 1.54/1.78 tff(4480,plain,
% 1.54/1.78 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[811, 4479, 750])).
% 1.54/1.78 tff(4481,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4482,plain,
% 1.54/1.78 (((~b(z, 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(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4483,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4482])).
% 1.54/1.78 tff(4484,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4483, 4481])).
% 1.54/1.78 tff(4485,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(elem!1), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4486,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), 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))))), s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4485, 4484])).
% 1.54/1.78 tff(4487,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4486, 192, 396, 583, 1242, 239])).
% 1.54/1.78 tff(4488,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[597, 4487, 3912])).
% 1.54/1.78 tff(4489,plain,
% 1.54/1.78 (~r(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2692, 4488, 118])).
% 1.54/1.78 tff(4490,plain,
% 1.54/1.78 (b(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[950, 4489, 115])).
% 1.54/1.78 tff(4491,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1267, 4490, 512, 38])).
% 1.54/1.78 tff(4492,plain,
% 1.54/1.78 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[535, 4491, 528])).
% 1.54/1.78 tff(4493,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4494,plain,
% 1.54/1.78 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4495,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4494])).
% 1.54/1.78 tff(4496,plain,
% 1.54/1.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4495, 4493])).
% 1.54/1.78 tff(4497,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4498,plain,
% 1.54/1.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 1.54/1.78 tff(4499,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4498, 77, 4492, 4480, 4478])).
% 1.54/1.78 tff(4500,plain,((~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(s(s(s(s(s(z))))), s(z))) | (s(elem!1) = s(s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4501,plain,
% 1.54/1.78 (~b(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4500, 4476, 2937, 4054, 115, 66, 528, 3449, 1563, 4009, 4247])).
% 1.54/1.78 tff(4502,plain,
% 1.54/1.78 (r(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[560, 4501])).
% 1.54/1.78 tff(4503,plain,
% 1.54/1.78 (~r(s(z), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4341, 77, 4502, 504])).
% 1.54/1.78 tff(4504,plain,
% 1.54/1.78 (b(s(z), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[658, 4503, 639])).
% 1.54/1.78 tff(4505,plain,
% 1.54/1.78 (~r(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1737, 4502, 37])).
% 1.54/1.78 tff(4506,plain,
% 1.54/1.78 (b(s(elem!1), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[950, 4505, 115])).
% 1.54/1.78 tff(4507,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4508,plain,
% 1.54/1.78 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4509,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4508])).
% 1.54/1.78 tff(4510,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4509, 4507])).
% 1.54/1.78 tff(4511,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4512,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4511, 4510])).
% 1.54/1.78 tff(4513,plain,
% 1.54/1.78 (~b(s(s(s(z))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4512, 192, 4506, 3447, 4504])).
% 1.54/1.78 tff(4514,plain,
% 1.54/1.78 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1267, 4506, 2937, 4054])).
% 1.54/1.78 tff(4515,plain,
% 1.54/1.78 (r(s(elem!1), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[535, 4514, 528])).
% 1.54/1.78 tff(4516,plain,
% 1.54/1.78 (~r(s(s(s(z))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3854, 77, 4515, 4056])).
% 1.54/1.78 tff(4517,plain,
% 1.54/1.78 ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[906, 60, 4516])).
% 1.54/1.78 tff(4518,plain,
% 1.54/1.78 (s(s(s(z))) = s(elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4517, 4513])).
% 1.54/1.78 tff(4519,plain,
% 1.54/1.78 (s(elem!1) = s(s(s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4518, 2700])).
% 1.54/1.78 tff(4520,plain,
% 1.54/1.78 (~(s(elem!1) = s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3844, 4414, 39])).
% 1.54/1.78 tff(4521,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4520, 4519])).
% 1.54/1.78 tff(4522,plain,((~r(s(z), z)) | (s(elem!1) = s(s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4523,plain,
% 1.54/1.78 (~r(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4522, 528, 115, 37, 39])).
% 1.54/1.78 tff(4524,plain,
% 1.54/1.78 (b(s(z), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[351, 4523])).
% 1.54/1.78 tff(4525,plain,
% 1.54/1.78 (~r(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2652, 321, 383])).
% 1.54/1.78 tff(4526,plain,
% 1.54/1.78 (b(z, s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[237, 4525])).
% 1.54/1.78 tff(4527,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3429, 321, 239, 383])).
% 1.54/1.78 tff(4528,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[133, 4527])).
% 1.54/1.78 tff(4529,plain,
% 1.54/1.78 (~r(s(z), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4176, 4528, 118])).
% 1.54/1.78 tff(4530,plain,
% 1.54/1.78 (b(s(z), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[427, 4529])).
% 1.54/1.78 tff(4531,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4532,plain,
% 1.54/1.78 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(4533,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4532])).
% 1.54/1.78 tff(4534,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4533, 4531])).
% 1.54/1.78 tff(4535,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(4536,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4535, 4534])).
% 1.54/1.78 tff(4537,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4536, 192, 515, 2458, 1408, 4530, 4526])).
% 1.54/1.78 tff(4538,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4539,plain,
% 1.54/1.78 (~r(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4538, 4524, 3447, 4056, 66, 1563])).
% 1.54/1.78 tff(4540,plain,
% 1.54/1.78 (b(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[339, 4539])).
% 1.54/1.78 tff(4541,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4048, 4540, 4009, 3449])).
% 1.54/1.78 tff(4542,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[113, 4541])).
% 1.54/1.78 tff(4543,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1753, 4540, 1563, 4009])).
% 1.54/1.78 tff(4544,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[526, 4543])).
% 1.54/1.78 tff(4545,plain,
% 1.54/1.78 (~r(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3828, 4544, 37, 2937, 4054, 4523, 528])).
% 1.54/1.78 tff(4546,plain,
% 1.54/1.78 (b(s(elem!1), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[560, 4545])).
% 1.54/1.78 tff(4547,plain,
% 1.54/1.78 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4500, 4546, 2937, 4054, 115, 66, 528, 3449, 1563, 4009, 4540])).
% 1.54/1.78 tff(4548,plain,
% 1.54/1.78 (~b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4475, 4547, 4009, 2937, 3447, 66, 4542, 37])).
% 1.54/1.78 tff(4549,plain,
% 1.54/1.78 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2314, 4547])).
% 1.54/1.78 tff(4550,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1229, 4549, 66, 37])).
% 1.54/1.78 tff(4551,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1313, 4550, 4548])).
% 1.54/1.78 tff(4552,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4553,plain,
% 1.54/1.78 (s(elem!1) = s(s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4552, 37, 115, 39])).
% 1.54/1.78 tff(4554,plain,
% 1.54/1.78 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4553])).
% 1.54/1.78 tff(4555,plain,
% 1.54/1.78 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4554])).
% 1.54/1.78 tff(4556,plain,
% 1.54/1.78 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4555])).
% 1.54/1.78 tff(4557,plain,
% 1.54/1.78 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4556])).
% 1.54/1.78 tff(4558,plain,
% 1.54/1.78 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4557, 1157])).
% 1.54/1.78 tff(4559,plain,
% 1.54/1.78 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4558])).
% 1.54/1.78 tff(4560,plain,
% 1.54/1.78 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1170, 4559])).
% 1.54/1.78 tff(4561,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1229, 4560, 66, 37])).
% 1.54/1.78 tff(4562,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1313, 4561])).
% 1.54/1.78 tff(4563,plain,
% 1.54/1.78 (elem!1 = s(s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3339, 1146])).
% 1.54/1.78 tff(4564,plain,
% 1.54/1.78 (s(s(s(z))) = elem!1),
% 1.54/1.78 inference(symmetry,[status(thm)],[4563])).
% 1.54/1.78 tff(4565,plain,
% 1.54/1.78 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4564, 1160])).
% 1.54/1.78 tff(4566,plain,
% 1.54/1.78 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.54/1.78 inference(transitivity,[status(thm)],[4565, 1976])).
% 1.54/1.78 tff(4567,plain,
% 1.54/1.78 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4566])).
% 1.54/1.78 tff(4568,plain,
% 1.54/1.78 (~(s(s(s(elem!1))) = elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[2419, 4567])).
% 1.54/1.78 tff(4569,plain,
% 1.54/1.78 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4563])).
% 1.54/1.78 tff(4570,plain,
% 1.54/1.78 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4569])).
% 1.54/1.78 tff(4571,plain,
% 1.54/1.78 (b(elem!1, s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[1408, 4570])).
% 1.54/1.78 tff(4572,plain,
% 1.54/1.78 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4563])).
% 1.54/1.78 tff(4573,plain,
% 1.54/1.78 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.54/1.78 inference(symmetry,[status(thm)],[4572])).
% 1.54/1.78 tff(4574,plain,
% 1.54/1.78 (b(s(z), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4299, 4573])).
% 1.54/1.78 tff(4575,plain,
% 1.54/1.78 (~b(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[2294, 4574, 4571, 1316])).
% 1.54/1.78 tff(4576,plain,
% 1.54/1.78 (r(s(s(s(elem!1))), elem!1)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1628, 4575, 4568])).
% 1.54/1.78 tff(4577,plain,
% 1.54/1.78 (r(s(elem!1), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(monotonicity,[status(thm)],[1146])).
% 1.54/1.78 tff(4578,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.54/1.78 inference(symmetry,[status(thm)],[4577])).
% 1.54/1.78 tff(4579,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4563])).
% 1.54/1.78 tff(4580,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.54/1.78 inference(symmetry,[status(thm)],[4579])).
% 1.54/1.78 tff(4581,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(elem!1), elem!1)),
% 1.54/1.78 inference(transitivity,[status(thm)],[4580, 4578])).
% 1.54/1.78 tff(4582,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3534, 192, 512, 38, 1408, 4299])).
% 1.54/1.78 tff(4583,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[406, 4582])).
% 1.54/1.78 tff(4584,plain,
% 1.54/1.78 (r(s(elem!1), elem!1)),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4583, 4581])).
% 1.54/1.78 tff(4585,plain,
% 1.54/1.78 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1623, 4584, 4576])).
% 1.54/1.78 tff(4586,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(elem!1))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[679, 4585, 2548])).
% 1.54/1.78 tff(4587,plain,
% 1.54/1.78 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4586, 2549])).
% 1.54/1.78 tff(4588,plain,
% 1.54/1.78 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4587, 2602])).
% 1.54/1.78 tff(4589,plain,
% 1.54/1.78 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4187, 77, 4583, 117])).
% 1.54/1.78 tff(4590,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[113, 4589])).
% 1.54/1.78 tff(4591,plain,
% 1.54/1.78 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3385, 192, 396, 512, 38, 4590])).
% 1.54/1.78 tff(4592,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4591, 3379, 4588])).
% 1.54/1.78 tff(4593,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(4594,plain,
% 1.54/1.78 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[4593, 4009, 2937, 4054, 4562, 4553, 3447, 66])).
% 1.54/1.78 tff(4595,plain,
% 1.54/1.78 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[133, 4594])).
% 1.54/1.78 tff(4596,plain,
% 1.54/1.78 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4553])).
% 1.54/1.78 tff(4597,plain,
% 1.54/1.78 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4596])).
% 1.54/1.78 tff(4598,plain,
% 1.54/1.78 (elem!1 = s(s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3339, 4553])).
% 1.54/1.78 tff(4599,plain,
% 1.54/1.78 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[4598])).
% 1.54/1.78 tff(4600,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[4599])).
% 1.54/1.78 tff(4601,plain,
% 1.54/1.78 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.54/1.78 inference(transitivity,[status(thm)],[4600, 4597])).
% 1.54/1.78 tff(4602,plain,
% 1.54/1.78 (r(elem!1, s(elem!1))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[4056, 4601])).
% 1.54/1.78 tff(4603,plain,
% 1.54/1.78 (~r(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[3429, 4595, 1563, 4056])).
% 1.54/1.78 tff(4604,plain,
% 1.54/1.78 (b(z, s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[339, 4603])).
% 1.54/1.78 tff(4605,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), z)),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[1753, 4604, 1563, 4009])).
% 1.54/1.78 tff(4606,plain,
% 1.54/1.79 (~b(s(elem!1), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2608, 4605, 4553])).
% 1.54/1.79 tff(4607,plain,
% 1.54/1.79 (r(s(elem!1), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[560, 4606])).
% 1.54/1.79 tff(4608,plain,
% 1.54/1.79 (~r(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2362, 4607, 4602])).
% 1.54/1.79 tff(4609,plain,
% 1.54/1.79 (b(elem!1, z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2354, 4608, 2779])).
% 1.54/1.79 tff(4610,plain,
% 1.54/1.79 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.54/1.79 inference(monotonicity,[status(thm)],[2474])).
% 1.54/1.79 tff(4611,plain,
% 1.54/1.79 (b(s(s(s(z))), z) <=> b(elem!1, z)),
% 1.54/1.79 inference(symmetry,[status(thm)],[4610])).
% 1.54/1.79 tff(4612,plain,
% 1.54/1.79 ((~b(s(s(s(z))), z)) <=> (~b(elem!1, z))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4611])).
% 1.54/1.79 tff(4613,plain,
% 1.54/1.79 (~b(elem!1, z)),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[247, 4612])).
% 1.54/1.79 tff(4614,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1435, 4613])).
% 1.54/1.79 tff(4615,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(elem!1, z)) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4616,plain,
% 1.54/1.79 (b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4615, 4609, 4553])).
% 1.54/1.79 tff(4617,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4618,plain,
% 1.54/1.79 (((~b(z, 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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4619,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4618])).
% 1.54/1.79 tff(4620,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4619, 4617])).
% 1.54/1.79 tff(4621,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4622,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 1.54/1.79 tff(4623,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4622, 192, 4009, 4604, 4616, 1563, 4595])).
% 1.54/1.79 tff(4624,plain,((~r(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4625,plain,
% 1.54/1.79 (~r(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4624, 115, 39])).
% 1.54/1.79 tff(4626,plain,
% 1.54/1.79 (b(z, s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[292, 4625])).
% 1.54/1.79 tff(4627,plain,
% 1.54/1.79 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2633, 504, 66])).
% 1.54/1.79 tff(4628,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[271, 4627])).
% 1.54/1.79 tff(4629,plain,
% 1.54/1.79 (~b(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[471, 192, 465, 464, 3461])).
% 1.54/1.79 tff(4630,plain,
% 1.54/1.79 (r(z, s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[339, 4629])).
% 1.54/1.79 tff(4631,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3456, 192, 464, 3461, 1408])).
% 1.54/1.79 tff(4632,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[390, 4631])).
% 1.54/1.79 tff(4633,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2460, 4632, 4630, 170, 239])).
% 1.54/1.79 tff(4634,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4635,plain,
% 1.54/1.79 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4634, 4628, 1408, 465, 39])).
% 1.54/1.79 tff(4636,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[181, 4635])).
% 1.54/1.79 tff(4637,plain,
% 1.54/1.79 (~r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4029, 4636, 504, 4628])).
% 1.54/1.79 tff(4638,plain,
% 1.54/1.79 (b(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[319, 4637])).
% 1.54/1.79 tff(4639,plain,
% 1.54/1.79 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3456, 192, 512, 38, 1408])).
% 1.54/1.79 tff(4640,plain,
% 1.54/1.79 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[390, 4639])).
% 1.54/1.79 tff(4641,plain,
% 1.54/1.79 (~r(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2652, 4640, 514])).
% 1.54/1.79 tff(4642,plain,
% 1.54/1.79 (b(z, s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[237, 4641])).
% 1.54/1.79 tff(4643,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[3429, 4640, 239, 514])).
% 1.54/1.79 tff(4644,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[133, 4643])).
% 1.54/1.79 tff(4645,plain,
% 1.54/1.79 (~r(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4176, 4644, 118])).
% 1.54/1.79 tff(4646,plain,
% 1.54/1.79 (b(s(z), s(s(s(z))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[427, 4645])).
% 1.54/1.79 tff(4647,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4648,plain,
% 1.54/1.79 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4649,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4648])).
% 1.54/1.79 tff(4650,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4649, 4647])).
% 1.54/1.79 tff(4651,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4652,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4651, 4650])).
% 1.54/1.79 tff(4653,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4652, 192, 465, 1408, 4646, 4642])).
% 1.54/1.79 tff(4654,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4655,plain,
% 1.54/1.79 (~b(s(s(s(s(z)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4654, 4628, 1408, 66, 465, 4638])).
% 1.54/1.79 tff(4656,plain,
% 1.54/1.79 (r(s(s(s(s(z)))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[217, 4655])).
% 1.54/1.79 tff(4657,plain,
% 1.54/1.79 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[83, 77, 4656, 66])).
% 1.54/1.79 tff(4658,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[113, 4657])).
% 1.54/1.79 tff(4659,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[2503, 77, 504, 67, 297])).
% 1.54/1.79 tff(4660,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4661,plain,
% 1.54/1.79 (~r(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4660, 504, 4656])).
% 1.54/1.79 tff(4662,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[526, 4661])).
% 1.54/1.79 tff(4663,plain,
% 1.54/1.79 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4664,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4663])).
% 1.54/1.79 tff(4665,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4664, 4190])).
% 1.54/1.79 tff(4666,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4667,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4666, 4665])).
% 1.54/1.79 tff(4668,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4667, 192, 813, 1745, 441, 239])).
% 1.54/1.79 tff(4669,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4670,plain,
% 1.54/1.79 (~b(z, s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4669, 4662, 4658, 4628])).
% 1.54/1.79 tff(4671,plain,
% 1.54/1.79 (r(z, s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[493, 4670])).
% 1.54/1.79 tff(4672,plain,
% 1.54/1.79 (~b(s(z), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4235, 192, 4636, 4638, 4658])).
% 1.54/1.79 tff(4673,plain,
% 1.54/1.79 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[438, 60, 4672, 380])).
% 1.54/1.79 tff(4674,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4675,plain,
% 1.54/1.79 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4676,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4675])).
% 1.54/1.79 tff(4677,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4676, 4674])).
% 1.54/1.79 tff(4678,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4679,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 1.54/1.79 tff(4680,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4679, 77, 504, 4673, 4671])).
% 1.54/1.79 tff(4681,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4682,plain,
% 1.54/1.79 (~r(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4681, 3447, 4626, 39])).
% 1.54/1.79 tff(4683,plain,
% 1.54/1.79 (b(s(z), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[351, 4682])).
% 1.54/1.79 tff(4684,plain,
% 1.54/1.79 (~b(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[935, 192, 4683, 4626, 3447])).
% 1.54/1.79 tff(4685,plain,
% 1.54/1.79 (r(s(s(s(z))), z)),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[253, 4684])).
% 1.54/1.79 tff(4686,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.79 tff(4687,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4688,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4689,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[4688])).
% 1.54/1.79 tff(4690,plain,
% 1.54/1.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)))),
% 1.54/1.79 inference(transitivity,[status(thm)],[4689, 4687])).
% 1.54/1.79 tff(4691,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(4692,plain,
% 1.54/1.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[4691, 4690])).
% 1.54/1.79 tff(4693,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4692, 77, 503, 296, 4686])).
% 1.54/1.79 tff(4694,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4695,plain,
% 1.54/1.79 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4694, 3356, 4685])).
% 1.54/1.79 tff(4696,plain,
% 1.54/1.79 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[375, 4695])).
% 1.54/1.79 tff(4697,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1414, 3461, 464, 515, 465, 1408])).
% 1.54/1.79 tff(4698,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(4699,plain,
% 1.54/1.79 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[4698, 4683, 3447, 4626, 39])).
% 1.54/1.79 tff(4700,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[181, 4699])).
% 1.54/1.79 tff(4701,plain,
% 1.54/1.79 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[1414, 512, 1408, 465, 515])).
% 1.54/1.79 tff(4702,plain,
% 1.54/1.79 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[319, 4701])).
% 1.54/1.79 tff(4703,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(4704,plain,
% 1.54/1.79 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(4705,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(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(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4704])).
% 1.54/1.80 tff(4706,plain,
% 1.54/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(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(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[4705, 4703])).
% 1.54/1.80 tff(4707,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(4708,plain,
% 1.54/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[4707, 4706])).
% 1.54/1.80 tff(4709,plain,
% 1.54/1.80 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[4708, 192, 396, 512, 1408, 440])).
% 1.54/1.80 tff(4710,plain,
% 1.54/1.80 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[390, 4709])).
% 1.54/1.80 tff(4711,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(4712,plain,
% 1.54/1.80 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.54/1.80 tff(4713,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[4712])).
% 1.54/1.80 tff(4714,plain,
% 1.54/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4713, 4711])).
% 1.64/1.80 tff(4715,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4716,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4715, 4714])).
% 1.64/1.80 tff(4717,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4716, 77, 308, 383, 408])).
% 1.64/1.80 tff(4718,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4719,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4718, 4710, 4702])).
% 1.64/1.80 tff(4720,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[427, 4719])).
% 1.64/1.80 tff(4721,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(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))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4722,plain,
% 1.64/1.80 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4723,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4722])).
% 1.64/1.80 tff(4724,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4723, 4721])).
% 1.64/1.80 tff(4725,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4726,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 1.64/1.80 tff(4727,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4726, 192, 515, 465, 512, 1408, 4720])).
% 1.64/1.80 tff(4728,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[406, 4727])).
% 1.64/1.80 tff(4729,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2544, 77, 1412, 527, 4728])).
% 1.64/1.80 tff(4730,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4731,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4730, 4696, 4626, 3447, 4700, 4683])).
% 1.64/1.80 tff(4732,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[217, 4731])).
% 1.64/1.80 tff(4733,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[313, 308, 66])).
% 1.64/1.80 tff(4734,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[181, 4733])).
% 1.64/1.80 tff(4735,plain,
% 1.64/1.80 (~r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2633, 3356, 66])).
% 1.64/1.80 tff(4736,plain,
% 1.64/1.80 (b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[351, 4735])).
% 1.64/1.80 tff(4737,plain,
% 1.64/1.80 (~b(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[935, 192, 4736, 4626, 3447])).
% 1.64/1.80 tff(4738,plain,
% 1.64/1.80 (r(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[253, 4737])).
% 1.64/1.80 tff(4739,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4694, 4738, 3356])).
% 1.64/1.80 tff(4740,plain,
% 1.64/1.80 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[375, 4739])).
% 1.64/1.80 tff(4741,plain,
% 1.64/1.80 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[449, 4740, 4734, 114])).
% 1.64/1.80 tff(4742,plain,
% 1.64/1.80 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[390, 4741])).
% 1.64/1.80 tff(4743,plain,
% 1.64/1.80 (~r(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4718, 4742, 308])).
% 1.64/1.80 tff(4744,plain,
% 1.64/1.80 (b(s(z), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[427, 4743])).
% 1.64/1.80 tff(4745,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4746,plain,
% 1.64/1.80 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4747,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4746])).
% 1.64/1.80 tff(4748,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4747, 4745])).
% 1.64/1.80 tff(4749,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4750,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4749, 4748])).
% 1.64/1.80 tff(4751,plain,
% 1.64/1.80 (~b(z, s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4750, 192, 4736, 4626, 3447, 4744])).
% 1.64/1.80 tff(4752,plain,
% 1.64/1.80 (r(z, s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[237, 4751])).
% 1.64/1.80 tff(4753,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4754,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4755,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4754, 4753])).
% 1.64/1.80 tff(4756,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4755, 77, 4738, 3356])).
% 1.64/1.80 tff(4757,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[133, 4756])).
% 1.64/1.80 tff(4758,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4759,plain,
% 1.64/1.80 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4760,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4759])).
% 1.64/1.80 tff(4761,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[4760, 4758])).
% 1.64/1.80 tff(4762,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4763,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 1.64/1.80 tff(4764,plain,
% 1.64/1.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4763, 192, 114, 4757, 4740])).
% 1.64/1.80 tff(4765,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[406, 4764])).
% 1.64/1.80 tff(4766,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3603, 77, 4765, 4752])).
% 1.64/1.80 tff(4767,plain,
% 1.64/1.80 (~r(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2652, 4752, 4742])).
% 1.64/1.80 tff(4768,plain,
% 1.64/1.80 (b(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[339, 4767])).
% 1.64/1.80 tff(4769,plain,
% 1.64/1.80 (~r(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2633, 296, 66])).
% 1.64/1.80 tff(4770,plain,
% 1.64/1.80 (b(s(z), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[351, 4769])).
% 1.64/1.80 tff(4771,plain,
% 1.64/1.80 (~b(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[935, 192, 4770, 4626, 3447])).
% 1.64/1.80 tff(4772,plain,
% 1.64/1.80 (r(s(s(s(z))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[253, 4771])).
% 1.64/1.80 tff(4773,plain,
% 1.64/1.80 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[3944, 77, 545, 4772])).
% 1.64/1.80 tff(4774,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4775,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4776,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 1.64/1.80 tff(4777,plain,
% 1.64/1.80 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4776, 77, 545, 4772])).
% 1.64/1.80 tff(4778,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4755, 77, 4772, 296])).
% 1.64/1.80 tff(4779,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[133, 4778])).
% 1.64/1.80 tff(4780,plain,
% 1.64/1.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(4781,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(4782,plain,
% 1.64/1.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 1.64/1.80 tff(4783,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4782, 77, 545, 538, 296])).
% 1.64/1.80 tff(4784,plain,((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4785,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4784, 545, 296])).
% 1.64/1.80 tff(4786,plain,
% 1.64/1.80 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[597, 815, 4785])).
% 1.64/1.80 tff(4787,plain,
% 1.64/1.80 (s(s(s(z))) = s(elem!1)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[2713, 4786, 221, 2696, 2703])).
% 1.64/1.80 tff(4788,plain,
% 1.64/1.80 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[856, 4787])).
% 1.64/1.80 tff(4789,plain,
% 1.64/1.80 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[841])).
% 1.64/1.80 tff(4790,plain,
% 1.64/1.80 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4789])).
% 1.64/1.80 tff(4791,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(z))))), z)),
% 1.64/1.80 inference(symmetry,[status(thm)],[4790])).
% 1.64/1.80 tff(4792,plain,
% 1.64/1.80 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(s(s(z))))), z))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4791])).
% 1.64/1.80 tff(4793,plain,
% 1.64/1.80 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[985, 4792])).
% 1.64/1.80 tff(4794,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[296, 4793])).
% 1.64/1.80 tff(4795,plain,((~(s(s(s(z))) = s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(4796,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[4795, 4787, 296])).
% 1.64/1.80 tff(4797,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[1685, 4796, 545])).
% 1.64/1.80 tff(4798,plain,
% 1.64/1.80 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[679, 4797, 4788])).
% 1.64/1.80 tff(4799,plain,
% 1.64/1.80 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4787])).
% 1.64/1.80 tff(4800,plain,
% 1.64/1.80 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.64/1.80 inference(transitivity,[status(thm)],[4799, 2792])).
% 1.64/1.80 tff(4801,plain,
% 1.64/1.80 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4800])).
% 1.64/1.80 tff(4802,plain,
% 1.64/1.80 (~(s(elem!1) = elem!1)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[1998, 4801])).
% 1.64/1.80 tff(4803,plain,
% 1.64/1.80 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[853, 815])).
% 1.64/1.80 tff(4804,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[526, 523])).
% 1.64/1.80 tff(4805,plain,
% 1.64/1.80 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4201])).
% 1.64/1.80 tff(4806,plain,
% 1.64/1.80 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(symmetry,[status(thm)],[4805])).
% 1.64/1.80 tff(4807,plain,
% 1.64/1.80 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[4806])).
% 1.64/1.80 tff(4808,plain,
% 1.64/1.80 (~r(s(s(s(elem!1))), z)),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[523, 4807])).
% 1.64/1.81 tff(4809,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[974, 4808])).
% 1.64/1.81 tff(4810,plain,((~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4811,plain,
% 1.64/1.81 (~(elem!1 = s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4810, 4796, 523])).
% 1.64/1.81 tff(4812,plain,
% 1.64/1.81 (~b(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2245, 1435, 465, 515])).
% 1.64/1.81 tff(4813,plain,
% 1.64/1.81 (r(elem!1, s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[1529, 4812, 1523])).
% 1.64/1.81 tff(4814,plain,
% 1.64/1.81 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4815,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4814])).
% 1.64/1.81 tff(4816,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4815, 516])).
% 1.64/1.81 tff(4817,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4818,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4817, 4816])).
% 1.64/1.81 tff(4819,plain,
% 1.64/1.81 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4818, 192, 515, 465, 1745])).
% 1.64/1.81 tff(4820,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[217, 4819])).
% 1.64/1.81 tff(4821,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4822,plain,
% 1.64/1.81 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4823,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4822])).
% 1.64/1.81 tff(4824,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4823, 4821])).
% 1.64/1.81 tff(4825,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4826,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4825, 4824])).
% 1.64/1.81 tff(4827,plain,
% 1.64/1.81 (~b(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4826, 192, 1435, 515, 1242, 465, 1745])).
% 1.64/1.81 tff(4828,plain,
% 1.64/1.81 (r(elem!1, s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2385, 4827, 3528])).
% 1.64/1.81 tff(4829,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4830,plain,
% 1.64/1.81 (((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4831,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4830])).
% 1.64/1.81 tff(4832,plain,
% 1.64/1.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4831, 4829])).
% 1.64/1.81 tff(4833,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4834,plain,
% 1.64/1.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4833, 4832])).
% 1.64/1.81 tff(4835,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4834, 77, 4828, 4820, 4813])).
% 1.64/1.81 tff(4836,plain,((~b(elem!1, z)) | (elem!1 = s(s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4837,plain,
% 1.64/1.81 (~b(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4836, 4811, 465, 4804, 1242, 4803, 515])).
% 1.64/1.81 tff(4838,plain,
% 1.64/1.81 (r(elem!1, z)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[2354, 4837, 2184])).
% 1.64/1.81 tff(4839,plain,
% 1.64/1.81 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.64/1.81 inference(symmetry,[status(thm)],[2792])).
% 1.64/1.81 tff(4840,plain,
% 1.64/1.81 ((elem!1 = s(s(s(z)))) <=> (elem!1 = s(elem!1))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4800, 4839])).
% 1.64/1.81 tff(4841,plain,
% 1.64/1.81 ((~(elem!1 = s(s(s(z))))) <=> (~(elem!1 = s(elem!1)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4840])).
% 1.64/1.81 tff(4842,plain,
% 1.64/1.81 (~(elem!1 = s(elem!1))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[1998, 4841])).
% 1.64/1.81 tff(4843,plain,
% 1.64/1.81 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4787])).
% 1.64/1.81 tff(4844,plain,
% 1.64/1.81 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4843])).
% 1.64/1.81 tff(4845,plain,
% 1.64/1.81 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[4844])).
% 1.64/1.81 tff(4846,plain,
% 1.64/1.81 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4845])).
% 1.64/1.81 tff(4847,plain,
% 1.64/1.81 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4846, 1978])).
% 1.64/1.81 tff(4848,plain,
% 1.64/1.81 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.64/1.81 inference(symmetry,[status(thm)],[4847])).
% 1.64/1.81 tff(4849,plain,
% 1.64/1.81 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4848])).
% 1.64/1.81 tff(4850,plain,
% 1.64/1.81 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4787])).
% 1.64/1.81 tff(4851,plain,
% 1.64/1.81 (s(s(z)) = elem!1),
% 1.64/1.81 inference(transitivity,[status(thm)],[16, 4850, 682])).
% 1.64/1.81 tff(4852,plain,
% 1.64/1.81 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4851])).
% 1.64/1.81 tff(4853,plain,
% 1.64/1.81 ((s(s(s(s(s(z))))) = s(s(z))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4852, 1978])).
% 1.64/1.81 tff(4854,plain,
% 1.64/1.81 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4853])).
% 1.64/1.81 tff(4855,plain,
% 1.64/1.81 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[3070, 4854])).
% 1.64/1.81 tff(4856,plain,
% 1.64/1.81 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4855, 4849])).
% 1.64/1.81 tff(4857,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[3218, 4856, 4842, 4796, 545, 4838, 4802, 4798])).
% 1.64/1.81 tff(4858,plain,((s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(elem!1), z)) | (elem!1 = s(s(s(z)))) | (elem!1 = z) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | r(s(s(s(s(z)))), z) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(s(s(s(z))), s(elem!1)) | r(s(elem!1), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(4859,plain,
% 1.64/1.81 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4858, 3053, 545, 2779, 4626, 1242, 4770, 523, 296, 4779, 4777, 4773])).
% 1.64/1.81 tff(4860,plain,
% 1.64/1.81 (s(s(s(s(s(s(z)))))) = s(s(elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4859])).
% 1.64/1.81 tff(4861,plain,
% 1.64/1.81 (s(s(elem!1)) = s(s(s(s(s(s(z))))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[4860])).
% 1.64/1.81 tff(4862,plain,
% 1.64/1.81 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[752, 4859])).
% 1.64/1.81 tff(4863,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[2277])).
% 1.64/1.81 tff(4864,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.81 inference(symmetry,[status(thm)],[4863])).
% 1.64/1.81 tff(4865,plain,
% 1.64/1.81 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[744, 723])).
% 1.64/1.81 tff(4866,plain,
% 1.64/1.81 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(monotonicity,[status(thm)],[2277])).
% 1.64/1.81 tff(4867,plain,
% 1.64/1.81 ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4866])).
% 1.64/1.81 tff(4868,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.64/1.81 tff(4869,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4870,plain,
% 1.64/1.81 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4871,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4870])).
% 1.64/1.81 tff(4872,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4871, 4869])).
% 1.64/1.81 tff(4873,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4874,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4873, 4872])).
% 1.64/1.81 tff(4875,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4874, 192, 4868, 515, 1242, 465, 1745])).
% 1.64/1.81 tff(4876,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4875, 4867])).
% 1.64/1.81 tff(4877,plain,
% 1.64/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4878,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4879,plain,
% 1.64/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4878, 4877])).
% 1.64/1.81 tff(4880,plain,
% 1.64/1.81 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4879, 60])).
% 1.64/1.81 tff(4881,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4880, 4876, 4865])).
% 1.64/1.81 tff(4882,plain,
% 1.64/1.81 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4881, 4864])).
% 1.64/1.81 tff(4883,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4884,plain,
% 1.64/1.81 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(4885,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[4884])).
% 1.64/1.81 tff(4886,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[4885, 4883])).
% 1.64/1.81 tff(4887,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(4888,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[4887, 4886])).
% 1.64/1.81 tff(4889,plain,
% 1.64/1.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[4888, 192, 4868, 515, 465])).
% 1.64/1.81 tff(4890,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.64/1.82 tff(4891,plain,
% 1.64/1.82 (s(z) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[4890])).
% 1.64/1.82 tff(4892,plain,
% 1.64/1.82 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4891])).
% 1.64/1.82 tff(4893,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[4892])).
% 1.64/1.82 tff(4894,plain,
% 1.64/1.82 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[727])).
% 1.64/1.82 tff(4895,plain,
% 1.64/1.82 (s(s(s(s(s(s(s(z))))))) = z),
% 1.64/1.82 inference(transitivity,[status(thm)],[4425, 4894, 4893, 20])).
% 1.64/1.82 tff(4896,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4083, 4895])).
% 1.64/1.82 tff(4897,plain,((~(s(s(s(s(elem!1)))) = s(z))) | (~(s(elem!1) = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4898,plain,
% 1.64/1.82 (~(s(s(s(s(elem!1)))) = s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4897, 723])).
% 1.64/1.82 tff(4899,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4900,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4901,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4900, 4899])).
% 1.64/1.82 tff(4902,plain,
% 1.64/1.82 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4901, 60, 4898, 4889])).
% 1.64/1.82 tff(4903,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4904,plain,
% 1.64/1.82 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4905,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4904])).
% 1.64/1.82 tff(4906,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4905, 4903])).
% 1.64/1.82 tff(4907,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4908,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 1.64/1.82 tff(4909,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4908, 77, 4820, 4902])).
% 1.64/1.82 tff(4910,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4909, 4882])).
% 1.64/1.82 tff(4911,plain,((~b(s(s(s(s(elem!1)))), z)) | (~(s(elem!1) = s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4912,plain,
% 1.64/1.82 (~b(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4911, 4862, 4626, 4804, 1242, 4770])).
% 1.64/1.82 tff(4913,plain,
% 1.64/1.82 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4914,plain,
% 1.64/1.82 (~(s(s(s(s(elem!1)))) = z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4913, 30])).
% 1.64/1.82 tff(4915,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4916,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4917,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4916, 4915])).
% 1.64/1.82 tff(4918,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4917, 60, 4914])).
% 1.64/1.82 tff(4919,plain,
% 1.64/1.82 (r(s(s(s(s(elem!1)))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4918, 4912])).
% 1.64/1.82 tff(4920,plain,
% 1.64/1.82 (~b(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[959, 4862, 39])).
% 1.64/1.82 tff(4921,plain,
% 1.64/1.82 (r(s(elem!1), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[950, 4920, 115])).
% 1.64/1.82 tff(4922,plain,
% 1.64/1.82 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[792, 668, 39, 67, 769])).
% 1.64/1.82 tff(4923,plain,
% 1.64/1.82 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[597, 4922, 1315])).
% 1.64/1.82 tff(4924,plain,
% 1.64/1.82 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4923])).
% 1.64/1.82 tff(4925,plain,
% 1.64/1.82 (s(s(s(s(z)))) = elem!1),
% 1.64/1.82 inference(transitivity,[status(thm)],[45, 4924, 682])).
% 1.64/1.82 tff(4926,plain,
% 1.64/1.82 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4925])).
% 1.64/1.82 tff(4927,plain,
% 1.64/1.82 (r(elem!1, s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[67, 4926])).
% 1.64/1.82 tff(4928,plain,
% 1.64/1.82 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[752, 4923])).
% 1.64/1.82 tff(4929,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1598, 4928])).
% 1.64/1.82 tff(4930,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4923])).
% 1.64/1.82 tff(4931,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4930, 703])).
% 1.64/1.82 tff(4932,plain,
% 1.64/1.82 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4931])).
% 1.64/1.82 tff(4933,plain,
% 1.64/1.82 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2314, 4928])).
% 1.64/1.82 tff(4934,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4933, 4932])).
% 1.64/1.82 tff(4935,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(s(z))))) <=> b(s(elem!1), elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4925])).
% 1.64/1.82 tff(4936,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1375, 668, 39, 67, 769])).
% 1.64/1.82 tff(4937,plain,
% 1.64/1.82 (b(s(elem!1), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4936, 4935])).
% 1.64/1.82 tff(4938,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3118, 4937, 4934, 667, 668, 4929, 4927])).
% 1.64/1.82 tff(4939,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | r(s(s(s(s(s(z))))), s(elem!1)) | b(s(s(s(s(s(z))))), s(z)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4940,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4939, 4921, 67, 4785, 39, 3173])).
% 1.64/1.82 tff(4941,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1313, 4940])).
% 1.64/1.82 tff(4942,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1330, 4941, 4626, 4770])).
% 1.64/1.82 tff(4943,plain,
% 1.64/1.82 (r(s(s(s(elem!1))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[992, 4942])).
% 1.64/1.82 tff(4944,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4945,plain,
% 1.64/1.82 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4946,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4945])).
% 1.64/1.82 tff(4947,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4946, 4944])).
% 1.64/1.82 tff(4948,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4949,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4948, 4947])).
% 1.64/1.82 tff(4950,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4949, 77, 4943, 4919])).
% 1.64/1.82 tff(4951,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[1598, 4862])).
% 1.64/1.82 tff(4952,assumption,(s(s(s(s(elem!1)))) = s(elem!1)), introduced(assumption)).
% 1.64/1.82 tff(4953,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4952])).
% 1.64/1.82 tff(4954,plain,
% 1.64/1.82 (s(s(s(elem!1))) = elem!1),
% 1.64/1.82 inference(transitivity,[status(thm)],[4894, 4953, 682])).
% 1.64/1.82 tff(4955,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2276, 4954])).
% 1.64/1.82 tff(4956,plain,((~(s(s(s(s(elem!1)))) = s(elem!1))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4957,plain,
% 1.64/1.82 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4956, 4951])).
% 1.64/1.82 tff(4958,assumption,(s(elem!1) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.82 tff(4959,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4958, 2405])).
% 1.64/1.82 tff(4960,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2422, 4959])).
% 1.64/1.82 tff(4961,plain,((~(s(elem!1) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(4962,plain,
% 1.64/1.82 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4961, 4957])).
% 1.64/1.82 tff(4963,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4964,plain,
% 1.64/1.82 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4965,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4964])).
% 1.64/1.82 tff(4966,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4965, 4963])).
% 1.64/1.82 tff(4967,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4968,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 1.64/1.82 tff(4969,plain,
% 1.64/1.82 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4968, 77, 545, 4919])).
% 1.64/1.82 tff(4970,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4971,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4972,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4971, 4970])).
% 1.64/1.82 tff(4973,plain,
% 1.64/1.82 ((s(elem!1) = s(s(s(s(elem!1))))) | b(s(elem!1), s(s(s(s(elem!1))))) | r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4972, 60])).
% 1.64/1.82 tff(4974,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4973, 4969, 4962])).
% 1.64/1.82 tff(4975,plain,
% 1.64/1.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4976,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4977,plain,
% 1.64/1.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 1.64/1.82 tff(4978,plain,
% 1.64/1.82 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4977, 77, 545, 4919])).
% 1.64/1.82 tff(4979,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4980,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4981,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 1.64/1.82 tff(4982,plain,
% 1.64/1.82 ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4981, 60])).
% 1.64/1.82 tff(4983,plain,
% 1.64/1.82 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4982, 4978, 4957])).
% 1.64/1.82 tff(4984,plain,
% 1.64/1.82 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2776, 4941, 4770, 545, 4921])).
% 1.64/1.82 tff(4985,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4859])).
% 1.64/1.82 tff(4986,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4985, 703])).
% 1.64/1.82 tff(4987,plain,
% 1.64/1.82 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4986])).
% 1.64/1.82 tff(4988,plain,
% 1.64/1.82 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2314, 4862])).
% 1.64/1.82 tff(4989,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4988, 4987])).
% 1.64/1.82 tff(4990,plain,
% 1.64/1.82 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[679, 4989, 4984])).
% 1.64/1.82 tff(4991,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4992,plain,
% 1.64/1.82 (((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4993,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4992])).
% 1.64/1.82 tff(4994,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[4993, 4991])).
% 1.64/1.82 tff(4995,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(4996,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4995, 4994])).
% 1.64/1.82 tff(4997,plain,
% 1.64/1.82 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4996, 192, 4990, 4983, 4974])).
% 1.64/1.82 tff(4998,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(4999,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5000,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[4999, 4998])).
% 1.64/1.82 tff(5001,plain,
% 1.64/1.82 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5000, 60])).
% 1.64/1.82 tff(5002,plain,
% 1.64/1.82 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5001, 4997, 4950])).
% 1.64/1.82 tff(5003,plain,
% 1.64/1.82 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5002])).
% 1.64/1.82 tff(5004,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[5003])).
% 1.64/1.82 tff(5005,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.64/1.82 inference(symmetry,[status(thm)],[5002])).
% 1.64/1.82 tff(5006,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), s(elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[4859])).
% 1.64/1.82 tff(5007,plain,
% 1.64/1.82 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[4694, 4772, 296])).
% 1.64/1.82 tff(5008,plain,
% 1.64/1.82 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[375, 5007])).
% 1.64/1.82 tff(5009,plain,
% 1.64/1.82 (b(s(s(s(z))), s(elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5008, 5006])).
% 1.64/1.82 tff(5010,plain,
% 1.64/1.82 (~(s(elem!1) = s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[3844, 4941, 39])).
% 1.64/1.82 tff(5011,plain,
% 1.64/1.82 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[2148, 60, 4773])).
% 1.64/1.82 tff(5012,plain,
% 1.64/1.82 (b(s(elem!1), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5011, 5010])).
% 1.64/1.82 tff(5013,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(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(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5014,plain,
% 1.64/1.82 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(5015,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[5014])).
% 1.64/1.82 tff(5016,plain,
% 1.64/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[5015, 5013])).
% 1.64/1.82 tff(5017,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(5018,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(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(z))))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[5017, 5016])).
% 1.64/1.82 tff(5019,plain,
% 1.64/1.82 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[5018, 192, 4983, 4974, 5012, 5009])).
% 1.64/1.82 tff(5020,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5021,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5022,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5021, 5020])).
% 1.64/1.83 tff(5023,plain,
% 1.64/1.83 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5022, 77, 4919, 4772])).
% 1.64/1.83 tff(5024,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5025,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5026,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5025, 5024])).
% 1.64/1.83 tff(5027,plain,
% 1.64/1.83 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5026, 60, 5023])).
% 1.64/1.83 tff(5028,plain,
% 1.64/1.83 (s(s(s(s(elem!1)))) = s(s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5027, 5019])).
% 1.64/1.83 tff(5029,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(s(s(elem!1))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5028])).
% 1.64/1.83 tff(5030,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5029, 5005, 4894, 5004, 691, 4861])).
% 1.64/1.83 tff(5031,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2419, 5030])).
% 1.64/1.83 tff(5032,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), z) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5033,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5032, 545, 39, 67, 115, 1242, 523, 296])).
% 1.64/1.83 tff(5034,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1188, 5033, 396])).
% 1.64/1.83 tff(5035,plain,
% 1.64/1.83 (s(s(s(z))) = s(elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2713, 5034, 4779, 4777, 4773])).
% 1.64/1.83 tff(5036,plain,
% 1.64/1.83 (s(s(s(z))) = s(s(s(s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5035, 5033])).
% 1.64/1.83 tff(5037,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[145, 5036])).
% 1.64/1.83 tff(5038,plain,((~r(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(s(z)))), z) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5039,plain,
% 1.64/1.83 (~r(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5038, 4768, 39, 67, 115, 4734, 4766, 3356])).
% 1.64/1.83 tff(5040,plain,
% 1.64/1.83 (b(s(elem!1), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[560, 5039])).
% 1.64/1.83 tff(5041,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3263, 583, 135])).
% 1.64/1.83 tff(5042,plain,
% 1.64/1.83 (~b(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1239, 583, 4626, 4736])).
% 1.64/1.83 tff(5043,plain,
% 1.64/1.83 (r(s(elem!1), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[950, 5042, 115])).
% 1.64/1.83 tff(5044,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2692, 5043, 66])).
% 1.64/1.83 tff(5045,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[792, 5043, 39, 67, 769])).
% 1.64/1.83 tff(5046,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[597, 5045, 5044, 5041])).
% 1.64/1.83 tff(5047,plain,((~b(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(elem!1)) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5048,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5047, 5040, 67, 39, 115, 135])).
% 1.64/1.83 tff(5049,plain,
% 1.64/1.83 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3172, 5048])).
% 1.64/1.83 tff(5050,plain,
% 1.64/1.83 (elem!1 = s(s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3339, 5049])).
% 1.64/1.83 tff(5051,plain,
% 1.64/1.83 (s(s(s(z))) = elem!1),
% 1.64/1.83 inference(symmetry,[status(thm)],[5050])).
% 1.64/1.83 tff(5052,plain,
% 1.64/1.83 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5049])).
% 1.64/1.83 tff(5053,plain,
% 1.64/1.83 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5052])).
% 1.64/1.83 tff(5054,plain,
% 1.64/1.83 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5053])).
% 1.64/1.83 tff(5055,plain,
% 1.64/1.83 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5054, 5051])).
% 1.64/1.83 tff(5056,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5055])).
% 1.64/1.83 tff(5057,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5051, 5054])).
% 1.64/1.83 tff(5058,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.64/1.83 inference(transitivity,[status(thm)],[5057, 1976])).
% 1.64/1.83 tff(5059,plain,
% 1.64/1.83 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5058])).
% 1.64/1.83 tff(5060,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[2419, 5059])).
% 1.64/1.83 tff(5061,plain,
% 1.64/1.83 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5050])).
% 1.64/1.83 tff(5062,plain,
% 1.64/1.83 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[5061])).
% 1.64/1.83 tff(5063,plain,
% 1.64/1.83 (b(s(z), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[4744, 5062])).
% 1.64/1.83 tff(5064,plain,
% 1.64/1.83 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5050])).
% 1.64/1.83 tff(5065,plain,
% 1.64/1.83 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5064])).
% 1.64/1.83 tff(5066,plain,
% 1.64/1.83 (b(elem!1, s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[3447, 5065])).
% 1.64/1.83 tff(5067,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(z)))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(symmetry,[status(thm)],[1356])).
% 1.64/1.83 tff(5068,plain,
% 1.64/1.83 ((~r(s(s(s(s(s(s(z)))))), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5067])).
% 1.64/1.83 tff(5069,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[1159, 4563])).
% 1.64/1.83 tff(5070,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[2294, 1316, 2237, 2268])).
% 1.64/1.83 tff(5071,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1628, 5070, 4568])).
% 1.64/1.83 tff(5072,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5071, 5069])).
% 1.64/1.83 tff(5073,plain,
% 1.64/1.83 (~r(s(s(s(s(s(s(z)))))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3763, 77, 2650, 5072])).
% 1.64/1.83 tff(5074,plain,
% 1.64/1.83 (~r(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5073, 5068])).
% 1.64/1.83 tff(5075,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1330, 1316, 465, 515])).
% 1.64/1.83 tff(5076,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[992, 5075])).
% 1.64/1.83 tff(5077,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5076, 5074])).
% 1.64/1.83 tff(5078,plain,((~b(s(s(s(elem!1))), s(z))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(5079,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5078, 5049, 4752, 5066, 5063, 4626, 4736])).
% 1.64/1.83 tff(5080,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1313, 5079])).
% 1.64/1.83 tff(5081,plain,
% 1.64/1.83 ((s(z) = elem!1) <=> (s(z) = s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5050])).
% 1.64/1.83 tff(5082,plain,
% 1.64/1.83 ((s(z) = elem!1) <=> (s(s(s(z))) = s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5081, 419])).
% 1.64/1.83 tff(5083,plain,
% 1.64/1.83 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[5082])).
% 1.64/1.83 tff(5084,plain,
% 1.64/1.83 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5083, 2186])).
% 1.64/1.83 tff(5085,plain,
% 1.64/1.83 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5084])).
% 1.64/1.83 tff(5086,plain,
% 1.64/1.83 (~(elem!1 = s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[34, 5085])).
% 1.64/1.83 tff(5087,plain,
% 1.64/1.83 (~r(z, s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3745, 5049, 4767])).
% 1.64/1.83 tff(5088,plain,
% 1.64/1.83 (b(z, s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[580, 5087])).
% 1.64/1.83 tff(5089,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[699, 5048])).
% 1.64/1.83 tff(5090,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.83 inference(symmetry,[status(thm)],[5049])).
% 1.64/1.83 tff(5091,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5054, 5090])).
% 1.64/1.83 tff(5092,plain,
% 1.64/1.83 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5091])).
% 1.64/1.83 tff(5093,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5054])).
% 1.64/1.83 tff(5094,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5093])).
% 1.64/1.83 tff(5095,plain,
% 1.64/1.83 (r(s(s(s(s(s(s(z)))))), s(z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5080, 5094])).
% 1.64/1.83 tff(5096,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5097,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5098,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 1.64/1.83 tff(5099,plain,
% 1.64/1.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5098, 77, 67, 5095])).
% 1.64/1.83 tff(5100,plain,
% 1.64/1.83 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5099, 5092])).
% 1.64/1.83 tff(5101,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[679, 5100, 5089])).
% 1.64/1.83 tff(5102,plain,
% 1.64/1.83 (~b(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1931, 5101, 5040, 5088])).
% 1.64/1.83 tff(5103,plain,
% 1.64/1.83 (r(s(s(s(elem!1))), z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[992, 5102])).
% 1.64/1.83 tff(5104,plain,
% 1.64/1.83 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[3084, 5103, 2779, 4626, 4736, 5086, 5080])).
% 1.64/1.83 tff(5105,plain,
% 1.64/1.83 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[1628, 5104, 5060])).
% 1.64/1.83 tff(5106,plain,
% 1.64/1.83 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5105, 5056])).
% 1.64/1.83 tff(5107,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(5108,plain,
% 1.64/1.83 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5107])).
% 1.64/1.83 tff(5109,plain,
% 1.64/1.83 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5108])).
% 1.64/1.83 tff(5110,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[1170, 5109])).
% 1.64/1.83 tff(5111,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5112,plain,
% 1.64/1.83 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5113,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5112])).
% 1.64/1.83 tff(5114,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5113, 5111])).
% 1.64/1.83 tff(5115,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5116,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 1.64/1.83 tff(5117,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5116, 77, 66, 5095])).
% 1.64/1.83 tff(5118,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5119,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5120,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 1.64/1.83 tff(5121,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5120, 60, 5117])).
% 1.64/1.83 tff(5122,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5121, 5110])).
% 1.64/1.83 tff(5123,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(5124,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(z)))) = s(s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5054])).
% 1.64/1.83 tff(5125,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5124, 5123])).
% 1.64/1.83 tff(5126,plain,
% 1.64/1.83 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5125])).
% 1.64/1.83 tff(5127,plain,
% 1.64/1.83 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5126])).
% 1.64/1.83 tff(5128,plain,
% 1.64/1.83 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5090])).
% 1.64/1.83 tff(5129,plain,
% 1.64/1.83 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[5128])).
% 1.64/1.83 tff(5130,plain,
% 1.64/1.83 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5129])).
% 1.64/1.83 tff(5131,plain,
% 1.64/1.83 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5089, 5130])).
% 1.64/1.83 tff(5132,plain,
% 1.64/1.83 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5131, 5127])).
% 1.64/1.83 tff(5133,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5134,plain,
% 1.64/1.83 (((~r(s(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(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5135,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5134])).
% 1.64/1.83 tff(5136,plain,
% 1.64/1.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[5135, 5133])).
% 1.64/1.83 tff(5137,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z)))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5138,plain,
% 1.64/1.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5137, 5136])).
% 1.64/1.83 tff(5139,plain,
% 1.64/1.83 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5138, 77, 67, 5095])).
% 1.64/1.83 tff(5140,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5141,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(5142,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[5141, 5140])).
% 1.64/1.83 tff(5143,plain,
% 1.64/1.83 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5142, 60, 5139])).
% 1.64/1.83 tff(5144,plain,
% 1.64/1.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[5143, 5132])).
% 1.64/1.83 tff(5145,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5146,plain,
% 1.64/1.83 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(5147,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[5146])).
% 1.64/1.83 tff(5148,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5147, 5145])).
% 1.64/1.84 tff(5149,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5150,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5149, 5148])).
% 1.64/1.84 tff(5151,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5150, 192, 4734, 114, 4757, 5144, 5122, 5106])).
% 1.64/1.84 tff(5152,plain,(b(s(s(s(s(s(z))))), z) | (~r(s(s(s(s(z)))), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5153,plain,
% 1.64/1.84 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5152, 4732, 39, 115, 135])).
% 1.64/1.84 tff(5154,plain,
% 1.64/1.84 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[319, 5153])).
% 1.64/1.84 tff(5155,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[83, 77, 4732, 66])).
% 1.64/1.84 tff(5156,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[113, 5155])).
% 1.64/1.84 tff(5157,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[449, 5156, 4700, 4696])).
% 1.64/1.84 tff(5158,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[390, 5157])).
% 1.64/1.84 tff(5159,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2456, 77, 321, 503, 383])).
% 1.64/1.84 tff(5160,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5161,plain,
% 1.64/1.84 (~r(z, s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5160, 5158, 4685])).
% 1.64/1.84 tff(5162,plain,
% 1.64/1.84 (b(z, s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[339, 5161])).
% 1.64/1.84 tff(5163,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5164,plain,
% 1.64/1.84 (((~b(s(z), 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(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5165,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5164])).
% 1.64/1.84 tff(5166,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5165, 5163])).
% 1.64/1.84 tff(5167,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5168,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5167, 5166])).
% 1.64/1.84 tff(5169,plain,
% 1.64/1.84 (~b(z, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5168, 192, 4700, 5162, 4626, 5154, 3447, 4696])).
% 1.64/1.84 tff(5170,plain,
% 1.64/1.84 (r(z, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[237, 5169])).
% 1.64/1.84 tff(5171,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5172,plain,
% 1.64/1.84 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5173,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5172])).
% 1.64/1.84 tff(5174,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5173, 5171])).
% 1.64/1.84 tff(5175,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5176,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5175, 5174])).
% 1.64/1.84 tff(5177,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5176, 77, 296, 2650, 117])).
% 1.64/1.84 tff(5178,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5179,plain,
% 1.64/1.84 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5178, 3356, 5170])).
% 1.64/1.84 tff(5180,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[133, 5179])).
% 1.64/1.84 tff(5181,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5182,plain,
% 1.64/1.84 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5183,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5182])).
% 1.64/1.84 tff(5184,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5183, 5181])).
% 1.64/1.84 tff(5185,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5186,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5185, 5184])).
% 1.64/1.84 tff(5187,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5186, 192, 4700, 5156, 5180, 4696])).
% 1.64/1.84 tff(5188,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[406, 5187])).
% 1.64/1.84 tff(5189,plain,
% 1.64/1.84 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5047, 583, 135, 39, 115, 4732])).
% 1.64/1.84 tff(5190,plain,
% 1.64/1.84 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3172, 5189])).
% 1.64/1.84 tff(5191,plain,
% 1.64/1.84 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5190])).
% 1.64/1.84 tff(5192,plain,
% 1.64/1.84 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(elem!1))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5191])).
% 1.64/1.84 tff(5193,plain,
% 1.64/1.84 (b(s(z), s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5154, 5192])).
% 1.64/1.84 tff(5194,plain,
% 1.64/1.84 (~b(z, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[649, 5193, 4683, 583])).
% 1.64/1.84 tff(5195,plain,
% 1.64/1.84 (~b(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4615, 5190, 4684])).
% 1.64/1.84 tff(5196,plain,
% 1.64/1.84 (r(elem!1, z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2354, 5195, 2779])).
% 1.64/1.84 tff(5197,plain,
% 1.64/1.84 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5190])).
% 1.64/1.84 tff(5198,plain,
% 1.64/1.84 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5197])).
% 1.64/1.84 tff(5199,plain,
% 1.64/1.84 (elem!1 = s(s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3339, 5190])).
% 1.64/1.84 tff(5200,plain,
% 1.64/1.84 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5199])).
% 1.64/1.84 tff(5201,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[5200])).
% 1.64/1.84 tff(5202,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(elem!1))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5201, 5198])).
% 1.64/1.84 tff(5203,plain,
% 1.64/1.84 (r(elem!1, s(elem!1))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5158, 5202])).
% 1.64/1.84 tff(5204,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5205,plain,
% 1.64/1.84 (((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z))) <=> ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5206,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5205])).
% 1.64/1.84 tff(5207,plain,
% 1.64/1.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5206, 5204])).
% 1.64/1.84 tff(5208,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, z)))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5209,plain,
% 1.64/1.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5208, 5207])).
% 1.64/1.84 tff(5210,plain,
% 1.64/1.84 ((~r(z, s(elem!1))) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5209, 77])).
% 1.64/1.84 tff(5211,plain,
% 1.64/1.84 (~r(z, s(elem!1))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5210, 5203, 5196])).
% 1.64/1.84 tff(5212,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[580, 5211, 5194])).
% 1.64/1.84 tff(5213,plain,((~b(s(elem!1), z)) | b(s(s(s(s(s(z))))), z) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5214,plain,
% 1.64/1.84 (~b(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5213, 135, 39, 115])).
% 1.64/1.84 tff(5215,plain,
% 1.64/1.84 (r(s(elem!1), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[560, 5214])).
% 1.64/1.84 tff(5216,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5038, 5162, 39, 4732, 115, 4700, 5215, 3356])).
% 1.64/1.84 tff(5217,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[3603, 77, 5216, 5188, 5170])).
% 1.64/1.84 tff(5218,plain,(b(s(s(s(s(s(z))))), z) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5219,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5218, 115, 39])).
% 1.64/1.84 tff(5220,plain,
% 1.64/1.84 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4654, 512, 1408, 118, 465, 239])).
% 1.64/1.84 tff(5221,plain,
% 1.64/1.84 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[319, 5220])).
% 1.64/1.84 tff(5222,plain,
% 1.64/1.84 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[943, 77, 1412, 527])).
% 1.64/1.84 tff(5223,plain,
% 1.64/1.84 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[390, 5222])).
% 1.64/1.84 tff(5224,plain,
% 1.64/1.84 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[4176, 408, 118])).
% 1.64/1.84 tff(5225,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[133, 5224])).
% 1.64/1.84 tff(5226,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[417, 408, 308])).
% 1.64/1.84 tff(5227,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[406, 5226])).
% 1.64/1.84 tff(5228,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[404, 5227, 5225, 393, 395])).
% 1.64/1.84 tff(5229,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5230,plain,
% 1.64/1.84 (~r(s(z), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5229, 5223, 5221, 118])).
% 1.64/1.84 tff(5231,plain,
% 1.64/1.84 (b(s(z), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[427, 5230])).
% 1.64/1.84 tff(5232,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[2544, 77, 1412, 527])).
% 1.64/1.84 tff(5233,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[406, 5232])).
% 1.64/1.84 tff(5234,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5235,plain,
% 1.64/1.84 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(5236,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5235])).
% 1.64/1.84 tff(5237,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[5236, 5234])).
% 1.64/1.84 tff(5238,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(5239,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[5238, 5237])).
% 1.64/1.84 tff(5240,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5239, 192, 512, 5223, 1408, 5233, 5231])).
% 1.64/1.84 tff(5241,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5242,plain,
% 1.64/1.84 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5241, 3447, 66, 4683, 4626, 5219])).
% 1.64/1.84 tff(5243,plain,
% 1.64/1.84 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[217, 5242])).
% 1.64/1.84 tff(5244,plain,
% 1.64/1.84 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[83, 77, 5243, 66])).
% 1.64/1.84 tff(5245,plain,
% 1.64/1.84 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[113, 5244])).
% 1.64/1.84 tff(5246,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(5247,plain,
% 1.64/1.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5246])).
% 1.64/1.84 tff(5248,plain,
% 1.64/1.84 (s(s(elem!1)) = s(s(z))),
% 1.64/1.84 inference(transitivity,[status(thm)],[1035, 5247, 15])).
% 1.64/1.84 tff(5249,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[5248])).
% 1.64/1.84 tff(5250,plain,
% 1.64/1.84 (s(elem!1) = s(z)),
% 1.64/1.84 inference(transitivity,[status(thm)],[1047, 5249, 10])).
% 1.64/1.84 tff(5251,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[115, 5250])).
% 1.64/1.84 tff(5252,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(5253,plain,
% 1.64/1.84 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5252, 115])).
% 1.64/1.84 tff(5254,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[449, 395, 4700, 5245])).
% 1.64/1.84 tff(5255,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[375, 5254])).
% 1.64/1.84 tff(5256,plain,
% 1.64/1.84 (~r(s(z), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[5229, 395, 308, 66])).
% 1.64/1.85 tff(5257,plain,
% 1.64/1.85 (b(s(z), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[427, 5256])).
% 1.64/1.85 tff(5258,plain,
% 1.64/1.85 (~b(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4750, 192, 4683, 4626, 3447, 5257])).
% 1.64/1.85 tff(5259,plain,
% 1.64/1.85 (r(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[237, 5258])).
% 1.64/1.85 tff(5260,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5261,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5262,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5261, 5260])).
% 1.64/1.85 tff(5263,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5262, 77, 462, 2650, 4686])).
% 1.64/1.85 tff(5264,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5265,plain,
% 1.64/1.85 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5264, 5259, 5255])).
% 1.64/1.85 tff(5266,plain,
% 1.64/1.85 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[493, 5265])).
% 1.64/1.85 tff(5267,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1157])).
% 1.64/1.85 tff(5268,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(5269,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(5270,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5271,plain,
% 1.64/1.85 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5272,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5271])).
% 1.64/1.85 tff(5273,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5272, 5270])).
% 1.64/1.85 tff(5274,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5275,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5274, 5273])).
% 1.64/1.85 tff(5276,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5275, 192, 1316, 1408, 3527, 5269])).
% 1.64/1.85 tff(5277,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5278,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5277, 1316, 1408, 3527])).
% 1.64/1.85 tff(5279,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1958, 60, 5278, 5268])).
% 1.64/1.85 tff(5280,plain,
% 1.64/1.85 (~b(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4750, 192, 515, 465, 1408, 3527])).
% 1.64/1.85 tff(5281,plain,
% 1.64/1.85 (r(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[237, 5280])).
% 1.64/1.85 tff(5282,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5283,plain,
% 1.64/1.85 (((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5284,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5283])).
% 1.64/1.85 tff(5285,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5284, 5282])).
% 1.64/1.85 tff(5286,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5287,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5286, 5285])).
% 1.64/1.85 tff(5288,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5287, 77, 5076, 5281, 5279])).
% 1.64/1.85 tff(5289,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5290,plain,
% 1.64/1.85 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5289, 3527, 4626, 4683, 3447, 5253])).
% 1.64/1.85 tff(5291,plain,
% 1.64/1.85 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1313, 5290])).
% 1.64/1.85 tff(5292,plain,
% 1.64/1.85 (~b(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4750, 192, 4683, 4626, 3447, 3527])).
% 1.64/1.85 tff(5293,plain,
% 1.64/1.85 (r(z, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[237, 5292])).
% 1.64/1.85 tff(5294,plain,
% 1.64/1.85 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5264, 5293, 5255])).
% 1.64/1.85 tff(5295,plain,
% 1.64/1.85 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[493, 5294])).
% 1.64/1.85 tff(5296,plain,
% 1.64/1.85 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[615, 192, 4683, 5295, 5219])).
% 1.64/1.85 tff(5297,plain,
% 1.64/1.85 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[438, 60, 5296, 380])).
% 1.64/1.85 tff(5298,plain,
% 1.64/1.85 (~b(z, s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1753, 1745, 239, 396])).
% 1.64/1.85 tff(5299,plain,
% 1.64/1.85 (r(z, s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[339, 5298])).
% 1.64/1.85 tff(5300,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2662, 77, 321, 409, 2650])).
% 1.64/1.85 tff(5301,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5302,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5301, 5299, 2650])).
% 1.64/1.85 tff(5303,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[406, 5302])).
% 1.64/1.85 tff(5304,plain,
% 1.64/1.85 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[404, 5303, 396, 395])).
% 1.64/1.85 tff(5305,plain,
% 1.64/1.85 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[133, 5304])).
% 1.64/1.85 tff(5306,plain,
% 1.64/1.85 (~b(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4669, 1745, 239, 441])).
% 1.64/1.85 tff(5307,plain,
% 1.64/1.85 (r(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[493, 5306])).
% 1.64/1.85 tff(5308,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5309,plain,
% 1.64/1.85 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5310,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5309])).
% 1.64/1.85 tff(5311,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5310, 5308])).
% 1.64/1.85 tff(5312,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5313,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 1.64/1.85 tff(5314,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5313, 77, 5307, 2650, 5305])).
% 1.64/1.85 tff(5315,plain,((~b(s(s(s(s(z)))), z)) | (~r(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)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5316,plain,
% 1.64/1.85 (~b(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5315, 5293, 4700, 395, 5219, 5245])).
% 1.64/1.85 tff(5317,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[526, 5316])).
% 1.64/1.85 tff(5318,plain,
% 1.64/1.85 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2692, 668, 66])).
% 1.64/1.85 tff(5319,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[4939, 5318, 668, 67, 769, 39, 667])).
% 1.64/1.85 tff(5320,plain,((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5321,plain,
% 1.64/1.85 (~r(s(elem!1), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5320, 667, 769, 39, 67])).
% 1.64/1.85 tff(5322,plain,
% 1.64/1.85 (b(s(elem!1), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[950, 5321, 115])).
% 1.64/1.85 tff(5323,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5324,plain,
% 1.64/1.85 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5325,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5324])).
% 1.64/1.85 tff(5326,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5325, 5323])).
% 1.64/1.85 tff(5327,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5328,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5327, 5326])).
% 1.64/1.85 tff(5329,plain,
% 1.64/1.85 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5328, 192, 515, 5322, 4626, 3447, 3527])).
% 1.64/1.85 tff(5330,plain,
% 1.64/1.85 (~b(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[935, 192, 515, 4626, 3447])).
% 1.64/1.85 tff(5331,plain,
% 1.64/1.85 (r(s(s(s(z))), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[253, 5330])).
% 1.64/1.85 tff(5332,plain,
% 1.64/1.85 (~b(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1239, 5322, 4626, 515])).
% 1.64/1.85 tff(5333,plain,
% 1.64/1.85 (r(s(elem!1), z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[560, 5332])).
% 1.64/1.85 tff(5334,plain,
% 1.64/1.85 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[3944, 77, 5333, 5331])).
% 1.64/1.85 tff(5335,plain,
% 1.64/1.85 (s(elem!1) = s(s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2148, 60, 5334, 5329])).
% 1.64/1.85 tff(5336,plain,
% 1.64/1.85 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5335])).
% 1.64/1.85 tff(5337,plain,
% 1.64/1.85 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5336])).
% 1.64/1.85 tff(5338,plain,
% 1.64/1.85 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5337])).
% 1.64/1.85 tff(5339,plain,
% 1.64/1.85 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5335])).
% 1.64/1.85 tff(5340,plain,
% 1.64/1.85 (elem!1 = s(s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[695, 5339, 15])).
% 1.64/1.85 tff(5341,plain,
% 1.64/1.85 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5337, 5340])).
% 1.64/1.85 tff(5342,plain,
% 1.64/1.85 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.64/1.85 inference(symmetry,[status(thm)],[5341])).
% 1.64/1.85 tff(5343,plain,
% 1.64/1.85 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5342])).
% 1.64/1.85 tff(5344,plain,
% 1.64/1.85 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3070, 5343])).
% 1.64/1.85 tff(5345,plain,
% 1.64/1.85 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5339])).
% 1.64/1.85 tff(5346,plain,
% 1.64/1.85 (s(s(z)) = elem!1),
% 1.64/1.85 inference(transitivity,[status(thm)],[16, 5345, 682])).
% 1.64/1.85 tff(5347,plain,
% 1.64/1.85 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5346])).
% 1.64/1.85 tff(5348,plain,
% 1.64/1.85 ((s(z) = s(s(z))) <=> (elem!1 = s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5347, 2186])).
% 1.64/1.85 tff(5349,plain,
% 1.64/1.85 ((~(s(z) = s(s(z)))) <=> (~(elem!1 = s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5348])).
% 1.64/1.85 tff(5350,plain,
% 1.64/1.85 (~(elem!1 = s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[2196, 5349])).
% 1.64/1.85 tff(5351,plain,
% 1.64/1.85 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2544, 77, 5331, 297])).
% 1.64/1.85 tff(5352,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[406, 5351])).
% 1.64/1.85 tff(5353,plain,
% 1.64/1.85 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2173])).
% 1.64/1.85 tff(5354,plain,
% 1.64/1.85 (~r(elem!1, s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3205, 5353])).
% 1.64/1.85 tff(5355,plain,
% 1.64/1.85 (b(elem!1, s(s(s(z))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2037, 5354, 1998])).
% 1.64/1.85 tff(5356,plain,
% 1.64/1.85 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5355, 3526])).
% 1.64/1.85 tff(5357,plain,
% 1.64/1.85 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2379, 192, 395, 394, 5356])).
% 1.64/1.85 tff(5358,plain,
% 1.64/1.85 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[2177])).
% 1.64/1.85 tff(5359,plain,
% 1.64/1.85 (r(elem!1, z) <=> r(s(s(z)), z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[5358])).
% 1.64/1.85 tff(5360,plain,
% 1.64/1.85 (r(s(s(z)), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[3199, 5359])).
% 1.64/1.85 tff(5361,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5362,plain,
% 1.64/1.85 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5363,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5362])).
% 1.64/1.85 tff(5364,plain,
% 1.64/1.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[5363, 5361])).
% 1.64/1.85 tff(5365,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5366,plain,
% 1.64/1.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5365, 5364])).
% 1.64/1.85 tff(5367,plain,
% 1.64/1.85 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5366, 77, 297])).
% 1.64/1.85 tff(5368,plain,
% 1.64/1.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5367, 5360])).
% 1.64/1.85 tff(5369,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(5370,plain,
% 1.64/1.85 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[5369])).
% 1.64/1.85 tff(5371,plain,
% 1.64/1.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[5370])).
% 1.64/1.85 tff(5372,plain,
% 1.64/1.85 (s(s(s(z))) = s(z)),
% 1.64/1.85 inference(transitivity,[status(thm)],[92, 5371, 10])).
% 1.64/1.85 tff(5373,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[34, 5372])).
% 1.64/1.85 tff(5374,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5375,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.85 tff(5376,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.85 tff(5377,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(5378,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(5379,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 1.64/1.85 tff(5380,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5379, 60, 5376, 5375, 5374])).
% 1.64/1.85 tff(5381,plain,(r(s(s(z)), s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5382,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5381, 5368, 5357])).
% 1.64/1.85 tff(5383,plain,((~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(elem!1) = s(s(s(z))))) | (elem!1 = s(s(s(z)))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(5384,plain,
% 1.64/1.85 (~r(elem!1, z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[5383, 5335, 395, 5352, 297, 1998, 5333])).
% 1.64/1.85 tff(5385,plain,
% 1.64/1.85 (b(elem!1, z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[2354, 5384, 2779])).
% 1.64/1.85 tff(5386,plain,
% 1.64/1.85 (~b(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2245, 5385, 4626, 515])).
% 1.64/1.86 tff(5387,plain,
% 1.64/1.86 (r(elem!1, s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1529, 5386, 5350])).
% 1.64/1.86 tff(5388,plain,
% 1.64/1.86 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2565, 5387, 667])).
% 1.64/1.86 tff(5389,plain,
% 1.64/1.86 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1628, 5388, 5344])).
% 1.64/1.86 tff(5390,plain,
% 1.64/1.86 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5389, 5338])).
% 1.64/1.86 tff(5391,plain,
% 1.64/1.86 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[959, 5322, 39])).
% 1.64/1.86 tff(5392,plain,
% 1.64/1.86 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[752, 5391])).
% 1.64/1.86 tff(5393,plain,
% 1.64/1.86 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[853, 5392])).
% 1.64/1.86 tff(5394,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5393, 3032])).
% 1.64/1.86 tff(5395,plain,
% 1.64/1.86 ((~(s(z) = s(s(z)))) <=> (~(s(z) = elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5347])).
% 1.64/1.86 tff(5396,plain,
% 1.64/1.86 (~(s(z) = elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2196, 5395])).
% 1.64/1.86 tff(5397,plain,
% 1.64/1.86 ((s(elem!1) = elem!1) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5335])).
% 1.64/1.86 tff(5398,plain,
% 1.64/1.86 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5397, 2011])).
% 1.64/1.86 tff(5399,plain,
% 1.64/1.86 ((elem!1 = s(s(s(z)))) <=> (s(elem!1) = elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[5398])).
% 1.64/1.86 tff(5400,plain,
% 1.64/1.86 ((~(elem!1 = s(s(s(z))))) <=> (~(s(elem!1) = elem!1))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5399])).
% 1.64/1.86 tff(5401,plain,
% 1.64/1.86 (~(s(elem!1) = elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1998, 5400])).
% 1.64/1.86 tff(5402,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2177])).
% 1.64/1.86 tff(5403,plain,
% 1.64/1.86 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5402])).
% 1.64/1.86 tff(5404,plain,
% 1.64/1.86 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2172])).
% 1.64/1.86 tff(5405,plain,
% 1.64/1.86 (b(s(elem!1), elem!1) <=> b(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5404, 5403])).
% 1.64/1.86 tff(5406,plain,
% 1.64/1.86 (~b(z, elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3887, 1435, 515, 2268])).
% 1.64/1.86 tff(5407,plain,
% 1.64/1.86 (r(z, elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2911, 5406, 1548])).
% 1.64/1.86 tff(5408,plain,
% 1.64/1.86 (~r(s(elem!1), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[4372, 5407, 545])).
% 1.64/1.86 tff(5409,plain,
% 1.64/1.86 (b(s(elem!1), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3123, 5408, 2795])).
% 1.64/1.86 tff(5410,plain,
% 1.64/1.86 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5409, 5405])).
% 1.64/1.86 tff(5411,plain,
% 1.64/1.86 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3522])).
% 1.64/1.86 tff(5412,plain,
% 1.64/1.86 (b(s(z), s(s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2268, 5411])).
% 1.64/1.86 tff(5413,plain,
% 1.64/1.86 (b(elem!1, z) <=> b(s(s(z)), z)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3522])).
% 1.64/1.86 tff(5414,plain,
% 1.64/1.86 (b(s(s(z)), z)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1435, 5413])).
% 1.64/1.86 tff(5415,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5416,plain,
% 1.64/1.86 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5417,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5416])).
% 1.64/1.86 tff(5418,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5417, 5415])).
% 1.64/1.86 tff(5419,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5420,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5419, 5418])).
% 1.64/1.86 tff(5421,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5420, 192, 515, 5414, 5412, 5410, 3527])).
% 1.64/1.86 tff(5422,plain,((~b(elem!1, z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(s(s(z))))) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (z = elem!1) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5423,plain,
% 1.64/1.86 (~b(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5422, 5385, 3527, 5335, 5401, 5333, 2885, 515])).
% 1.64/1.86 tff(5424,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5425,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5426,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5425, 5424])).
% 1.64/1.86 tff(5427,plain,
% 1.64/1.86 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5426, 60])).
% 1.64/1.86 tff(5428,plain,
% 1.64/1.86 (r(s(z), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5427, 5423, 5396])).
% 1.64/1.86 tff(5429,plain,
% 1.64/1.86 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[2177])).
% 1.64/1.86 tff(5430,plain,
% 1.64/1.86 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5429])).
% 1.64/1.86 tff(5431,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.64/1.86 tff(5432,plain,
% 1.64/1.86 (r(s(z), s(s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5431, 5430])).
% 1.64/1.86 tff(5433,plain,
% 1.64/1.86 (r(elem!1, s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3522])).
% 1.64/1.86 tff(5434,plain,
% 1.64/1.86 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3838])).
% 1.64/1.86 tff(5435,plain,
% 1.64/1.86 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5434, 1978])).
% 1.64/1.86 tff(5436,plain,
% 1.64/1.86 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[5435])).
% 1.64/1.86 tff(5437,plain,
% 1.64/1.86 ((elem!1 = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5436, 1977])).
% 1.64/1.86 tff(5438,plain,
% 1.64/1.86 (elem!1 = s(s(s(elem!1)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2205, 5437])).
% 1.64/1.86 tff(5439,plain,
% 1.64/1.86 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[3838])).
% 1.64/1.86 tff(5440,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(s(s(s(elem!1))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5439])).
% 1.64/1.86 tff(5441,plain,
% 1.64/1.86 (s(s(s(z))) = s(elem!1)),
% 1.64/1.86 inference(symmetry,[status(thm)],[2172])).
% 1.64/1.86 tff(5442,plain,
% 1.64/1.86 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(elem!1) = s(s(s(s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5441, 5440])).
% 1.64/1.86 tff(5443,plain,
% 1.64/1.86 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5442, 2405])).
% 1.64/1.86 tff(5444,plain,
% 1.64/1.86 ((~(s(s(s(z))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5443])).
% 1.64/1.86 tff(5445,plain,
% 1.64/1.86 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[2419, 5444])).
% 1.64/1.86 tff(5446,plain,
% 1.64/1.86 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2424, 5445])).
% 1.64/1.86 tff(5447,plain,
% 1.64/1.86 (~(elem!1 = s(s(s(elem!1))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2429, 5446])).
% 1.64/1.86 tff(5448,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5447, 5438])).
% 1.64/1.86 tff(5449,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5450,plain,
% 1.64/1.86 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5449, 2172])).
% 1.64/1.86 tff(5451,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.64/1.86 tff(5452,plain,
% 1.64/1.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[83, 77, 67, 118])).
% 1.64/1.86 tff(5453,plain,
% 1.64/1.86 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[111, 60, 5452, 106])).
% 1.64/1.86 tff(5454,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5455,plain,
% 1.64/1.86 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5456,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5455])).
% 1.64/1.86 tff(5457,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5456, 5454])).
% 1.64/1.86 tff(5458,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5459,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 1.64/1.86 tff(5460,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5459, 192, 3134, 2039, 5453])).
% 1.64/1.86 tff(5461,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[3150, 5460, 5451])).
% 1.64/1.86 tff(5462,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5463,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5464,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 1.64/1.86 tff(5465,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5464, 77, 5431, 5461, 67])).
% 1.64/1.86 tff(5466,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5467,plain,
% 1.64/1.86 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5466, 5431, 67, 5451, 2039, 118])).
% 1.64/1.86 tff(5468,plain,
% 1.64/1.86 (r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2227, 5467, 5450])).
% 1.64/1.86 tff(5469,plain,
% 1.64/1.86 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5468, 5433])).
% 1.64/1.86 tff(5470,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5471,plain,
% 1.64/1.86 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5472,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5471])).
% 1.64/1.86 tff(5473,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5472, 5470])).
% 1.64/1.86 tff(5474,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5475,plain,
% 1.64/1.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5474, 5473])).
% 1.64/1.86 tff(5476,plain,
% 1.64/1.86 (~r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5475, 77, 619, 5469])).
% 1.64/1.86 tff(5477,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5476, 5432])).
% 1.64/1.86 tff(5478,plain,((~r(s(z), elem!1)) | (~(s(elem!1) = s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5479,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5478, 5428, 619, 67, 5394, 5335, 66])).
% 1.64/1.86 tff(5480,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5479, 5390])).
% 1.64/1.86 tff(5481,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (elem!1 = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | (s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5482,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5481, 3173, 3053, 4683, 5243, 395, 3527, 5317, 5297, 39, 115, 5291])).
% 1.64/1.86 tff(5483,plain,((s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(5484,plain,
% 1.64/1.86 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5483, 395, 5257, 39, 115])).
% 1.64/1.86 tff(5485,plain,
% 1.64/1.86 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5484])).
% 1.64/1.86 tff(5486,plain,
% 1.64/1.86 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5485])).
% 1.64/1.86 tff(5487,plain,
% 1.64/1.86 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.64/1.86 inference(symmetry,[status(thm)],[5486])).
% 1.64/1.86 tff(5488,plain,
% 1.64/1.86 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5487])).
% 1.64/1.86 tff(5489,plain,
% 1.64/1.86 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5488, 1157])).
% 1.64/1.86 tff(5490,plain,
% 1.64/1.86 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5489, 5267])).
% 1.64/1.86 tff(5491,plain,
% 1.64/1.86 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5490])).
% 1.64/1.86 tff(5492,plain,
% 1.64/1.86 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1170, 5491])).
% 1.64/1.86 tff(5493,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5494,plain,
% 1.64/1.86 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(5495,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[5494])).
% 1.64/1.86 tff(5496,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[5495, 5493])).
% 1.64/1.86 tff(5497,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(5498,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[5497, 5496])).
% 1.64/1.86 tff(5499,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[5498, 192, 1005, 515, 465, 813, 239])).
% 1.64/1.86 tff(5500,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.86 tff(5501,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1330, 1005, 515, 465])).
% 1.64/1.86 tff(5502,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1313, 5501])).
% 1.64/1.86 tff(5503,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[2498, 465, 515, 239])).
% 1.64/1.86 tff(5504,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[65, 5503])).
% 1.64/1.86 tff(5505,plain,
% 1.64/1.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5506,plain,
% 1.64/1.87 (((~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)))))))) <=> ((~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(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5507,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(elem!1))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5506])).
% 1.64/1.87 tff(5508,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5507, 5505])).
% 1.64/1.87 tff(5509,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5510,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(elem!1))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5509, 5508])).
% 1.64/1.87 tff(5511,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5510, 77, 5504, 5502])).
% 1.64/1.87 tff(5512,plain,
% 1.64/1.87 (((~![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)))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5513,plain,
% 1.64/1.87 ((~![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)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5514,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 1.64/1.87 tff(5515,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5514, 60, 5511, 5500, 5499])).
% 1.64/1.87 tff(5516,plain,((~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5517,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5516, 5492, 4626, 5266, 4683, 5219])).
% 1.64/1.87 tff(5518,plain,
% 1.64/1.87 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5484])).
% 1.64/1.87 tff(5519,plain,
% 1.64/1.87 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5518, 3030])).
% 1.64/1.87 tff(5520,plain,
% 1.64/1.87 ((elem!1 = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 1.64/1.87 inference(symmetry,[status(thm)],[5519])).
% 1.64/1.87 tff(5521,plain,
% 1.64/1.87 ((elem!1 = s(s(s(s(z))))) <=> (elem!1 = s(elem!1))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5520, 4839])).
% 1.64/1.87 tff(5522,plain,
% 1.64/1.87 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(elem!1 = s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5521])).
% 1.64/1.87 tff(5523,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5315, 5259, 4700, 395, 5219, 5245])).
% 1.64/1.87 tff(5524,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5289, 5257, 4626, 4683, 3447, 5253])).
% 1.64/1.87 tff(5525,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1313, 5524])).
% 1.64/1.87 tff(5526,plain,
% 1.64/1.87 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2608, 583, 524])).
% 1.64/1.87 tff(5527,plain,
% 1.64/1.87 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3172, 5526])).
% 1.64/1.87 tff(5528,plain,
% 1.64/1.87 (~b(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1239, 583, 4626, 4683])).
% 1.64/1.87 tff(5529,plain,
% 1.64/1.87 (r(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[950, 5528, 115])).
% 1.64/1.87 tff(5530,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2692, 5529, 66])).
% 1.64/1.87 tff(5531,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4939, 5530, 5529, 5243, 667, 39, 5527])).
% 1.64/1.87 tff(5532,plain,((~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5533,plain,
% 1.64/1.87 (~b(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5532, 5525, 39, 115, 5523])).
% 1.64/1.87 tff(5534,plain,
% 1.64/1.87 (r(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[560, 5533])).
% 1.64/1.87 tff(5535,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4776, 77, 5534, 4685])).
% 1.64/1.87 tff(5536,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[748])).
% 1.64/1.87 tff(5537,plain,
% 1.64/1.87 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5536])).
% 1.64/1.87 tff(5538,plain,
% 1.64/1.87 ((~r(s(s(s(z))), s(elem!1))) <=> (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5537])).
% 1.64/1.87 tff(5539,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[2696, 5538])).
% 1.64/1.87 tff(5540,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4686, 5539])).
% 1.64/1.87 tff(5541,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | r(s(s(s(z))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5542,plain,
% 1.64/1.87 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5541, 5535, 5255])).
% 1.64/1.87 tff(5543,plain,
% 1.64/1.87 (~(elem!1 = s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[853, 5542])).
% 1.64/1.87 tff(5544,plain,
% 1.64/1.87 (~(elem!1 = s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5543, 5522])).
% 1.64/1.87 tff(5545,plain,
% 1.64/1.87 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5520])).
% 1.64/1.87 tff(5546,plain,
% 1.64/1.87 (~(s(elem!1) = elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5543, 5545])).
% 1.64/1.87 tff(5547,plain,
% 1.64/1.87 (elem!1 = s(s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3339, 5484])).
% 1.64/1.87 tff(5548,plain,
% 1.64/1.87 (s(s(s(z))) = elem!1),
% 1.64/1.87 inference(symmetry,[status(thm)],[5547])).
% 1.64/1.87 tff(5549,plain,
% 1.64/1.87 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5548])).
% 1.64/1.87 tff(5550,plain,
% 1.64/1.87 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5549])).
% 1.64/1.87 tff(5551,plain,
% 1.64/1.87 (~(s(s(s(elem!1))) = elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5253, 5550])).
% 1.64/1.87 tff(5552,plain,
% 1.64/1.87 (~b(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4615, 5484, 4684])).
% 1.64/1.87 tff(5553,plain,
% 1.64/1.87 (r(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2354, 5552, 2779])).
% 1.64/1.87 tff(5554,plain,
% 1.64/1.87 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1772, 5484])).
% 1.64/1.87 tff(5555,plain,
% 1.64/1.87 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[699, 5554])).
% 1.64/1.87 tff(5556,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5484])).
% 1.64/1.87 tff(5557,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5556])).
% 1.64/1.87 tff(5558,plain,
% 1.64/1.87 ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5557])).
% 1.64/1.87 tff(5559,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5560,plain,
% 1.64/1.87 (((~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))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5561,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5560])).
% 1.64/1.87 tff(5562,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5561, 5559])).
% 1.64/1.87 tff(5563,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5564,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5563, 5562])).
% 1.64/1.87 tff(5565,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5564, 77, 5243, 5525])).
% 1.64/1.87 tff(5566,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5565, 5558])).
% 1.64/1.87 tff(5567,plain,
% 1.64/1.87 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[679, 5566, 5555])).
% 1.64/1.87 tff(5568,plain,
% 1.64/1.87 (~r(s(s(s(elem!1))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3218, 5567, 5534, 5553, 5551, 5546, 5544])).
% 1.64/1.87 tff(5569,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[992, 5568, 5517])).
% 1.64/1.87 tff(5570,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5571,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5570, 308, 115, 39])).
% 1.64/1.87 tff(5572,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[390, 5571])).
% 1.64/1.87 tff(5573,plain,
% 1.64/1.87 (~r(s(z), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4718, 5572, 308])).
% 1.64/1.87 tff(5574,plain,
% 1.64/1.87 (b(s(z), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[427, 5573])).
% 1.64/1.87 tff(5575,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5289, 5574, 4626, 4683, 3447, 5253])).
% 1.64/1.87 tff(5576,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1313, 5575])).
% 1.64/1.87 tff(5577,plain,
% 1.64/1.87 (~r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4538, 5572, 3447, 4683, 66, 5219])).
% 1.64/1.87 tff(5578,plain,
% 1.64/1.87 (b(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[339, 5577])).
% 1.64/1.87 tff(5579,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1753, 5578, 5219, 4700])).
% 1.64/1.87 tff(5580,plain,
% 1.64/1.87 (~b(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5532, 5576, 39, 115, 5579])).
% 1.64/1.87 tff(5581,plain,
% 1.64/1.87 (r(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[560, 5580])).
% 1.64/1.87 tff(5582,plain,
% 1.64/1.87 (~r(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4681, 1408, 465, 39])).
% 1.64/1.87 tff(5583,plain,
% 1.64/1.87 (b(s(z), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[351, 5582])).
% 1.64/1.87 tff(5584,plain,
% 1.64/1.87 (~b(s(elem!1), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5328, 192, 5583, 953, 465, 1408, 3527])).
% 1.64/1.87 tff(5585,plain,
% 1.64/1.87 (~b(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[935, 192, 5583, 465, 1408])).
% 1.64/1.87 tff(5586,plain,
% 1.64/1.87 (r(s(s(s(z))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[253, 5585])).
% 1.64/1.87 tff(5587,plain,
% 1.64/1.87 (~r(s(elem!1), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3944, 77, 545, 5586])).
% 1.64/1.87 tff(5588,plain,
% 1.64/1.87 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2148, 60, 5587])).
% 1.64/1.87 tff(5589,plain,
% 1.64/1.87 (s(elem!1) = s(s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5588, 5584])).
% 1.64/1.87 tff(5590,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5589])).
% 1.64/1.87 tff(5591,plain,
% 1.64/1.87 (~r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4538, 383, 1408, 5583, 66, 239])).
% 1.64/1.87 tff(5592,plain,
% 1.64/1.87 (b(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[339, 5591])).
% 1.64/1.87 tff(5593,plain,
% 1.64/1.87 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5589])).
% 1.64/1.87 tff(5594,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5593])).
% 1.64/1.87 tff(5595,plain,
% 1.64/1.87 (r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[383, 5594])).
% 1.64/1.87 tff(5596,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1763, 5595, 239, 5592, 545])).
% 1.64/1.87 tff(5597,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[597, 5596, 961])).
% 1.64/1.87 tff(5598,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5597, 5590])).
% 1.64/1.87 tff(5599,plain,
% 1.64/1.87 (r(z, s(elem!1)) <=> r(z, s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5589])).
% 1.64/1.87 tff(5600,plain,
% 1.64/1.87 (r(z, s(s(s(z)))) <=> r(z, s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5599])).
% 1.64/1.87 tff(5601,plain,
% 1.64/1.87 (~b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4750, 192, 5583, 465, 1408, 3527])).
% 1.64/1.87 tff(5602,plain,
% 1.64/1.87 (r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[237, 5601])).
% 1.64/1.87 tff(5603,plain,
% 1.64/1.87 (r(z, s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5602, 5600])).
% 1.64/1.87 tff(5604,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4698, 5583, 1408, 465, 39])).
% 1.64/1.87 tff(5605,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[181, 5604])).
% 1.64/1.87 tff(5606,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1753, 5592, 239, 5605])).
% 1.64/1.87 tff(5607,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[526, 5606])).
% 1.64/1.87 tff(5608,plain,
% 1.64/1.87 (s(s(s(z))) = s(elem!1)),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5589, 2699])).
% 1.64/1.87 tff(5609,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3310, 5608, 5607, 5603])).
% 1.64/1.87 tff(5610,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[406, 5609])).
% 1.64/1.87 tff(5611,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5612,plain,
% 1.64/1.87 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5613,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5612])).
% 1.64/1.87 tff(5614,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5613, 5611])).
% 1.64/1.87 tff(5615,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, 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)))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5616,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 1.64/1.87 tff(5617,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5616, 192, 5605, 5592, 239, 5610, 5598])).
% 1.64/1.87 tff(5618,plain,((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5619,plain,
% 1.64/1.87 (~b(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5618, 5581, 5219, 5572, 4626, 3447, 5574, 39])).
% 1.64/1.87 tff(5620,plain,
% 1.64/1.87 (r(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[950, 5619, 115])).
% 1.64/1.87 tff(5621,plain,
% 1.64/1.87 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5320, 5620, 5576, 39, 5243])).
% 1.64/1.87 tff(5622,plain,
% 1.64/1.87 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3172, 5621])).
% 1.64/1.87 tff(5623,plain,
% 1.64/1.87 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5622])).
% 1.64/1.87 tff(5624,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5623])).
% 1.64/1.87 tff(5625,plain,
% 1.64/1.87 (r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5572, 5624])).
% 1.64/1.87 tff(5626,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4776, 77, 5581, 4685])).
% 1.64/1.87 tff(5627,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5626, 5625])).
% 1.64/1.87 tff(5628,plain,((~r(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5629,plain,
% 1.64/1.87 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5628, 115, 39])).
% 1.64/1.87 tff(5630,plain,
% 1.64/1.87 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[319, 5629])).
% 1.64/1.87 tff(5631,plain,
% 1.64/1.87 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4235, 192, 4700, 5630, 5245])).
% 1.64/1.87 tff(5632,plain,
% 1.64/1.87 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[438, 60, 5631, 380])).
% 1.64/1.87 tff(5633,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[113, 5452])).
% 1.64/1.87 tff(5634,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4763, 192, 5633, 5225, 440])).
% 1.64/1.87 tff(5635,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[406, 5634])).
% 1.64/1.87 tff(5636,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5637,plain,
% 1.64/1.87 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5638,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5637])).
% 1.64/1.87 tff(5639,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[5638, 5636])).
% 1.64/1.87 tff(5640,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5641,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5640, 5639])).
% 1.64/1.87 tff(5642,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5641, 77, 67, 5635, 408])).
% 1.64/1.87 tff(5643,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5644,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5643, 408, 67, 118])).
% 1.64/1.87 tff(5645,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[375, 5644])).
% 1.64/1.87 tff(5646,plain,
% 1.64/1.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(5647,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(5648,plain,
% 1.64/1.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5647, 5646])).
% 1.64/1.87 tff(5649,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5648, 77, 619, 408, 5645])).
% 1.64/1.87 tff(5650,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5651,plain,
% 1.64/1.87 (~r(s(z), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5650, 5632, 5243, 66])).
% 1.64/1.87 tff(5652,plain,
% 1.64/1.87 (b(s(z), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[427, 5651])).
% 1.64/1.87 tff(5653,plain,
% 1.64/1.87 (~b(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4750, 192, 4683, 4626, 3447, 5652])).
% 1.64/1.87 tff(5654,plain,
% 1.64/1.87 (r(z, s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[237, 5653])).
% 1.64/1.87 tff(5655,plain,
% 1.64/1.87 (~b(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5289, 5652, 4626, 4683, 3447, 5253])).
% 1.64/1.87 tff(5656,plain,
% 1.64/1.87 (r(s(s(s(elem!1))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1313, 5655])).
% 1.64/1.87 tff(5657,plain,
% 1.64/1.87 (~r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4538, 383, 3447, 4683, 66, 5219])).
% 1.64/1.87 tff(5658,plain,
% 1.64/1.87 (b(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[339, 5657])).
% 1.64/1.87 tff(5659,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1753, 5658, 5219, 4700])).
% 1.64/1.87 tff(5660,plain,
% 1.64/1.87 (~b(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5532, 5659, 39, 115, 5656])).
% 1.64/1.87 tff(5661,plain,
% 1.64/1.87 (r(s(elem!1), z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[560, 5660])).
% 1.64/1.87 tff(5662,plain,
% 1.64/1.87 (~b(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5618, 5661, 5219, 383, 4626, 3447, 5652, 39])).
% 1.64/1.87 tff(5663,plain,
% 1.64/1.87 (r(s(elem!1), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[950, 5662, 115])).
% 1.64/1.87 tff(5664,plain,
% 1.64/1.87 (s(s(s(s(z)))) = s(elem!1)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5320, 5663, 5656, 39, 5243])).
% 1.64/1.87 tff(5665,plain,
% 1.64/1.87 (s(elem!1) = s(s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3172, 5664])).
% 1.64/1.87 tff(5666,plain,
% 1.64/1.87 (elem!1 = s(s(s(z)))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[3339, 5665])).
% 1.64/1.87 tff(5667,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5666])).
% 1.64/1.87 tff(5668,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[5667])).
% 1.64/1.87 tff(5669,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[383, 5668])).
% 1.64/1.87 tff(5670,plain,
% 1.64/1.87 (r(elem!1, s(elem!1)) <=> r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5665])).
% 1.64/1.87 tff(5671,plain,
% 1.64/1.87 ((~r(elem!1, s(elem!1))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[5670])).
% 1.64/1.87 tff(5672,plain,
% 1.64/1.87 (~b(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4615, 5665, 4684])).
% 1.64/1.87 tff(5673,plain,
% 1.64/1.87 (r(elem!1, z)),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2354, 5672, 2779])).
% 1.64/1.87 tff(5674,plain,
% 1.64/1.87 (~r(elem!1, s(elem!1))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[2362, 5673, 5661])).
% 1.64/1.87 tff(5675,plain,
% 1.64/1.87 (~r(elem!1, s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[5674, 5671])).
% 1.64/1.87 tff(5676,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5675, 5669])).
% 1.64/1.87 tff(5677,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(5678,plain,
% 1.64/1.87 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5677, 115, 39])).
% 1.64/1.87 tff(5679,plain,
% 1.64/1.87 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[390, 5678])).
% 1.64/1.87 tff(5680,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[449, 5679, 4700, 5245])).
% 1.64/1.87 tff(5681,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[375, 5680])).
% 1.64/1.87 tff(5682,plain,
% 1.64/1.87 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5264, 5681, 5654])).
% 1.64/1.87 tff(5683,plain,
% 1.64/1.87 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[493, 5682])).
% 1.64/1.87 tff(5684,plain,
% 1.64/1.87 (~b(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[4048, 5683, 4700, 5245])).
% 1.64/1.87 tff(5685,plain,
% 1.64/1.87 (r(z, s(s(s(s(z)))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[339, 5684])).
% 1.64/1.87 tff(5686,plain,
% 1.64/1.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[5301, 5685, 5654])).
% 1.64/1.87 tff(5687,plain,
% 1.64/1.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[406, 5686])).
% 1.64/1.87 tff(5688,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5689,plain,
% 1.64/1.88 (((~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(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5690,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5689])).
% 1.64/1.88 tff(5691,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5690, 5688])).
% 1.64/1.88 tff(5692,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5693,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5692, 5691])).
% 1.64/1.88 tff(5694,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5693, 192, 5630, 5679, 5687, 5652])).
% 1.64/1.88 tff(5695,plain,((s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5696,plain,
% 1.64/1.88 (s(elem!1) = s(z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5695, 39])).
% 1.64/1.88 tff(5697,plain,
% 1.64/1.88 (z = elem!1),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1550, 5696])).
% 1.64/1.88 tff(5698,plain,
% 1.64/1.88 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.88 tff(5699,plain,
% 1.64/1.88 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5698])).
% 1.64/1.88 tff(5700,plain,
% 1.64/1.88 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.88 tff(5701,plain,
% 1.64/1.88 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5700, 2011])).
% 1.64/1.88 tff(5702,plain,
% 1.64/1.88 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5701])).
% 1.64/1.88 tff(5703,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[209, 5702])).
% 1.64/1.88 tff(5704,plain,
% 1.64/1.88 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.88 tff(5705,plain,
% 1.64/1.88 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(symmetry,[status(thm)],[1978])).
% 1.64/1.88 tff(5706,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.88 tff(5707,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5706, 1978])).
% 1.64/1.88 tff(5708,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(transitivity,[status(thm)],[5707, 5705])).
% 1.64/1.88 tff(5709,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5708])).
% 1.64/1.88 tff(5710,plain,
% 1.64/1.88 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[266, 5709])).
% 1.64/1.88 tff(5711,plain,
% 1.64/1.88 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.88 tff(5712,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5696])).
% 1.64/1.88 tff(5713,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5712])).
% 1.64/1.88 tff(5714,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[66, 5713])).
% 1.64/1.88 tff(5715,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1543])).
% 1.64/1.88 tff(5716,plain,
% 1.64/1.88 (r(s(z), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5715])).
% 1.64/1.88 tff(5717,plain,
% 1.64/1.88 (r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[308, 5716])).
% 1.64/1.88 tff(5718,plain,
% 1.64/1.88 (r(s(elem!1), z)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[504, 2071])).
% 1.64/1.88 tff(5719,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.64/1.88 tff(5720,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5719, 5718])).
% 1.64/1.88 tff(5721,plain,((~(s(elem!1) = s(z))) | r(s(elem!1), z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5722,plain,
% 1.64/1.88 (r(s(elem!1), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5721, 1543, 504])).
% 1.64/1.88 tff(5723,plain,
% 1.64/1.88 (~r(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4017, 308, 504])).
% 1.64/1.88 tff(5724,plain,
% 1.64/1.88 (b(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[339, 5723])).
% 1.64/1.88 tff(5725,plain,
% 1.64/1.88 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1763, 5724, 239, 538, 5722])).
% 1.64/1.88 tff(5726,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5725, 5717])).
% 1.64/1.88 tff(5727,plain,((~r(s(z), s(s(s(s(z)))))) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5728,plain,
% 1.64/1.88 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5727, 4628, 5696, 5714, 504])).
% 1.64/1.88 tff(5729,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[319, 5728])).
% 1.64/1.88 tff(5730,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1543])).
% 1.64/1.88 tff(5731,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5730])).
% 1.64/1.88 tff(5732,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5731, 747])).
% 1.64/1.88 tff(5733,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5732])).
% 1.64/1.88 tff(5734,plain,
% 1.64/1.88 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[50, 5733])).
% 1.64/1.88 tff(5735,plain,
% 1.64/1.88 (r(s(elem!1), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[504, 2069])).
% 1.64/1.88 tff(5736,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1995])).
% 1.64/1.88 tff(5737,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5736, 1978])).
% 1.64/1.88 tff(5738,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5737])).
% 1.64/1.88 tff(5739,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[266, 5738])).
% 1.64/1.88 tff(5740,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[2061])).
% 1.64/1.88 tff(5741,plain,
% 1.64/1.88 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5740])).
% 1.64/1.88 tff(5742,plain,
% 1.64/1.88 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5741, 2080])).
% 1.64/1.88 tff(5743,plain,
% 1.64/1.88 (r(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[116, 5742])).
% 1.64/1.88 tff(5744,plain,
% 1.64/1.88 (~r(s(s(s(elem!1))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1623, 5743, 5735])).
% 1.64/1.88 tff(5745,plain,
% 1.64/1.88 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1628, 5744, 2065])).
% 1.64/1.88 tff(5746,plain,
% 1.64/1.88 (b(s(s(s(z))), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5745, 2062])).
% 1.64/1.88 tff(5747,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[2635, 1999])).
% 1.64/1.88 tff(5748,plain,
% 1.64/1.88 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[3136, 5747, 5746, 382])).
% 1.64/1.88 tff(5749,plain,
% 1.64/1.88 (r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2227, 5748, 5739])).
% 1.64/1.88 tff(5750,assumption,(r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.88 tff(5751,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5752,plain,
% 1.64/1.88 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5753,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5752])).
% 1.64/1.88 tff(5754,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5753, 5751])).
% 1.64/1.88 tff(5755,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5756,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 1.64/1.88 tff(5757,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5756, 77, 1618, 5750, 795])).
% 1.64/1.88 tff(5758,plain,((~r(s(elem!1), s(s(s(s(s(z))))))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5759,plain,
% 1.64/1.88 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5758, 5749, 5735])).
% 1.64/1.88 tff(5760,plain,
% 1.64/1.88 (b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[811, 5759, 5734])).
% 1.64/1.88 tff(5761,plain,
% 1.64/1.88 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1543])).
% 1.64/1.88 tff(5762,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(symmetry,[status(thm)],[5761])).
% 1.64/1.88 tff(5763,plain,
% 1.64/1.88 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5762])).
% 1.64/1.88 tff(5764,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.88 tff(5765,plain,
% 1.64/1.88 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5764, 5763])).
% 1.64/1.88 tff(5766,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[814, 5765])).
% 1.64/1.88 tff(5767,plain,(b(s(z), s(s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5768,plain,
% 1.64/1.88 (b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5767, 5760, 1543])).
% 1.64/1.88 tff(5769,plain,
% 1.64/1.88 (~r(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[262, 220, 2635, 116])).
% 1.64/1.88 tff(5770,plain,
% 1.64/1.88 (b(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[292, 5769])).
% 1.64/1.88 tff(5771,plain,
% 1.64/1.88 (~b(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[471, 192, 5770, 512, 38])).
% 1.64/1.88 tff(5772,plain,
% 1.64/1.88 (r(z, s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[339, 5771])).
% 1.64/1.88 tff(5773,plain,
% 1.64/1.88 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1995])).
% 1.64/1.88 tff(5774,plain,
% 1.64/1.88 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5773, 2011])).
% 1.64/1.88 tff(5775,plain,
% 1.64/1.88 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5774])).
% 1.64/1.88 tff(5776,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[209, 5775])).
% 1.64/1.88 tff(5777,plain,
% 1.64/1.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2097, 5776, 118, 512, 1543, 2635, 5772, 5722])).
% 1.64/1.88 tff(5778,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[181, 5777])).
% 1.64/1.88 tff(5779,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5780,plain,
% 1.64/1.88 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5781,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5780])).
% 1.64/1.88 tff(5782,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5781, 5779])).
% 1.64/1.88 tff(5783,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5784,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5783, 5782])).
% 1.64/1.88 tff(5785,plain,
% 1.64/1.88 ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5784, 192, 5778, 38, 382])).
% 1.64/1.88 tff(5786,plain,
% 1.64/1.88 (~b(s(z), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5785, 5768])).
% 1.64/1.88 tff(5787,plain,
% 1.64/1.88 (r(s(z), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[427, 5786])).
% 1.64/1.88 tff(5788,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.88 tff(5789,plain,
% 1.64/1.88 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5790,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5789])).
% 1.64/1.88 tff(5791,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5790, 2040])).
% 1.64/1.88 tff(5792,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5793,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5792, 5791])).
% 1.64/1.88 tff(5794,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5793, 192, 2039, 5788, 3133, 221])).
% 1.64/1.88 tff(5795,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5796,plain,
% 1.64/1.88 (~b(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5795, 5747, 5746, 220])).
% 1.64/1.88 tff(5797,plain,
% 1.64/1.88 (r(elem!1, s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[2037, 5796, 5776])).
% 1.64/1.88 tff(5798,plain,
% 1.64/1.88 (r(s(z), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[504, 2068])).
% 1.64/1.88 tff(5799,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5800,plain,
% 1.64/1.88 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5801,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5800])).
% 1.64/1.88 tff(5802,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5801, 5799])).
% 1.64/1.88 tff(5803,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5804,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 1.64/1.88 tff(5805,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5804, 77, 5798, 5797, 5787])).
% 1.64/1.88 tff(5806,plain,((~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(5807,plain,
% 1.64/1.88 (~r(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5806, 512, 5696, 66, 5729, 504])).
% 1.64/1.88 tff(5808,plain,
% 1.64/1.88 (b(s(s(s(z))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[920, 5807])).
% 1.64/1.88 tff(5809,plain,
% 1.64/1.88 (~b(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[4681, 5808, 504, 39])).
% 1.64/1.88 tff(5810,plain,
% 1.64/1.88 (r(z, s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[292, 5809])).
% 1.64/1.88 tff(5811,plain,
% 1.64/1.88 (r(elem!1, s(z))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5810, 5711])).
% 1.64/1.88 tff(5812,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5813,plain,
% 1.64/1.88 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5814,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5813])).
% 1.64/1.88 tff(5815,plain,
% 1.64/1.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[5814, 5812])).
% 1.64/1.88 tff(5816,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5817,plain,
% 1.64/1.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5816, 5815])).
% 1.64/1.88 tff(5818,plain,
% 1.64/1.88 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5817, 77, 5811, 66])).
% 1.64/1.88 tff(5819,plain,
% 1.64/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(5820,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(5821,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[5820, 5819])).
% 1.64/1.88 tff(5822,plain,
% 1.64/1.88 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5821, 60])).
% 1.64/1.88 tff(5823,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[5822, 5818, 5710])).
% 1.64/1.88 tff(5824,plain,
% 1.64/1.88 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[5707])).
% 1.64/1.88 tff(5825,plain,
% 1.64/1.88 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[266, 5824])).
% 1.64/1.88 tff(5826,plain,
% 1.64/1.88 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[835, 5810, 66])).
% 1.64/1.89 tff(5827,plain,
% 1.64/1.89 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2881])).
% 1.64/1.89 tff(5828,plain,
% 1.64/1.89 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5827])).
% 1.64/1.89 tff(5829,plain,
% 1.64/1.89 (r(z, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5750, 5828])).
% 1.64/1.89 tff(5830,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[487, 5829])).
% 1.64/1.89 tff(5831,plain,((~r(elem!1, s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5832,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5831, 5826, 5697])).
% 1.64/1.89 tff(5833,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2227, 5832, 5825])).
% 1.64/1.89 tff(5834,plain,
% 1.64/1.89 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[2011])).
% 1.64/1.89 tff(5835,plain,
% 1.64/1.89 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5701, 5834])).
% 1.64/1.89 tff(5836,plain,
% 1.64/1.89 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5835])).
% 1.64/1.89 tff(5837,plain,
% 1.64/1.89 (~(s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[209, 5836])).
% 1.64/1.89 tff(5838,plain,
% 1.64/1.89 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5696])).
% 1.64/1.89 tff(5839,plain,
% 1.64/1.89 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[5838])).
% 1.64/1.89 tff(5840,plain,
% 1.64/1.89 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5697])).
% 1.64/1.89 tff(5841,plain,
% 1.64/1.89 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5840, 5839])).
% 1.64/1.89 tff(5842,plain,
% 1.64/1.89 (r(s(elem!1), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[504, 5841])).
% 1.64/1.89 tff(5843,plain,
% 1.64/1.89 (r(s(z), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[504, 5840])).
% 1.64/1.89 tff(5844,plain,
% 1.64/1.89 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(5845,plain,
% 1.64/1.89 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.64/1.89 inference(symmetry,[status(thm)],[5844])).
% 1.64/1.89 tff(5846,plain,
% 1.64/1.89 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5845])).
% 1.64/1.89 tff(5847,plain,
% 1.64/1.89 (~(s(s(z)) = s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[2196, 5846])).
% 1.64/1.89 tff(5848,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1995])).
% 1.64/1.89 tff(5849,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5848, 3030])).
% 1.64/1.89 tff(5850,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5849, 3031])).
% 1.64/1.89 tff(5851,plain,
% 1.64/1.89 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5850])).
% 1.64/1.89 tff(5852,plain,
% 1.64/1.89 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[48, 5851])).
% 1.64/1.89 tff(5853,plain,
% 1.64/1.89 (~r(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4176, 117, 66])).
% 1.64/1.89 tff(5854,plain,
% 1.64/1.89 (b(s(z), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[427, 5853])).
% 1.64/1.89 tff(5855,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2881])).
% 1.64/1.89 tff(5856,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5855, 3030])).
% 1.64/1.89 tff(5857,plain,
% 1.64/1.89 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5856, 3031])).
% 1.64/1.89 tff(5858,plain,
% 1.64/1.89 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5857])).
% 1.64/1.89 tff(5859,plain,
% 1.64/1.89 (~(s(s(s(s(z)))) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[48, 5858])).
% 1.64/1.89 tff(5860,plain,
% 1.64/1.89 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2881])).
% 1.64/1.89 tff(5861,plain,
% 1.64/1.89 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5860, 1978])).
% 1.64/1.89 tff(5862,plain,
% 1.64/1.89 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5861])).
% 1.64/1.89 tff(5863,plain,
% 1.64/1.89 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[266, 5862])).
% 1.64/1.89 tff(5864,plain,
% 1.64/1.89 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2881])).
% 1.64/1.89 tff(5865,plain,
% 1.64/1.89 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5864, 2011])).
% 1.64/1.89 tff(5866,plain,
% 1.64/1.89 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5865])).
% 1.64/1.89 tff(5867,plain,
% 1.64/1.89 (~(elem!1 = s(s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[209, 5866])).
% 1.64/1.89 tff(5868,plain,
% 1.64/1.89 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2881])).
% 1.64/1.89 tff(5869,plain,
% 1.64/1.89 (~r(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1582, 67, 39])).
% 1.64/1.89 tff(5870,plain,
% 1.64/1.89 (b(z, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[292, 5869])).
% 1.64/1.89 tff(5871,plain,
% 1.64/1.89 (b(elem!1, s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5870, 5868])).
% 1.64/1.89 tff(5872,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5873,plain,
% 1.64/1.89 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5874,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5873])).
% 1.64/1.89 tff(5875,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5874, 5872])).
% 1.64/1.89 tff(5876,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5877,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5876, 5875])).
% 1.64/1.89 tff(5878,plain,
% 1.64/1.89 (~b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5877, 192, 5871, 3581, 5854])).
% 1.64/1.89 tff(5879,plain,
% 1.64/1.89 (r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2037, 5878, 5867])).
% 1.64/1.89 tff(5880,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5881,plain,
% 1.64/1.89 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5882,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5881])).
% 1.64/1.89 tff(5883,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5882, 5880])).
% 1.64/1.89 tff(5884,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5885,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 1.64/1.89 tff(5886,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5885, 77, 5879, 117])).
% 1.64/1.89 tff(5887,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2227, 5886, 5863])).
% 1.64/1.89 tff(5888,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5459, 192, 5887, 2039, 156])).
% 1.64/1.89 tff(5889,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3150, 5888, 5859])).
% 1.64/1.89 tff(5890,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5464, 77, 5431, 5889, 67])).
% 1.64/1.89 tff(5891,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(z = elem!1)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5892,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5891, 117, 2039, 5431, 1995, 39])).
% 1.64/1.89 tff(5893,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[217, 5892])).
% 1.64/1.89 tff(5894,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3534, 192, 5893, 38, 3581, 5854])).
% 1.64/1.89 tff(5895,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[406, 5894])).
% 1.64/1.89 tff(5896,plain,
% 1.64/1.89 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4187, 77, 5895, 117])).
% 1.64/1.89 tff(5897,plain,
% 1.64/1.89 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[111, 60, 5896, 106])).
% 1.64/1.89 tff(5898,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3585, 117, 38, 39])).
% 1.64/1.89 tff(5899,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[181, 5898])).
% 1.64/1.89 tff(5900,plain,
% 1.64/1.89 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[4235, 192, 5899, 38, 5897])).
% 1.64/1.89 tff(5901,plain,
% 1.64/1.89 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5767, 5900, 1543])).
% 1.64/1.89 tff(5902,plain,
% 1.64/1.89 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[811, 5901, 5734])).
% 1.64/1.89 tff(5903,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5758, 5902, 1618])).
% 1.64/1.89 tff(5904,plain,
% 1.64/1.89 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2227, 5903, 5739])).
% 1.64/1.89 tff(5905,plain,
% 1.64/1.89 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5459, 192, 5904, 2039, 5897])).
% 1.64/1.89 tff(5906,plain,
% 1.64/1.89 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3150, 5905, 5852])).
% 1.64/1.89 tff(5907,plain,
% 1.64/1.89 (elem!1 = z),
% 1.64/1.89 inference(symmetry,[status(thm)],[1995])).
% 1.64/1.89 tff(5908,plain,
% 1.64/1.89 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5907])).
% 1.64/1.89 tff(5909,plain,
% 1.64/1.89 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[5908])).
% 1.64/1.89 tff(5910,plain,
% 1.64/1.89 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1995])).
% 1.64/1.89 tff(5911,plain,
% 1.64/1.89 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5910])).
% 1.64/1.89 tff(5912,plain,
% 1.64/1.89 (~(s(s(elem!1)) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1076, 5911])).
% 1.64/1.89 tff(5913,plain,
% 1.64/1.89 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2060])).
% 1.64/1.89 tff(5914,plain,
% 1.64/1.89 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[5913])).
% 1.64/1.89 tff(5915,plain,
% 1.64/1.89 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(elem!1)), elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5914])).
% 1.64/1.89 tff(5916,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.89 tff(5917,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(5918,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5919,plain,
% 1.64/1.89 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5920,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5919])).
% 1.64/1.89 tff(5921,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5920, 5918])).
% 1.64/1.89 tff(5922,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5923,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5922, 5921])).
% 1.64/1.89 tff(5924,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5923, 77, 3140, 5916, 5917])).
% 1.64/1.89 tff(5925,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5926,plain,
% 1.64/1.89 (~r(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5925, 5916, 3140])).
% 1.64/1.89 tff(5927,plain,
% 1.64/1.89 (~r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5926, 5915])).
% 1.64/1.89 tff(5928,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5929,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5930,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5929, 5928])).
% 1.64/1.89 tff(5931,plain,
% 1.64/1.89 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5930, 60])).
% 1.64/1.89 tff(5932,plain,
% 1.64/1.89 (b(s(s(elem!1)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5931, 5927, 5912])).
% 1.64/1.89 tff(5933,plain,
% 1.64/1.89 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[2060, 5907])).
% 1.64/1.89 tff(5934,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(5935,plain,
% 1.64/1.89 (b(s(s(z)), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5934, 5933])).
% 1.64/1.89 tff(5936,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.64/1.89 tff(5937,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5936, 5935])).
% 1.64/1.89 tff(5938,plain,((~b(s(s(elem!1)), elem!1)) | b(s(s(z)), z) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5939,plain,
% 1.64/1.89 (b(s(s(z)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5938, 5932, 1543])).
% 1.64/1.89 tff(5940,plain,
% 1.64/1.89 (b(s(s(z)), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5939, 5909])).
% 1.64/1.89 tff(5941,plain,
% 1.64/1.89 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[5774, 5834])).
% 1.64/1.89 tff(5942,plain,
% 1.64/1.89 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5941])).
% 1.64/1.89 tff(5943,plain,
% 1.64/1.89 (~(s(s(s(z))) = elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[209, 5942])).
% 1.64/1.89 tff(5944,plain,
% 1.64/1.89 (~r(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[3145, 3140, 409])).
% 1.64/1.89 tff(5945,plain,
% 1.64/1.89 (b(s(s(s(z))), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2025, 5944, 5943])).
% 1.64/1.89 tff(5946,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5947,plain,
% 1.64/1.89 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5948,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5947])).
% 1.64/1.89 tff(5949,plain,
% 1.64/1.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5948, 5946])).
% 1.64/1.89 tff(5950,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5951,plain,
% 1.64/1.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[5950, 5949])).
% 1.64/1.89 tff(5952,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5951, 77, 3140, 3537, 409])).
% 1.64/1.89 tff(5953,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(5954,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[5953, 3140, 409])).
% 1.64/1.89 tff(5955,plain,
% 1.64/1.89 (b(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[2037, 5954, 5776])).
% 1.64/1.89 tff(5956,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5957,plain,
% 1.64/1.89 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(5958,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[5957])).
% 1.64/1.89 tff(5959,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[5958, 5956])).
% 1.64/1.89 tff(5960,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(5961,plain,
% 1.64/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[5960, 5959])).
% 1.64/1.90 tff(5962,plain,
% 1.64/1.90 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[5961, 192, 3134, 2039, 5955, 5945, 5940])).
% 1.64/1.90 tff(5963,plain,
% 1.64/1.90 (((~![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)))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(5964,plain,
% 1.64/1.90 ((~![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)))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(5965,plain,
% 1.64/1.90 ((~![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))))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[5964, 5963])).
% 1.64/1.90 tff(5966,plain,
% 1.64/1.90 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[5965, 60, 5962, 36])).
% 1.64/1.90 tff(5967,plain,
% 1.64/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(5968,plain,
% 1.64/1.90 (((~r(s(s(s(s(z)))), 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(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.90 inference(rewrite,[status(thm)],[])).
% 1.64/1.90 tff(5969,plain,
% 1.64/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.64/1.90 inference(monotonicity,[status(thm)],[5968])).
% 1.64/1.90 tff(5970,plain,
% 1.64/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.90 inference(transitivity,[status(thm)],[5969, 5967])).
% 1.64/1.90 tff(5971,plain,
% 1.64/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(5972,plain,
% 1.64/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[5971, 5970])).
% 1.64/1.90 tff(5973,plain,
% 1.64/1.90 ($false),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[5972, 77, 5916, 409, 5966])).
% 1.64/1.90 tff(5974,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.90 tff(5975,plain,
% 1.64/1.90 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[5974, 5895, 5904, 2039, 1543, 5906])).
% 1.64/1.90 tff(5976,plain,
% 1.64/1.90 (b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[5381, 5975])).
% 1.64/1.90 tff(5977,plain,
% 1.64/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5978,plain,
% 1.74/1.90 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(5979,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5978])).
% 1.74/1.90 tff(5980,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[5979, 5977])).
% 1.74/1.90 tff(5981,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(5982,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[5981, 5980])).
% 1.74/1.90 tff(5983,plain,
% 1.74/1.90 (~b(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5982, 192, 5899, 5893, 38, 5897, 5976])).
% 1.74/1.90 tff(5984,plain,
% 1.74/1.90 (s(s(z)) = s(s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[2060])).
% 1.74/1.90 tff(5985,plain,
% 1.74/1.90 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5984, 1995])).
% 1.74/1.90 tff(5986,plain,
% 1.74/1.90 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(transitivity,[status(thm)],[5908, 5985])).
% 1.74/1.90 tff(5987,plain,
% 1.74/1.90 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5986])).
% 1.74/1.90 tff(5988,plain,
% 1.74/1.90 (~r(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3145, 5906, 5895])).
% 1.74/1.90 tff(5989,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2025, 5988, 5943])).
% 1.74/1.90 tff(5990,plain,
% 1.74/1.90 (~r(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5953, 5906, 5895])).
% 1.74/1.90 tff(5991,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2037, 5990, 5776])).
% 1.74/1.90 tff(5992,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(5993,plain,
% 1.74/1.90 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[5992])).
% 1.74/1.90 tff(5994,plain,
% 1.74/1.90 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[5993])).
% 1.74/1.90 tff(5995,plain,
% 1.74/1.90 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[3070, 5994])).
% 1.74/1.90 tff(5996,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.90 tff(5997,plain,
% 1.74/1.90 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5961, 192, 3134, 2039, 5788, 3133])).
% 1.74/1.90 tff(5998,plain,
% 1.74/1.90 (~b(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5997, 5996])).
% 1.74/1.90 tff(5999,plain,
% 1.74/1.90 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5965, 60, 5998, 36])).
% 1.74/1.90 tff(6000,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6001,plain,
% 1.74/1.90 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6002,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6001])).
% 1.74/1.90 tff(6003,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6002, 6000])).
% 1.74/1.90 tff(6004,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6005,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6004, 6003])).
% 1.74/1.90 tff(6006,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6005, 77, 117, 5999])).
% 1.74/1.90 tff(6007,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6008,plain,
% 1.74/1.90 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6009,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6008])).
% 1.74/1.90 tff(6010,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6009, 6007])).
% 1.74/1.90 tff(6011,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6012,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6011, 6010])).
% 1.74/1.90 tff(6013,plain,
% 1.74/1.90 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6012, 192, 3134, 2039])).
% 1.74/1.90 tff(6014,plain,
% 1.74/1.90 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6013, 5996])).
% 1.74/1.90 tff(6015,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2401, 60, 6014])).
% 1.74/1.90 tff(6016,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6015, 6006, 5995])).
% 1.74/1.90 tff(6017,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6018,plain,
% 1.74/1.90 (~b(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6017, 117, 5904, 2039, 5991, 5989])).
% 1.74/1.90 tff(6019,plain,
% 1.74/1.90 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6018, 5987])).
% 1.74/1.90 tff(6020,plain,
% 1.74/1.90 (r(s(s(elem!1)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5931, 6019, 5912])).
% 1.74/1.90 tff(6021,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.74/1.90 tff(6022,plain,
% 1.74/1.90 (r(s(s(z)), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6021, 5913])).
% 1.74/1.90 tff(6023,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.90 tff(6024,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6023, 6022])).
% 1.74/1.90 tff(6025,plain,((~r(s(s(elem!1)), elem!1)) | r(s(s(z)), elem!1) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6026,plain,
% 1.74/1.90 (r(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6025, 6020, 1543])).
% 1.74/1.90 tff(6027,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6028,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6029,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6028, 6027])).
% 1.74/1.90 tff(6030,plain,
% 1.74/1.90 (~r(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6029, 77, 5431, 6026])).
% 1.74/1.90 tff(6031,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6032,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6033,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6032, 6031])).
% 1.74/1.90 tff(6034,plain,
% 1.74/1.90 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6033, 60, 6030])).
% 1.74/1.90 tff(6035,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6034, 5983, 5847])).
% 1.74/1.90 tff(6036,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~r(s(elem!1), elem!1)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6037,plain,
% 1.74/1.90 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6036, 5823, 5696, 5729, 5843, 5842, 39])).
% 1.74/1.90 tff(6038,plain,
% 1.74/1.90 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[133, 6037])).
% 1.74/1.90 tff(6039,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1543])).
% 1.74/1.90 tff(6040,plain,
% 1.74/1.90 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[6039])).
% 1.74/1.90 tff(6041,plain,
% 1.74/1.90 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2061])).
% 1.74/1.90 tff(6042,plain,
% 1.74/1.90 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[6041])).
% 1.74/1.90 tff(6043,plain,
% 1.74/1.90 (r(s(z), s(s(s(z)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6042, 6040])).
% 1.74/1.90 tff(6044,plain,
% 1.74/1.90 (r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[408, 6043])).
% 1.74/1.90 tff(6045,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3689, 6044, 1618])).
% 1.74/1.90 tff(6046,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1628, 6045, 2065])).
% 1.74/1.90 tff(6047,plain,
% 1.74/1.90 (b(s(s(s(z))), elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6046, 2062])).
% 1.74/1.90 tff(6048,plain,
% 1.74/1.90 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2061])).
% 1.74/1.90 tff(6049,plain,
% 1.74/1.90 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.90 tff(6050,plain,
% 1.74/1.90 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6049, 6048])).
% 1.74/1.90 tff(6051,plain,
% 1.74/1.90 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[408, 6042])).
% 1.74/1.90 tff(6052,plain,
% 1.74/1.90 (~r(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1671, 6051, 37])).
% 1.74/1.90 tff(6053,plain,
% 1.74/1.90 (b(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1021, 6052])).
% 1.74/1.90 tff(6054,plain,
% 1.74/1.90 (b(elem!1, s(s(s(z))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6053, 6050])).
% 1.74/1.90 tff(6055,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[2045, 192, 2039, 6054, 6047, 221])).
% 1.74/1.90 tff(6056,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(z, s(z))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(6057,plain,
% 1.74/1.90 (~r(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6056, 5823, 6038, 5696, 5810, 5842])).
% 1.74/1.90 tff(6058,plain,
% 1.74/1.90 (b(s(z), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[427, 6057])).
% 1.74/1.90 tff(6059,plain,
% 1.74/1.90 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3534, 192, 512, 5729, 5808, 6058])).
% 1.74/1.90 tff(6060,plain,
% 1.74/1.90 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[406, 6059])).
% 1.74/1.90 tff(6061,plain,
% 1.74/1.90 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[493, 5826])).
% 1.74/1.90 tff(6062,plain,
% 1.74/1.90 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3456, 192, 512, 5729, 5808])).
% 1.74/1.90 tff(6063,plain,
% 1.74/1.90 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[390, 6062])).
% 1.74/1.90 tff(6064,plain,
% 1.74/1.90 (~r(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[3429, 6038, 4628, 6063])).
% 1.74/1.90 tff(6065,plain,
% 1.74/1.90 (b(z, s(s(s(s(z)))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[339, 6064])).
% 1.74/1.90 tff(6066,plain,
% 1.74/1.90 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 1.74/1.90 inference(monotonicity,[status(thm)],[2060])).
% 1.74/1.90 tff(6067,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6068,plain,
% 1.74/1.90 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(6069,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[6068])).
% 1.74/1.90 tff(6070,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[6069, 6067])).
% 1.74/1.90 tff(6071,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(6072,plain,
% 1.74/1.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[6071, 6070])).
% 1.74/1.90 tff(6073,plain,
% 1.74/1.90 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[6072, 77, 3139, 5917])).
% 1.74/1.90 tff(6074,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[5965, 60, 36, 6073])).
% 1.74/1.90 tff(6075,plain,
% 1.74/1.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6076,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6077,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6076, 6075])).
% 1.74/1.91 tff(6078,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6077, 77, 3139, 5917])).
% 1.74/1.91 tff(6079,plain,
% 1.74/1.91 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.74/1.91 inference(commutativity,[status(thm)],[])).
% 1.74/1.91 tff(6080,plain,
% 1.74/1.91 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6079])).
% 1.74/1.91 tff(6081,plain,
% 1.74/1.91 (~(s(s(s(z))) = s(s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[36, 6080])).
% 1.74/1.91 tff(6082,plain,
% 1.74/1.91 (b(s(s(s(z))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1557, 60, 6081, 6078])).
% 1.74/1.91 tff(6083,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6084,plain,
% 1.74/1.91 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6085,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6084])).
% 1.74/1.91 tff(6086,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6085, 6083])).
% 1.74/1.91 tff(6087,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6088,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6087, 6086])).
% 1.74/1.91 tff(6089,plain,
% 1.74/1.91 (~r(s(z), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6088, 77, 5431, 5917])).
% 1.74/1.91 tff(6090,plain,
% 1.74/1.91 (((~![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))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6091,plain,
% 1.74/1.91 ((~![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))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6092,plain,
% 1.74/1.91 ((~![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)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6091, 6090])).
% 1.74/1.91 tff(6093,plain,
% 1.74/1.91 (b(s(z), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6092, 60, 2196, 6089])).
% 1.74/1.91 tff(6094,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6095,plain,
% 1.74/1.91 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6096,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6095])).
% 1.74/1.91 tff(6097,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6096, 6094])).
% 1.74/1.91 tff(6098,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6099,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6098, 6097])).
% 1.74/1.91 tff(6100,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6099, 192, 6093, 6082, 3527, 6074])).
% 1.74/1.91 tff(6101,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6102,plain,
% 1.74/1.91 (~r(s(s(z)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6101, 3139, 3527, 5431])).
% 1.74/1.91 tff(6103,plain,
% 1.74/1.91 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6025, 6102, 1543])).
% 1.74/1.91 tff(6104,plain,
% 1.74/1.91 (b(s(s(elem!1)), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5931, 6103, 5912])).
% 1.74/1.91 tff(6105,plain,
% 1.74/1.91 (b(s(s(z)), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6104, 6066])).
% 1.74/1.91 tff(6106,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3145, 3139, 409])).
% 1.74/1.91 tff(6107,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3150, 6106, 5852])).
% 1.74/1.91 tff(6108,plain,
% 1.74/1.91 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.91 tff(6109,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1242, 6108])).
% 1.74/1.91 tff(6110,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6111,plain,
% 1.74/1.91 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6112,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6111])).
% 1.74/1.91 tff(6113,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6112, 6110])).
% 1.74/1.91 tff(6114,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6115,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 1.74/1.91 tff(6116,plain,
% 1.74/1.91 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6115, 192, 6109, 3134, 6107, 2039, 6105])).
% 1.74/1.91 tff(6117,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[2881])).
% 1.74/1.91 tff(6118,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(symmetry,[status(thm)],[6117])).
% 1.74/1.91 tff(6119,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.74/1.91 tff(6120,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6119, 6118])).
% 1.74/1.91 tff(6121,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[524, 6120])).
% 1.74/1.91 tff(6122,plain,((~b(s(s(s(s(z)))), elem!1)) | b(s(s(s(s(z)))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6123,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6122, 6107, 1995])).
% 1.74/1.91 tff(6124,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4669, 6123, 239, 813])).
% 1.74/1.91 tff(6125,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[113, 6124])).
% 1.74/1.91 tff(6126,plain,
% 1.74/1.91 (b(s(s(z)), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5938, 6104, 1543])).
% 1.74/1.91 tff(6127,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.91 tff(6128,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.74/1.91 tff(6129,plain,
% 1.74/1.91 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6130,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6129])).
% 1.74/1.91 tff(6131,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6130, 3608])).
% 1.74/1.91 tff(6132,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6133,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6132, 6131])).
% 1.74/1.91 tff(6134,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6133, 192, 1242, 6128, 1745, 6127])).
% 1.74/1.91 tff(6135,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6136,plain,
% 1.74/1.91 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6135, 6126, 6123, 1242])).
% 1.74/1.91 tff(6137,plain,
% 1.74/1.91 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5381, 6136])).
% 1.74/1.91 tff(6138,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.91 tff(6139,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6140,plain,
% 1.74/1.91 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6141,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6140])).
% 1.74/1.91 tff(6142,plain,
% 1.74/1.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6141, 6139])).
% 1.74/1.91 tff(6143,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(6144,plain,
% 1.74/1.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6143, 6142])).
% 1.74/1.91 tff(6145,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6144, 77, 2280, 5916, 6138])).
% 1.74/1.91 tff(6146,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6147,plain,
% 1.74/1.91 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6146, 6137, 6125])).
% 1.74/1.91 tff(6148,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2401, 60, 6147, 6116, 4216])).
% 1.74/1.91 tff(6149,plain,((~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6150,plain,
% 1.74/1.91 (~r(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6149, 5833, 5823, 5696, 6065, 6058, 5843, 4628, 6061, 6060])).
% 1.74/1.91 tff(6151,plain,
% 1.74/1.91 (b(s(s(s(z))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2025, 6150, 5837])).
% 1.74/1.91 tff(6152,plain,
% 1.74/1.91 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3136, 6151, 5833, 5823])).
% 1.74/1.91 tff(6153,plain,
% 1.74/1.91 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[375, 6152])).
% 1.74/1.91 tff(6154,plain,
% 1.74/1.91 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.91 tff(6155,plain,
% 1.74/1.91 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[6154, 3030])).
% 1.74/1.91 tff(6156,plain,
% 1.74/1.91 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(transitivity,[status(thm)],[6155, 3031])).
% 1.74/1.91 tff(6157,plain,
% 1.74/1.91 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[6156])).
% 1.74/1.91 tff(6158,plain,
% 1.74/1.91 (~(s(s(s(s(z)))) = elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[48, 6157])).
% 1.74/1.91 tff(6159,plain,
% 1.74/1.91 (~b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5795, 6151, 5823, 6038])).
% 1.74/1.91 tff(6160,plain,
% 1.74/1.91 (r(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2037, 6159, 5703])).
% 1.74/1.91 tff(6161,plain,
% 1.74/1.91 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5953, 6160, 6060])).
% 1.74/1.91 tff(6162,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3150, 6161, 6158])).
% 1.74/1.91 tff(6163,plain,
% 1.74/1.91 (b(s(s(s(s(z)))), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6122, 6162, 5697])).
% 1.74/1.91 tff(6164,plain,
% 1.74/1.91 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1753, 6163, 4628, 6065])).
% 1.74/1.91 tff(6165,plain,
% 1.74/1.91 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[181, 6164])).
% 1.74/1.91 tff(6166,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[3484, 77, 6165, 6063, 6153])).
% 1.74/1.91 tff(6167,plain,((~b(s(s(s(s(z)))), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6168,plain,
% 1.74/1.91 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6167, 504, 39])).
% 1.74/1.91 tff(6169,plain,
% 1.74/1.91 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[217, 6168])).
% 1.74/1.91 tff(6170,plain,
% 1.74/1.91 (~r(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[200, 6169, 39])).
% 1.74/1.91 tff(6171,plain,
% 1.74/1.91 (b(s(s(s(z))), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[920, 6170])).
% 1.74/1.91 tff(6172,plain,
% 1.74/1.91 (~r(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1582, 6169, 39])).
% 1.74/1.91 tff(6173,plain,
% 1.74/1.91 (b(z, s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[292, 6172])).
% 1.74/1.91 tff(6174,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[4681, 6173, 6171, 504, 39])).
% 1.74/1.91 tff(6175,plain,((~r(s(z), z)) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(6176,plain,
% 1.74/1.91 (~r(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[6175, 39])).
% 1.74/1.91 tff(6177,plain,
% 1.74/1.91 (b(s(z), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[351, 6176])).
% 1.74/1.91 tff(6178,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6177, 5704])).
% 1.74/1.91 tff(6179,plain,
% 1.74/1.91 (~r(z, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1671, 37, 6051])).
% 1.74/1.91 tff(6180,plain,
% 1.74/1.91 (b(z, s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1021, 6179])).
% 1.74/1.91 tff(6181,plain,
% 1.74/1.91 (b(elem!1, s(s(s(z))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6180, 6050])).
% 1.74/1.91 tff(6182,plain,
% 1.74/1.91 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[5831, 4265, 1995])).
% 1.74/1.91 tff(6183,plain,
% 1.74/1.91 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[2227, 6182, 5739])).
% 1.74/1.91 tff(6184,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6185,plain,
% 1.74/1.91 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(6186,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6185])).
% 1.74/1.92 tff(6187,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6186, 6184])).
% 1.74/1.92 tff(6188,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6189,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6188, 6187])).
% 1.74/1.92 tff(6190,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6189, 192, 3134, 5788, 221, 440])).
% 1.74/1.92 tff(6191,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6192,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6191, 6183, 6181, 5225])).
% 1.74/1.92 tff(6193,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[375, 6192])).
% 1.74/1.92 tff(6194,plain,
% 1.74/1.92 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.92 inference(transitivity,[status(thm)],[5737, 5705])).
% 1.74/1.92 tff(6195,plain,
% 1.74/1.92 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6194])).
% 1.74/1.92 tff(6196,plain,
% 1.74/1.92 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[266, 6195])).
% 1.74/1.92 tff(6197,plain,
% 1.74/1.92 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.92 tff(6198,plain,
% 1.74/1.92 (r(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[37, 6197])).
% 1.74/1.92 tff(6199,plain,
% 1.74/1.92 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5817, 77, 6198, 118])).
% 1.74/1.92 tff(6200,plain,
% 1.74/1.92 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5822, 6199, 6196])).
% 1.74/1.92 tff(6201,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6202,plain,
% 1.74/1.92 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6203,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6202])).
% 1.74/1.92 tff(6204,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6203, 6201])).
% 1.74/1.92 tff(6205,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6206,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6205, 6204])).
% 1.74/1.92 tff(6207,plain,
% 1.74/1.92 (~b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6206, 192, 2268, 6183, 6200])).
% 1.74/1.92 tff(6208,plain,
% 1.74/1.92 (r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[438, 60, 6207, 380])).
% 1.74/1.92 tff(6209,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5648, 77, 6208, 408, 6193])).
% 1.74/1.92 tff(6210,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6211,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6210, 408, 6178, 66, 5696])).
% 1.74/1.92 tff(6212,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[292, 6211])).
% 1.74/1.92 tff(6213,plain,
% 1.74/1.92 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.92 tff(6214,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6213])).
% 1.74/1.92 tff(6215,plain,
% 1.74/1.92 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6155])).
% 1.74/1.92 tff(6216,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[48, 6215])).
% 1.74/1.92 tff(6217,plain,
% 1.74/1.92 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.92 tff(6218,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6212, 6217])).
% 1.74/1.92 tff(6219,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3543, 192, 6218, 218, 461])).
% 1.74/1.92 tff(6220,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2385, 6219, 6216])).
% 1.74/1.92 tff(6221,plain,
% 1.74/1.92 (r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6220, 6214])).
% 1.74/1.92 tff(6222,plain,
% 1.74/1.92 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[4176, 408, 66])).
% 1.74/1.92 tff(6223,plain,
% 1.74/1.92 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[133, 6222])).
% 1.74/1.92 tff(6224,plain,
% 1.74/1.92 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.92 inference(symmetry,[status(thm)],[6066])).
% 1.74/1.92 tff(6225,plain,
% 1.74/1.92 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6224])).
% 1.74/1.92 tff(6226,plain,
% 1.74/1.92 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.92 tff(6227,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[1996])).
% 1.74/1.92 tff(6228,plain,
% 1.74/1.92 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[5849])).
% 1.74/1.92 tff(6229,plain,
% 1.74/1.92 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[48, 6228])).
% 1.74/1.92 tff(6230,plain,
% 1.74/1.92 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.92 tff(6231,plain,
% 1.74/1.92 (~r(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6210, 408, 2268, 118, 1543])).
% 1.74/1.92 tff(6232,plain,
% 1.74/1.92 (b(z, s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[292, 6231])).
% 1.74/1.92 tff(6233,plain,
% 1.74/1.92 (b(elem!1, s(z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6232, 6230])).
% 1.74/1.92 tff(6234,plain,
% 1.74/1.92 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3543, 192, 6233, 512, 38])).
% 1.74/1.92 tff(6235,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2385, 6234, 6229])).
% 1.74/1.92 tff(6236,plain,
% 1.74/1.92 (r(z, s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6235, 6227])).
% 1.74/1.92 tff(6237,plain,
% 1.74/1.92 (elem!1 = z),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[2884, 1995])).
% 1.74/1.92 tff(6238,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6239,plain,
% 1.74/1.92 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6240,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6239])).
% 1.74/1.92 tff(6241,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6240, 6238])).
% 1.74/1.92 tff(6242,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6243,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.74/1.92 tff(6244,plain,
% 1.74/1.92 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6243, 192, 2268, 6233, 512])).
% 1.74/1.92 tff(6245,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[3150, 6244, 5852])).
% 1.74/1.92 tff(6246,plain,
% 1.74/1.92 (z = elem!1),
% 1.74/1.92 inference(symmetry,[status(thm)],[2167])).
% 1.74/1.92 tff(6247,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6246])).
% 1.74/1.92 tff(6248,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(symmetry,[status(thm)],[6247])).
% 1.74/1.92 tff(6249,plain,
% 1.74/1.92 (r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[3140, 6248])).
% 1.74/1.92 tff(6250,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[883, 77, 296, 2280])).
% 1.74/1.92 tff(6251,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6250, 6249])).
% 1.74/1.92 tff(6252,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(elem!1 = z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6253,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6252, 296, 6245, 6237])).
% 1.74/1.92 tff(6254,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[113, 6253])).
% 1.74/1.92 tff(6255,plain,
% 1.74/1.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[449, 2963, 440, 6254])).
% 1.74/1.92 tff(6256,plain,
% 1.74/1.92 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[390, 6255])).
% 1.74/1.92 tff(6257,plain,
% 1.74/1.92 (~r(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5160, 6256, 6236])).
% 1.74/1.92 tff(6258,plain,
% 1.74/1.92 (b(s(s(s(z))), z)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[253, 6257])).
% 1.74/1.92 tff(6259,plain,
% 1.74/1.92 (b(s(s(s(z))), elem!1)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6258, 6226])).
% 1.74/1.92 tff(6260,plain,
% 1.74/1.92 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2061])).
% 1.74/1.92 tff(6261,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6260])).
% 1.74/1.92 tff(6262,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6261])).
% 1.74/1.92 tff(6263,plain,
% 1.74/1.92 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6235, 6262])).
% 1.74/1.92 tff(6264,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 1.74/1.92 tff(6265,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2061])).
% 1.74/1.92 tff(6266,plain,
% 1.74/1.92 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.92 tff(6267,plain,
% 1.74/1.92 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6266, 6265])).
% 1.74/1.92 tff(6268,plain,
% 1.74/1.92 (r(elem!1, s(s(s(z))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1648, 6267])).
% 1.74/1.92 tff(6269,plain,
% 1.74/1.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5953, 6268, 3140])).
% 1.74/1.92 tff(6270,plain,
% 1.74/1.92 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[154, 6269, 6264])).
% 1.74/1.92 tff(6271,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2061, 6260])).
% 1.74/1.92 tff(6272,plain,
% 1.74/1.92 (s(s(elem!1)) = s(s(z))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2168])).
% 1.74/1.92 tff(6273,plain,
% 1.74/1.92 (s(s(z)) = s(s(elem!1))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6272])).
% 1.74/1.92 tff(6274,plain,
% 1.74/1.92 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6273])).
% 1.74/1.92 tff(6275,plain,
% 1.74/1.92 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6274])).
% 1.74/1.92 tff(6276,plain,
% 1.74/1.92 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6275])).
% 1.74/1.92 tff(6277,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(6278,plain,
% 1.74/1.92 (s(s(s(z))) = s(s(s(s(z))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6274, 6277, 6276])).
% 1.74/1.92 tff(6279,plain,
% 1.74/1.92 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6278])).
% 1.74/1.92 tff(6280,plain,
% 1.74/1.92 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6279, 952])).
% 1.74/1.92 tff(6281,plain,
% 1.74/1.92 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6280])).
% 1.74/1.92 tff(6282,plain,
% 1.74/1.92 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6277])).
% 1.74/1.92 tff(6283,plain,
% 1.74/1.92 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6276])).
% 1.74/1.92 tff(6284,plain,
% 1.74/1.92 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6283, 6282, 6275])).
% 1.74/1.92 tff(6285,plain,
% 1.74/1.92 (s(s(s(s(s(z))))) = s(s(s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6284])).
% 1.74/1.92 tff(6286,plain,
% 1.74/1.92 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6285, 6281])).
% 1.74/1.92 tff(6287,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[102, 6286])).
% 1.74/1.92 tff(6288,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6289,plain,
% 1.74/1.92 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6288, 6237])).
% 1.74/1.92 tff(6290,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.92 tff(6291,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[2167])).
% 1.74/1.92 tff(6292,plain,
% 1.74/1.92 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(symmetry,[status(thm)],[6291])).
% 1.74/1.92 tff(6293,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1648, 6292])).
% 1.74/1.92 tff(6294,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(6295,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6294, 6293])).
% 1.74/1.92 tff(6296,plain,((~r(z, s(s(s(elem!1))))) | r(elem!1, s(s(s(elem!1)))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6297,plain,
% 1.74/1.92 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6296, 1648, 6237])).
% 1.74/1.92 tff(6298,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.92 tff(6299,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(6300,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6301,plain,
% 1.74/1.92 (((~r(s(s(s(elem!1))), s(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(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6302,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6301])).
% 1.74/1.92 tff(6303,plain,
% 1.74/1.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[6302, 6300])).
% 1.74/1.92 tff(6304,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(6305,plain,
% 1.74/1.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 1.74/1.92 tff(6306,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6305, 77, 6290, 6299, 6298])).
% 1.74/1.92 tff(6307,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(6308,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[6307, 6297, 6290])).
% 1.74/1.92 tff(6309,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[5001, 6308, 6289])).
% 1.74/1.92 tff(6310,plain,
% 1.74/1.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[6309, 6271])).
% 1.74/1.92 tff(6311,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6312,plain,
% 1.74/1.92 (((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(6313,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[6312])).
% 1.74/1.92 tff(6314,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6313, 6311])).
% 1.74/1.93 tff(6315,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6316,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6315, 6314])).
% 1.74/1.93 tff(6317,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6316, 192, 396, 512, 38, 6310, 6270, 221])).
% 1.74/1.93 tff(6318,plain,((~r(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6319,plain,
% 1.74/1.93 ((~r(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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6318, 146])).
% 1.74/1.93 tff(6320,plain,
% 1.74/1.93 (~r(z, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6319, 2963, 1543, 5225, 38, 512, 6263, 6245])).
% 1.74/1.93 tff(6321,plain,
% 1.74/1.93 (b(z, s(s(s(elem!1))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1021, 6320])).
% 1.74/1.93 tff(6322,plain,
% 1.74/1.93 (b(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6321, 6050])).
% 1.74/1.93 tff(6323,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6324,plain,
% 1.74/1.93 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6325,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6324])).
% 1.74/1.93 tff(6326,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6325, 6323])).
% 1.74/1.93 tff(6327,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6328,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6327, 6326])).
% 1.74/1.93 tff(6329,plain,
% 1.74/1.93 (~b(s(s(z)), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6328, 192, 2268, 2237, 5788, 3133, 5996])).
% 1.74/1.93 tff(6330,plain,
% 1.74/1.93 (r(s(s(z)), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5965, 60, 6329, 36])).
% 1.74/1.93 tff(6331,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6332,plain,
% 1.74/1.93 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6333,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6332])).
% 1.74/1.93 tff(6334,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6333, 6331])).
% 1.74/1.93 tff(6335,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6336,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6335, 6334])).
% 1.74/1.93 tff(6337,plain,
% 1.74/1.93 (~r(s(s(z)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6336, 77, 408, 6330])).
% 1.74/1.93 tff(6338,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6339,plain,
% 1.74/1.93 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6340,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6339])).
% 1.74/1.93 tff(6341,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6340, 6338])).
% 1.74/1.93 tff(6342,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6343,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6342, 6341])).
% 1.74/1.93 tff(6344,plain,
% 1.74/1.93 (~b(s(s(z)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6343, 192, 2268, 2237, 5996])).
% 1.74/1.93 tff(6345,plain,
% 1.74/1.93 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6033, 60, 6344])).
% 1.74/1.93 tff(6346,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6345, 6337, 5847])).
% 1.74/1.93 tff(6347,plain,((~b(s(s(z)), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6348,plain,
% 1.74/1.93 (~b(s(s(z)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6347, 6322, 2268, 6233, 408, 6259])).
% 1.74/1.93 tff(6349,plain,
% 1.74/1.93 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6348, 6225])).
% 1.74/1.93 tff(6350,plain,
% 1.74/1.93 (r(s(s(elem!1)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5931, 6349, 5912])).
% 1.74/1.93 tff(6351,plain,
% 1.74/1.93 (r(s(s(z)), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6025, 6350, 1543])).
% 1.74/1.93 tff(6352,plain,
% 1.74/1.93 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2045, 192, 6322, 6259, 5225])).
% 1.74/1.93 tff(6353,plain,
% 1.74/1.93 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5822, 6352, 6196])).
% 1.74/1.93 tff(6354,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6355,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6356,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6355, 6354])).
% 1.74/1.93 tff(6357,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6356, 77, 6353, 6351])).
% 1.74/1.93 tff(6358,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6359,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6360,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6359, 6358])).
% 1.74/1.93 tff(6361,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6360, 60, 3070, 6357])).
% 1.74/1.93 tff(6362,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.93 inference(commutativity,[status(thm)],[])).
% 1.74/1.93 tff(6363,plain,
% 1.74/1.93 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.93 inference(symmetry,[status(thm)],[6362])).
% 1.74/1.93 tff(6364,plain,
% 1.74/1.93 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6363])).
% 1.74/1.93 tff(6365,plain,
% 1.74/1.93 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[5374, 6364])).
% 1.74/1.93 tff(6366,plain,
% 1.74/1.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6367,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6368,plain,
% 1.74/1.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6367, 6366])).
% 1.74/1.93 tff(6369,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6368, 77, 6245, 6351])).
% 1.74/1.93 tff(6370,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6371,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6372,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6371, 6370])).
% 1.74/1.93 tff(6373,plain,
% 1.74/1.93 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6372, 60, 6369])).
% 1.74/1.93 tff(6374,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6373, 6365])).
% 1.74/1.93 tff(6375,plain,
% 1.74/1.93 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5925, 6351, 6245])).
% 1.74/1.93 tff(6376,plain,
% 1.74/1.93 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5381, 6375])).
% 1.74/1.93 tff(6377,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6378,plain,
% 1.74/1.93 (((~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(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6379,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6378])).
% 1.74/1.93 tff(6380,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[6379, 6377])).
% 1.74/1.93 tff(6381,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(6382,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6381, 6380])).
% 1.74/1.93 tff(6383,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6382, 192, 2963, 6254, 6376, 6374, 6361])).
% 1.74/1.93 tff(6384,plain,((~r(s(s(s(s(s(z))))), z)) | (~(s(elem!1) = s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(6385,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6384, 376, 6178, 408, 5696, 461, 218, 66])).
% 1.74/1.93 tff(6386,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[271, 6385])).
% 1.74/1.93 tff(6387,plain,
% 1.74/1.93 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3429, 6386, 6223, 6221])).
% 1.74/1.93 tff(6388,plain,
% 1.74/1.93 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[390, 6387])).
% 1.74/1.93 tff(6389,plain,
% 1.74/1.93 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.93 tff(6390,plain,
% 1.74/1.93 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[6389])).
% 1.74/1.93 tff(6391,plain,
% 1.74/1.93 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[6385, 6390])).
% 1.74/1.93 tff(6392,plain,
% 1.74/1.93 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5822, 6391, 5710])).
% 1.74/1.93 tff(6393,plain,
% 1.74/1.93 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6243, 192, 2268, 2237, 512])).
% 1.74/1.93 tff(6394,plain,
% 1.74/1.93 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3150, 6393, 5852])).
% 1.74/1.93 tff(6395,plain,
% 1.74/1.93 (~b(s(s(s(z))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[3136, 3134, 440, 2039])).
% 1.74/1.93 tff(6396,plain,
% 1.74/1.93 (r(s(s(s(z))), elem!1)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2025, 6395, 5943])).
% 1.74/1.93 tff(6397,plain,
% 1.74/1.93 (~b(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[6191, 3134, 440, 221])).
% 1.74/1.93 tff(6398,plain,
% 1.74/1.93 (r(elem!1, s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[2037, 6397, 5776])).
% 1.74/1.93 tff(6399,plain,
% 1.74/1.93 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5953, 6398, 6394])).
% 1.74/1.93 tff(6400,plain,
% 1.74/1.93 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[406, 6399])).
% 1.74/1.93 tff(6401,plain,
% 1.74/1.93 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5925, 5917, 3140])).
% 1.74/1.93 tff(6402,plain,
% 1.74/1.93 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[5381, 6401])).
% 1.74/1.93 tff(6403,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6404,plain,
% 1.74/1.93 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(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(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(6405,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6404])).
% 1.74/1.94 tff(6406,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6405, 6403])).
% 1.74/1.94 tff(6407,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6408,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6407, 6406])).
% 1.74/1.94 tff(6409,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6408, 192, 512, 38, 395, 6402, 394, 6074])).
% 1.74/1.94 tff(6410,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6411,plain,
% 1.74/1.94 (~r(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6410, 6400, 38, 395, 512, 6396, 6394])).
% 1.74/1.94 tff(6412,plain,
% 1.74/1.94 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6025, 6411, 1543])).
% 1.74/1.94 tff(6413,plain,
% 1.74/1.94 (b(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5931, 6412, 5912])).
% 1.74/1.94 tff(6414,plain,
% 1.74/1.94 (b(s(s(z)), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5934, 6066])).
% 1.74/1.94 tff(6415,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.94 tff(6416,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6415, 6414])).
% 1.74/1.94 tff(6417,plain,((~b(s(s(elem!1)), elem!1)) | b(s(s(z)), elem!1) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6418,plain,
% 1.74/1.94 (b(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6417, 6413, 1543])).
% 1.74/1.94 tff(6419,plain,
% 1.74/1.94 (~b(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6343, 192, 2268, 2237, 6418])).
% 1.74/1.94 tff(6420,plain,
% 1.74/1.94 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6033, 60, 6419])).
% 1.74/1.94 tff(6421,plain,
% 1.74/1.94 (r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6420, 5847])).
% 1.74/1.94 tff(6422,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6423,plain,
% 1.74/1.94 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6424,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6423])).
% 1.74/1.94 tff(6425,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6424, 6422])).
% 1.74/1.94 tff(6426,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6427,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6426, 6425])).
% 1.74/1.94 tff(6428,plain,
% 1.74/1.94 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6427, 192, 2268, 2237, 3134, 2039, 6418])).
% 1.74/1.94 tff(6429,plain,
% 1.74/1.94 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2401, 60, 6428, 4216])).
% 1.74/1.94 tff(6430,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6431,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6432,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6431, 6430])).
% 1.74/1.94 tff(6433,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6432, 77, 6429, 118, 6421])).
% 1.74/1.94 tff(6434,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6435,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6434, 6392, 6178, 6218, 66, 5696, 461, 6388, 218, 376, 6223])).
% 1.74/1.94 tff(6436,plain,
% 1.74/1.94 (r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2227, 6435, 5825])).
% 1.74/1.94 tff(6437,plain,
% 1.74/1.94 (r(z, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5831, 6436, 5697])).
% 1.74/1.94 tff(6438,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[481, 6437, 39, 6212, 461])).
% 1.74/1.94 tff(6439,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[181, 6438])).
% 1.74/1.94 tff(6440,plain,
% 1.74/1.94 (~b(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3439, 6439, 6212, 6388, 461, 6386, 6223])).
% 1.74/1.94 tff(6441,plain,
% 1.74/1.94 (r(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[237, 6440])).
% 1.74/1.94 tff(6442,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[404, 6439, 6223, 6388])).
% 1.74/1.94 tff(6443,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[406, 6442])).
% 1.74/1.94 tff(6444,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5301, 6443, 6441, 6221])).
% 1.74/1.94 tff(6445,plain,((~r(s(s(s(z))), s(z))) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6446,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6445, 408, 39])).
% 1.74/1.94 tff(6447,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[920, 6446])).
% 1.74/1.94 tff(6448,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4698, 6447, 6177, 6212, 39])).
% 1.74/1.94 tff(6449,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[181, 6448])).
% 1.74/1.94 tff(6450,plain,
% 1.74/1.94 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.94 inference(transitivity,[status(thm)],[5865, 5834])).
% 1.74/1.94 tff(6451,plain,
% 1.74/1.94 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6450])).
% 1.74/1.94 tff(6452,plain,
% 1.74/1.94 (~(s(s(s(z))) = elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[209, 6451])).
% 1.74/1.94 tff(6453,plain,
% 1.74/1.94 (b(elem!1, s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[465, 5868])).
% 1.74/1.94 tff(6454,plain,
% 1.74/1.94 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2881])).
% 1.74/1.94 tff(6455,plain,
% 1.74/1.94 (b(s(z), elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[515, 6454])).
% 1.74/1.94 tff(6456,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6457,plain,
% 1.74/1.94 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6458,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6457])).
% 1.74/1.94 tff(6459,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6458, 6456])).
% 1.74/1.94 tff(6460,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6461,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6460, 6459])).
% 1.74/1.94 tff(6462,plain,
% 1.74/1.94 (~b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6461, 192, 6455, 6453, 1408])).
% 1.74/1.94 tff(6463,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2025, 6462, 6452])).
% 1.74/1.94 tff(6464,plain,
% 1.74/1.94 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[2881])).
% 1.74/1.94 tff(6465,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.74/1.94 inference(symmetry,[status(thm)],[6464])).
% 1.74/1.94 tff(6466,plain,
% 1.74/1.94 (r(s(s(s(z))), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6463, 6465])).
% 1.74/1.94 tff(6467,plain,
% 1.74/1.94 (~r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5160, 383, 6466])).
% 1.74/1.94 tff(6468,plain,
% 1.74/1.94 (b(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[339, 6467])).
% 1.74/1.94 tff(6469,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4718, 383, 408])).
% 1.74/1.94 tff(6470,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[319, 6469])).
% 1.74/1.94 tff(6471,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1414, 6470, 465, 1408, 515])).
% 1.74/1.94 tff(6472,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[217, 6471])).
% 1.74/1.94 tff(6473,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5643, 6472, 408, 118])).
% 1.74/1.94 tff(6474,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[375, 6473])).
% 1.74/1.94 tff(6475,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4694, 6474, 6466])).
% 1.74/1.94 tff(6476,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[271, 6475])).
% 1.74/1.94 tff(6477,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1753, 6476, 396, 6468])).
% 1.74/1.94 tff(6478,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6122, 6477, 2881])).
% 1.74/1.94 tff(6479,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3150, 6478, 5859])).
% 1.74/1.94 tff(6480,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6481,plain,
% 1.74/1.94 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6482,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6481])).
% 1.74/1.94 tff(6483,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6482, 6480])).
% 1.74/1.94 tff(6484,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6485,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6484, 6483])).
% 1.74/1.94 tff(6486,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6485, 77, 6479, 383, 6463])).
% 1.74/1.94 tff(6487,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6488,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6487, 6449, 5697, 408, 66, 6212, 6447, 6177])).
% 1.74/1.94 tff(6489,plain,
% 1.74/1.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[390, 6488])).
% 1.74/1.94 tff(6490,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[404, 6489, 6223, 6449])).
% 1.74/1.94 tff(6491,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[406, 6490])).
% 1.74/1.94 tff(6492,plain,
% 1.74/1.94 (~b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6461, 192, 6178, 6218, 6447])).
% 1.74/1.94 tff(6493,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2025, 6492, 5837])).
% 1.74/1.94 tff(6494,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3145, 6491, 6493])).
% 1.74/1.94 tff(6495,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3150, 6494, 6158])).
% 1.74/1.94 tff(6496,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6122, 6495, 5697])).
% 1.74/1.94 tff(6497,plain,
% 1.74/1.94 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.94 tff(6498,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.74/1.94 inference(symmetry,[status(thm)],[6497])).
% 1.74/1.94 tff(6499,plain,
% 1.74/1.94 (r(s(s(s(z))), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6493, 6498])).
% 1.74/1.94 tff(6500,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5229, 395, 408, 118])).
% 1.74/1.94 tff(6501,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[319, 6500])).
% 1.74/1.94 tff(6502,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2055, 192, 512, 6501, 395, 1408])).
% 1.74/1.94 tff(6503,plain,((~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))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6504,plain,
% 1.74/1.94 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6503, 6489, 6447, 408, 66])).
% 1.74/1.94 tff(6505,plain,
% 1.74/1.94 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[217, 6504])).
% 1.74/1.94 tff(6506,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5643, 6505, 408, 66])).
% 1.74/1.94 tff(6507,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[375, 6506])).
% 1.74/1.94 tff(6508,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4694, 6507, 6499])).
% 1.74/1.94 tff(6509,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[271, 6508])).
% 1.74/1.94 tff(6510,plain,
% 1.74/1.94 (~b(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1753, 6509, 6449, 6496])).
% 1.74/1.94 tff(6511,plain,
% 1.74/1.94 (r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[339, 6510])).
% 1.74/1.94 tff(6512,plain,
% 1.74/1.94 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5229, 6489, 408, 66])).
% 1.74/1.94 tff(6513,plain,
% 1.74/1.94 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[319, 6512])).
% 1.74/1.94 tff(6514,plain,
% 1.74/1.94 (~b(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[3439, 6509, 6212, 6449, 6489, 6513, 6223])).
% 1.74/1.94 tff(6515,plain,
% 1.74/1.94 (r(z, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[237, 6514])).
% 1.74/1.94 tff(6516,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5301, 6515, 6511, 6491])).
% 1.74/1.94 tff(6517,plain,((~r(s(z), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6518,plain,
% 1.74/1.94 (~r(s(z), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6517, 39])).
% 1.74/1.94 tff(6519,plain,
% 1.74/1.94 (b(s(z), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[427, 6518])).
% 1.74/1.94 tff(6520,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[200, 67, 39])).
% 1.74/1.94 tff(6521,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[920, 6520])).
% 1.74/1.94 tff(6522,plain,
% 1.74/1.94 (b(elem!1, s(z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[5870, 6217])).
% 1.74/1.94 tff(6523,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5877, 192, 6522, 6521, 6519])).
% 1.74/1.94 tff(6524,plain,
% 1.74/1.94 (r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2037, 6523, 5703])).
% 1.74/1.94 tff(6525,plain,
% 1.74/1.94 (r(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6524, 5699])).
% 1.74/1.94 tff(6526,plain,
% 1.74/1.94 (~b(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6461, 192, 6178, 6522, 6521])).
% 1.74/1.94 tff(6527,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2025, 6526, 5837])).
% 1.74/1.94 tff(6528,plain,
% 1.74/1.94 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.94 tff(6529,plain,
% 1.74/1.94 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.74/1.94 inference(symmetry,[status(thm)],[6528])).
% 1.74/1.94 tff(6530,plain,
% 1.74/1.94 (r(z, s(s(s(z))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[3537, 6529])).
% 1.74/1.94 tff(6531,plain,
% 1.74/1.94 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[449, 395, 396, 441])).
% 1.74/1.94 tff(6532,plain,
% 1.74/1.94 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[375, 6531])).
% 1.74/1.94 tff(6533,plain,
% 1.74/1.94 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5264, 6532, 6530])).
% 1.74/1.94 tff(6534,plain,
% 1.74/1.94 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[493, 6533])).
% 1.74/1.94 tff(6535,plain,
% 1.74/1.94 (~b(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4048, 6534, 396, 441])).
% 1.74/1.94 tff(6536,plain,
% 1.74/1.94 (r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[339, 6535])).
% 1.74/1.94 tff(6537,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5301, 6536, 6530])).
% 1.74/1.94 tff(6538,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[406, 6537])).
% 1.74/1.94 tff(6539,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[404, 6538, 395, 396])).
% 1.74/1.94 tff(6540,plain,
% 1.74/1.94 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[133, 6539])).
% 1.74/1.94 tff(6541,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6542,plain,
% 1.74/1.94 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(6543,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[6542])).
% 1.74/1.94 tff(6544,plain,
% 1.74/1.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[6543, 6541])).
% 1.74/1.94 tff(6545,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(6546,plain,
% 1.74/1.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[6545, 6544])).
% 1.74/1.94 tff(6547,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6546, 77, 3537, 6540])).
% 1.74/1.94 tff(6548,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5822, 6547, 6196])).
% 1.74/1.94 tff(6549,plain,
% 1.74/1.94 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5831, 6533, 1995])).
% 1.74/1.94 tff(6550,plain,
% 1.74/1.94 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2227, 6549, 5739])).
% 1.74/1.94 tff(6551,plain,
% 1.74/1.94 (r(s(s(z)), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6345, 5847])).
% 1.74/1.94 tff(6552,plain,
% 1.74/1.94 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6427, 192, 2268, 2237, 3134, 2039, 5996])).
% 1.74/1.94 tff(6553,plain,
% 1.74/1.94 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[2401, 60, 6552, 4216])).
% 1.74/1.94 tff(6554,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6432, 77, 6553, 118, 6551])).
% 1.74/1.94 tff(6555,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(6556,plain,
% 1.74/1.94 (~b(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6555, 6550, 2268, 2237, 118, 6548])).
% 1.74/1.94 tff(6557,plain,
% 1.74/1.94 (~b(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6417, 6556, 1543])).
% 1.74/1.94 tff(6558,plain,
% 1.74/1.94 (r(s(s(elem!1)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5931, 6557, 5912])).
% 1.74/1.94 tff(6559,plain,
% 1.74/1.94 (r(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6025, 6558, 1543])).
% 1.74/1.94 tff(6560,plain,
% 1.74/1.94 (~r(s(s(z)), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[6072, 77, 3139, 6559])).
% 1.74/1.94 tff(6561,plain,
% 1.74/1.94 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[5965, 60, 36, 6560])).
% 1.74/1.94 tff(6562,plain,
% 1.74/1.94 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.94 tff(6563,plain,
% 1.74/1.94 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.74/1.94 inference(symmetry,[status(thm)],[6562])).
% 1.74/1.94 tff(6564,plain,
% 1.74/1.94 (r(s(s(s(z))), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[3139, 6563])).
% 1.74/1.94 tff(6565,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[4694, 6532, 6564])).
% 1.74/1.94 tff(6566,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[271, 6565])).
% 1.74/1.95 tff(6567,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5315, 6566, 396, 441, 6530, 395])).
% 1.74/1.95 tff(6568,plain,
% 1.74/1.95 (~b(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6122, 6567, 1995])).
% 1.74/1.95 tff(6569,plain,
% 1.74/1.95 (r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3150, 6568, 5852])).
% 1.74/1.95 tff(6570,plain,
% 1.74/1.95 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5925, 6559, 6569])).
% 1.74/1.95 tff(6571,plain,
% 1.74/1.95 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5381, 6570])).
% 1.74/1.95 tff(6572,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6573,plain,
% 1.74/1.95 (((~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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(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(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6574,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6573])).
% 1.74/1.95 tff(6575,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6574, 6572])).
% 1.74/1.95 tff(6576,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6577,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6576, 6575])).
% 1.74/1.95 tff(6578,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6577, 192, 396, 395, 441, 6571, 6538, 6561])).
% 1.74/1.95 tff(6579,plain,((~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6580,plain,
% 1.74/1.95 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6579, 182, 114, 6527, 5696, 6178, 6522, 66, 6524])).
% 1.74/1.95 tff(6581,plain,
% 1.74/1.95 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[390, 6580])).
% 1.74/1.95 tff(6582,plain,
% 1.74/1.95 (~r(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5160, 383, 6564])).
% 1.74/1.95 tff(6583,plain,
% 1.74/1.95 (b(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[339, 6582])).
% 1.74/1.95 tff(6584,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6485, 77, 3140, 383, 3139])).
% 1.74/1.95 tff(6585,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6586,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6585, 383, 3139])).
% 1.74/1.95 tff(6587,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3150, 6586, 5852])).
% 1.74/1.95 tff(6588,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6122, 6119, 1995])).
% 1.74/1.95 tff(6589,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6590,plain,
% 1.74/1.95 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6591,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6590])).
% 1.74/1.95 tff(6592,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6591, 6589])).
% 1.74/1.95 tff(6593,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6594,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6593, 6592])).
% 1.74/1.95 tff(6595,plain,
% 1.74/1.95 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6594, 192, 396, 6109, 6119, 441])).
% 1.74/1.95 tff(6596,plain,
% 1.74/1.95 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5822, 6595, 6196])).
% 1.74/1.95 tff(6597,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.74/1.95 tff(6598,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6356, 77, 6597, 5917])).
% 1.74/1.95 tff(6599,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6360, 60, 3070, 6598])).
% 1.74/1.95 tff(6600,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6601,plain,
% 1.74/1.95 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6602,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6601])).
% 1.74/1.95 tff(6603,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6602, 6600])).
% 1.74/1.95 tff(6604,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6605,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6604, 6603])).
% 1.74/1.95 tff(6606,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6605, 192, 6082, 221, 6074, 6599])).
% 1.74/1.95 tff(6607,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6608,plain,
% 1.74/1.95 (~r(s(s(z)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6607, 6596, 3139, 221])).
% 1.74/1.95 tff(6609,plain,
% 1.74/1.95 (~r(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6025, 6608, 1543])).
% 1.74/1.95 tff(6610,plain,
% 1.74/1.95 (b(s(s(elem!1)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5931, 6609, 5912])).
% 1.74/1.95 tff(6611,plain,
% 1.74/1.95 (b(s(s(z)), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5938, 6610, 1543])).
% 1.74/1.95 tff(6612,plain,
% 1.74/1.95 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6135, 6611, 6588, 1242])).
% 1.74/1.95 tff(6613,plain,
% 1.74/1.95 (r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5381, 6612])).
% 1.74/1.95 tff(6614,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6615,plain,
% 1.74/1.95 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6616,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6615])).
% 1.74/1.95 tff(6617,plain,
% 1.74/1.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6616, 6614])).
% 1.74/1.95 tff(6618,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6619,plain,
% 1.74/1.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6618, 6617])).
% 1.74/1.95 tff(6620,plain,
% 1.74/1.95 (~r(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6619, 77, 308, 6613])).
% 1.74/1.95 tff(6621,plain,
% 1.74/1.95 (b(s(s(z)), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6417, 6610, 1543])).
% 1.74/1.95 tff(6622,plain,
% 1.74/1.95 (~b(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6343, 192, 2268, 2237, 6621])).
% 1.74/1.95 tff(6623,plain,
% 1.74/1.95 ((s(s(z)) = s(z)) | r(s(s(z)), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6033, 60, 6622])).
% 1.74/1.95 tff(6624,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6623, 6620, 5847])).
% 1.74/1.95 tff(6625,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6626,plain,
% 1.74/1.95 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6625, 6587, 2268, 2237, 6583, 1543, 3139, 308, 396, 441])).
% 1.74/1.95 tff(6627,plain,
% 1.74/1.95 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[133, 6626])).
% 1.74/1.95 tff(6628,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6122, 6587, 1995])).
% 1.74/1.95 tff(6629,plain,
% 1.74/1.95 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1753, 6628, 396, 6583])).
% 1.74/1.95 tff(6630,plain,
% 1.74/1.95 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[271, 6629])).
% 1.74/1.95 tff(6631,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5178, 6630, 6627, 2650])).
% 1.74/1.95 tff(6632,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6633,plain,
% 1.74/1.95 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6632, 6581, 182, 6178, 6522, 5696, 6527, 6525, 114])).
% 1.74/1.95 tff(6634,plain,
% 1.74/1.95 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[319, 6633])).
% 1.74/1.95 tff(6635,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6585, 6581, 6527])).
% 1.74/1.95 tff(6636,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3150, 6635, 6158])).
% 1.74/1.95 tff(6637,plain,
% 1.74/1.95 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.95 tff(6638,plain,
% 1.74/1.95 (r(s(s(s(z))), z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6527, 6498])).
% 1.74/1.95 tff(6639,plain,
% 1.74/1.95 (~r(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[5160, 6581, 6638])).
% 1.74/1.95 tff(6640,plain,
% 1.74/1.95 (b(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[339, 6639])).
% 1.74/1.95 tff(6641,plain,
% 1.74/1.95 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6640, 6637])).
% 1.74/1.95 tff(6642,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6643,plain,
% 1.74/1.95 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(6644,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6643])).
% 1.74/1.95 tff(6645,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.95 inference(transitivity,[status(thm)],[6644, 6642])).
% 1.74/1.95 tff(6646,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(6647,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[6646, 6645])).
% 1.74/1.95 tff(6648,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6647, 192, 6178, 6522, 6641, 6636, 6634])).
% 1.74/1.95 tff(6649,plain,((~r(s(s(s(s(z)))), s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(6650,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[6649, 39])).
% 1.74/1.95 tff(6651,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[217, 6650])).
% 1.74/1.95 tff(6652,plain,
% 1.74/1.95 (~r(s(elem!1), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2076, 6176, 5696])).
% 1.74/1.95 tff(6653,plain,
% 1.74/1.95 (b(s(elem!1), z)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[560, 6652])).
% 1.74/1.95 tff(6654,plain,
% 1.74/1.95 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.74/1.95 inference(symmetry,[status(thm)],[6389])).
% 1.74/1.95 tff(6655,plain,
% 1.74/1.95 (b(s(z), s(elem!1)) <=> b(s(z), s(z))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5696])).
% 1.74/1.95 tff(6656,plain,
% 1.74/1.95 (b(s(z), s(z)) <=> b(s(z), s(elem!1))),
% 1.74/1.95 inference(symmetry,[status(thm)],[6655])).
% 1.74/1.95 tff(6657,plain,
% 1.74/1.95 ((~b(s(z), s(z))) <=> (~b(s(z), s(elem!1)))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[6656])).
% 1.74/1.95 tff(6658,plain,
% 1.74/1.95 (~b(s(z), s(elem!1))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1504, 6657])).
% 1.74/1.95 tff(6659,plain,
% 1.74/1.95 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.95 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.95 tff(6660,plain,
% 1.74/1.95 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 1.74/1.95 inference(symmetry,[status(thm)],[6659])).
% 1.74/1.95 tff(6661,plain,
% 1.74/1.95 (b(s(s(s(z))), z)),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[3133, 6660])).
% 1.74/1.95 tff(6662,plain,
% 1.74/1.95 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2533, 116, 239, 515, 37])).
% 1.74/1.95 tff(6663,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[665, 660, 118])).
% 1.74/1.95 tff(6664,plain,
% 1.74/1.95 (~r(z, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[3909, 660, 37])).
% 1.74/1.95 tff(6665,plain,
% 1.74/1.95 (b(z, s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[580, 6664])).
% 1.74/1.95 tff(6666,plain,
% 1.74/1.95 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[592, 6665, 239, 583])).
% 1.74/1.96 tff(6667,plain,
% 1.74/1.96 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[597, 6666, 6663])).
% 1.74/1.96 tff(6668,plain,
% 1.74/1.96 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6667])).
% 1.74/1.96 tff(6669,plain,
% 1.74/1.96 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6668])).
% 1.74/1.96 tff(6670,plain,
% 1.74/1.96 (r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[660, 6669])).
% 1.74/1.96 tff(6671,assumption,(~r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.96 tff(6672,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6671, 6670])).
% 1.74/1.96 tff(6673,plain,((~r(s(z), s(elem!1))) | r(s(z), s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6674,plain,
% 1.74/1.96 (~r(s(z), s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6673, 6662, 239, 583, 37, 118])).
% 1.74/1.96 tff(6675,plain,
% 1.74/1.96 (s(z) = s(elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[658, 6674, 652])).
% 1.74/1.96 tff(6676,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6675])).
% 1.74/1.96 tff(6677,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6676])).
% 1.74/1.96 tff(6678,plain,
% 1.74/1.96 (s(s(z)) = s(s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6675])).
% 1.74/1.96 tff(6679,plain,
% 1.74/1.96 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6678])).
% 1.74/1.96 tff(6680,plain,
% 1.74/1.96 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6679])).
% 1.74/1.96 tff(6681,plain,
% 1.74/1.96 (r(s(s(s(z))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6680, 6677])).
% 1.74/1.96 tff(6682,plain,
% 1.74/1.96 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6675])).
% 1.74/1.96 tff(6683,plain,
% 1.74/1.96 (r(s(s(s(z))), s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[116, 6682])).
% 1.74/1.96 tff(6684,plain,
% 1.74/1.96 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6683, 6681])).
% 1.74/1.96 tff(6685,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6679])).
% 1.74/1.96 tff(6686,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6685, 1157])).
% 1.74/1.96 tff(6687,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6686])).
% 1.74/1.96 tff(6688,plain,
% 1.74/1.96 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[102, 6687])).
% 1.74/1.96 tff(6689,plain,
% 1.74/1.96 (s(elem!1) = s(z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[638, 6675])).
% 1.74/1.96 tff(6690,plain,
% 1.74/1.96 (z = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1550, 6689])).
% 1.74/1.96 tff(6691,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6690])).
% 1.74/1.96 tff(6692,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6691])).
% 1.74/1.96 tff(6693,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6679])).
% 1.74/1.96 tff(6694,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6693, 6692])).
% 1.74/1.96 tff(6695,plain,
% 1.74/1.96 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6690])).
% 1.74/1.96 tff(6696,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2639, 6695])).
% 1.74/1.96 tff(6697,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6696, 6694])).
% 1.74/1.96 tff(6698,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1030, 6697, 6688, 239, 118, 37, 6684])).
% 1.74/1.96 tff(6699,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | b(s(z), s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6700,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6699, 2639, 118, 37, 239, 652, 583, 515])).
% 1.74/1.96 tff(6701,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[920, 6700])).
% 1.74/1.96 tff(6702,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), 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))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6703,plain,
% 1.74/1.96 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), 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))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6704,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6703])).
% 1.74/1.96 tff(6705,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6704, 6702])).
% 1.74/1.96 tff(6706,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6707,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6706, 6705])).
% 1.74/1.96 tff(6708,plain,
% 1.74/1.96 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6707, 192, 515, 512, 2639])).
% 1.74/1.96 tff(6709,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6708, 6701])).
% 1.74/1.96 tff(6710,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[390, 6709])).
% 1.74/1.96 tff(6711,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3484, 77, 170, 6710])).
% 1.74/1.96 tff(6712,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[375, 6711])).
% 1.74/1.96 tff(6713,plain,
% 1.74/1.96 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[491, 60, 4265, 486])).
% 1.74/1.96 tff(6714,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[500, 192, 2639, 6713, 239, 6712])).
% 1.74/1.96 tff(6715,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | b(s(z), s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6716,plain,
% 1.74/1.96 (~r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6715, 6661, 66, 6177, 6651, 530, 170, 6658, 6653])).
% 1.74/1.96 tff(6717,plain,
% 1.74/1.96 (b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[292, 6716])).
% 1.74/1.96 tff(6718,plain,
% 1.74/1.96 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[481, 6717, 39, 170, 3461])).
% 1.74/1.96 tff(6719,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5697])).
% 1.74/1.96 tff(6720,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6719])).
% 1.74/1.96 tff(6721,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[5696])).
% 1.74/1.96 tff(6722,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6721])).
% 1.74/1.96 tff(6723,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6722])).
% 1.74/1.96 tff(6724,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6723])).
% 1.74/1.96 tff(6725,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6724, 6720])).
% 1.74/1.96 tff(6726,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3133, 6725])).
% 1.74/1.96 tff(6727,plain,
% 1.74/1.96 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6722])).
% 1.74/1.96 tff(6728,plain,
% 1.74/1.96 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6727, 125])).
% 1.74/1.96 tff(6729,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6728])).
% 1.74/1.96 tff(6730,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6729, 5267])).
% 1.74/1.96 tff(6731,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6730])).
% 1.74/1.96 tff(6732,plain,
% 1.74/1.96 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[102, 6731])).
% 1.74/1.96 tff(6733,plain,
% 1.74/1.96 (~b(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5516, 6717, 6732, 6726, 6177, 530])).
% 1.74/1.96 tff(6734,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[493, 6733, 6718])).
% 1.74/1.96 tff(6735,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(s(s(z))))), s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6736,plain,
% 1.74/1.96 (~b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6735, 170, 39])).
% 1.74/1.96 tff(6737,plain,
% 1.74/1.96 (r(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2025, 6736, 5837])).
% 1.74/1.96 tff(6738,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3150, 6586, 5859])).
% 1.74/1.96 tff(6739,plain,
% 1.74/1.96 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2881])).
% 1.74/1.96 tff(6740,plain,
% 1.74/1.96 (r(s(s(s(z))), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3139, 6465])).
% 1.74/1.96 tff(6741,plain,
% 1.74/1.96 (~r(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5160, 383, 6740])).
% 1.74/1.96 tff(6742,plain,
% 1.74/1.96 (b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[339, 6741])).
% 1.74/1.96 tff(6743,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6742, 6739])).
% 1.74/1.96 tff(6744,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6745,plain,
% 1.74/1.96 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6746,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6745])).
% 1.74/1.96 tff(6747,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6746, 6744])).
% 1.74/1.96 tff(6748,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(6749,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6748, 6747])).
% 1.74/1.96 tff(6750,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6749, 192, 2268, 6743, 6738, 38])).
% 1.74/1.96 tff(6751,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~(z = elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6752,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6751, 3461, 6178, 5697, 6737])).
% 1.74/1.96 tff(6753,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[390, 6752])).
% 1.74/1.96 tff(6754,plain,
% 1.74/1.96 (~b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2055, 192, 6651, 3461, 6753])).
% 1.74/1.96 tff(6755,plain,
% 1.74/1.96 (r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[920, 6754])).
% 1.74/1.96 tff(6756,plain,
% 1.74/1.96 (~r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[280, 6755, 66])).
% 1.74/1.96 tff(6757,plain,
% 1.74/1.96 (b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[292, 6756])).
% 1.74/1.96 tff(6758,plain,
% 1.74/1.96 (b(elem!1, s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6757, 6217])).
% 1.74/1.96 tff(6759,plain,
% 1.74/1.96 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[481, 6757, 39, 170, 3461])).
% 1.74/1.96 tff(6760,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5831, 6759, 5697])).
% 1.74/1.96 tff(6761,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2227, 6760, 5825])).
% 1.74/1.96 tff(6762,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[367, 77, 6755, 66])).
% 1.74/1.96 tff(6763,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[375, 6762])).
% 1.74/1.96 tff(6764,plain,
% 1.74/1.96 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6434, 6763, 6178, 6761, 66, 5696, 3461, 6753, 6651, 6758, 3587])).
% 1.74/1.96 tff(6765,plain,
% 1.74/1.96 (r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5822, 6764, 5710])).
% 1.74/1.96 tff(6766,plain,
% 1.74/1.96 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6765, 6654])).
% 1.74/1.96 tff(6767,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[529, 6766])).
% 1.74/1.96 tff(6768,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6769,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6768, 39])).
% 1.74/1.96 tff(6770,plain,
% 1.74/1.96 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[181, 6769])).
% 1.74/1.96 tff(6771,plain,
% 1.74/1.96 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.96 tff(6772,plain,
% 1.74/1.96 (b(s(z), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[515, 6771])).
% 1.74/1.96 tff(6773,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1995])).
% 1.74/1.96 tff(6774,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(symmetry,[status(thm)],[6773])).
% 1.74/1.96 tff(6775,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[2062])).
% 1.74/1.96 tff(6776,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(transitivity,[status(thm)],[6775, 6774])).
% 1.74/1.96 tff(6777,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), z)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3133, 6776])).
% 1.74/1.96 tff(6778,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[3133, 6775])).
% 1.74/1.96 tff(6779,plain,
% 1.74/1.96 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1543])).
% 1.74/1.96 tff(6780,plain,
% 1.74/1.96 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6779, 2186])).
% 1.74/1.96 tff(6781,plain,
% 1.74/1.96 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6780])).
% 1.74/1.96 tff(6782,plain,
% 1.74/1.96 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(commutativity,[status(thm)],[])).
% 1.74/1.96 tff(6783,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6782])).
% 1.74/1.96 tff(6784,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.96 tff(6785,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6784, 6783])).
% 1.74/1.96 tff(6786,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.74/1.96 tff(6787,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6786, 6785])).
% 1.74/1.96 tff(6788,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6789,plain,
% 1.74/1.96 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6788, 6289])).
% 1.74/1.96 tff(6790,plain,
% 1.74/1.96 (s(s(s(elem!1))) = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2790, 2784])).
% 1.74/1.96 tff(6791,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6790])).
% 1.74/1.96 tff(6792,plain,
% 1.74/1.96 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6791, 701])).
% 1.74/1.96 tff(6793,plain,
% 1.74/1.96 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6792])).
% 1.74/1.96 tff(6794,plain,
% 1.74/1.96 (s(s(s(s(elem!1)))) = s(elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2424, 6790])).
% 1.74/1.96 tff(6795,plain,
% 1.74/1.96 (s(elem!1) = s(s(s(s(elem!1))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6794])).
% 1.74/1.96 tff(6796,plain,
% 1.74/1.96 (elem!1 = s(elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[2784])).
% 1.74/1.96 tff(6797,plain,
% 1.74/1.96 (elem!1 = s(s(s(s(elem!1))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6796, 6795])).
% 1.74/1.96 tff(6798,plain,
% 1.74/1.96 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6797, 6793])).
% 1.74/1.96 tff(6799,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.96 tff(6800,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6799, 6798])).
% 1.74/1.96 tff(6801,plain,((~(s(elem!1) = elem!1)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(6802,plain,
% 1.74/1.96 (~(s(elem!1) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6801, 6789])).
% 1.74/1.96 tff(6803,plain,
% 1.74/1.96 (~(elem!1 = s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6802, 6781])).
% 1.74/1.96 tff(6804,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.74/1.96 tff(6805,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2081])).
% 1.74/1.96 tff(6806,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[459, 308, 118])).
% 1.74/1.96 tff(6807,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[920, 6806])).
% 1.74/1.96 tff(6808,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6807, 6805])).
% 1.74/1.96 tff(6809,plain,
% 1.74/1.96 (~b(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2294, 6808, 6804, 6772])).
% 1.74/1.96 tff(6810,plain,
% 1.74/1.96 (r(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1529, 6809, 6803])).
% 1.74/1.96 tff(6811,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[5817, 77, 6810, 118])).
% 1.74/1.96 tff(6812,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1543])).
% 1.74/1.96 tff(6813,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(symmetry,[status(thm)],[6812])).
% 1.74/1.96 tff(6814,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(transitivity,[status(thm)],[6805, 6813])).
% 1.74/1.96 tff(6815,plain,
% 1.74/1.96 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6807, 6814])).
% 1.74/1.96 tff(6816,plain,
% 1.74/1.96 (~b(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1931, 6815, 583, 1005])).
% 1.74/1.96 tff(6817,plain,
% 1.74/1.96 (r(z, s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[580, 6816])).
% 1.74/1.96 tff(6818,plain,
% 1.74/1.96 (~r(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[570, 6817, 5717])).
% 1.74/1.96 tff(6819,plain,
% 1.74/1.96 (b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[339, 6818])).
% 1.74/1.96 tff(6820,plain,
% 1.74/1.96 (~b(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1330, 6808, 1005, 515])).
% 1.74/1.96 tff(6821,plain,
% 1.74/1.96 (r(z, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[292, 6820])).
% 1.74/1.96 tff(6822,plain,
% 1.74/1.96 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[835, 6821, 118])).
% 1.74/1.96 tff(6823,plain,
% 1.74/1.96 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[493, 6822])).
% 1.74/1.96 tff(6824,plain,
% 1.74/1.96 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4048, 6823, 396, 6819])).
% 1.74/1.96 tff(6825,plain,
% 1.74/1.96 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[113, 6824])).
% 1.74/1.96 tff(6826,plain,
% 1.74/1.96 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[4052, 6823, 396, 308, 6821])).
% 1.74/1.96 tff(6827,plain,
% 1.74/1.96 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[271, 6826])).
% 1.74/1.96 tff(6828,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[6252, 6827, 6825, 6237])).
% 1.74/1.96 tff(6829,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[3150, 6828, 5852])).
% 1.74/1.96 tff(6830,plain,
% 1.74/1.96 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[6819, 6108])).
% 1.74/1.96 tff(6831,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6832,plain,
% 1.74/1.96 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(6833,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[6832])).
% 1.74/1.96 tff(6834,plain,
% 1.74/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6833, 6831])).
% 1.74/1.97 tff(6835,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6836,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6835, 6834])).
% 1.74/1.97 tff(6837,plain,
% 1.74/1.97 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6836, 192, 396, 6830, 6829])).
% 1.74/1.97 tff(6838,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5822, 6837, 6811, 6196])).
% 1.74/1.97 tff(6839,plain,((~r(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(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6840,plain,
% 1.74/1.97 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6839, 6778, 118, 396, 6777, 515, 583, 1543])).
% 1.74/1.97 tff(6841,plain,
% 1.74/1.97 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[319, 6840])).
% 1.74/1.97 tff(6842,plain,
% 1.74/1.97 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2881])).
% 1.74/1.97 tff(6843,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~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))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(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))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6844,plain,
% 1.74/1.97 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6845,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6844])).
% 1.74/1.97 tff(6846,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6845, 6843])).
% 1.74/1.97 tff(6847,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6848,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~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))), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6847, 6846])).
% 1.74/1.97 tff(6849,plain,
% 1.74/1.97 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6848, 192, 2268, 512, 3133])).
% 1.74/1.97 tff(6850,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6849, 395])).
% 1.74/1.97 tff(6851,plain,
% 1.74/1.97 (r(s(s(s(z))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[920, 6850])).
% 1.74/1.97 tff(6852,plain,
% 1.74/1.97 (~b(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2683, 6851, 396, 118, 512])).
% 1.74/1.97 tff(6853,plain,
% 1.74/1.97 (r(z, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[339, 6852])).
% 1.74/1.97 tff(6854,plain,
% 1.74/1.97 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[123, 6851, 118])).
% 1.74/1.97 tff(6855,plain,
% 1.74/1.97 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[133, 6854])).
% 1.74/1.97 tff(6856,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[404, 6855, 396, 395])).
% 1.74/1.97 tff(6857,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[406, 6856])).
% 1.74/1.97 tff(6858,plain,
% 1.74/1.97 (~r(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[5301, 6857, 6853])).
% 1.74/1.97 tff(6859,plain,
% 1.74/1.97 (b(z, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[237, 6858])).
% 1.74/1.97 tff(6860,plain,
% 1.74/1.97 (b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6859, 6842])).
% 1.74/1.97 tff(6861,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6862,plain,
% 1.74/1.97 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6863,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6862])).
% 1.74/1.97 tff(6864,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6863, 6861])).
% 1.74/1.97 tff(6865,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6866,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6865, 6864])).
% 1.74/1.97 tff(6867,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6866, 192, 2268, 38, 395, 6860, 3527])).
% 1.74/1.97 tff(6868,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6869,plain,
% 1.74/1.97 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6868, 6841, 6772, 3527, 1995, 396, 118, 512, 3133])).
% 1.74/1.97 tff(6870,plain,
% 1.74/1.97 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[390, 6869])).
% 1.74/1.97 tff(6871,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.97 tff(6872,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6873,plain,
% 1.74/1.97 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6874,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6873])).
% 1.74/1.97 tff(6875,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6874, 6872])).
% 1.74/1.97 tff(6876,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6877,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6876, 6875])).
% 1.74/1.97 tff(6878,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6877, 192, 2268, 6871, 38, 3133, 3527])).
% 1.74/1.97 tff(6879,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6880,plain,
% 1.74/1.97 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6879, 6841, 6772, 3133, 3527])).
% 1.74/1.97 tff(6881,plain,
% 1.74/1.97 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2385, 6880, 6229])).
% 1.74/1.97 tff(6882,plain,
% 1.74/1.97 (~r(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2032, 77, 6881, 6870])).
% 1.74/1.97 tff(6883,plain,
% 1.74/1.97 (b(elem!1, s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2037, 6882, 5776])).
% 1.74/1.97 tff(6884,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6885,plain,
% 1.74/1.97 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6886,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6885])).
% 1.74/1.97 tff(6887,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6886, 6884])).
% 1.74/1.97 tff(6888,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6889,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6888, 6887])).
% 1.74/1.97 tff(6890,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6889, 192, 6772, 6883, 3133, 3527])).
% 1.74/1.97 tff(6891,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(6892,plain,
% 1.74/1.97 (~b(s(s(s(z))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6891, 6519, 6770, 66, 6651, 6177, 6653, 5696])).
% 1.74/1.97 tff(6893,plain,
% 1.74/1.97 (r(s(s(s(z))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2025, 6892, 5837])).
% 1.74/1.97 tff(6894,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6895,plain,
% 1.74/1.97 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(6896,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[6895])).
% 1.74/1.97 tff(6897,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[6896, 6894])).
% 1.74/1.97 tff(6898,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(6899,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(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)))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[6898, 6897])).
% 1.74/1.97 tff(6900,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6899, 192, 512, 6807, 3527])).
% 1.74/1.97 tff(6901,plain,
% 1.74/1.97 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[406, 6900])).
% 1.74/1.97 tff(6902,plain,
% 1.74/1.97 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3145, 6901, 3139])).
% 1.74/1.97 tff(6903,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[3150, 6902, 5852])).
% 1.74/1.97 tff(6904,plain,
% 1.74/1.97 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2061])).
% 1.74/1.97 tff(6905,plain,
% 1.74/1.97 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(symmetry,[status(thm)],[6904])).
% 1.74/1.97 tff(6906,plain,
% 1.74/1.97 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[3527, 6905])).
% 1.74/1.97 tff(6907,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[6122, 6903, 1995])).
% 1.74/1.97 tff(6908,plain,
% 1.74/1.97 (~b(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2988, 6907, 6906, 515, 512, 6808])).
% 1.74/1.97 tff(6909,plain,
% 1.74/1.97 (r(z, s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[292, 6908])).
% 1.74/1.97 tff(6910,plain,
% 1.74/1.97 (~r(z, s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4038, 6909, 308])).
% 1.74/1.98 tff(6911,plain,
% 1.74/1.98 (b(z, s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[339, 6910])).
% 1.74/1.98 tff(6912,plain,
% 1.74/1.98 (b(elem!1, s(s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6911, 6108])).
% 1.74/1.98 tff(6913,plain,
% 1.74/1.98 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6836, 192, 396, 6912, 6903])).
% 1.74/1.98 tff(6914,plain,
% 1.74/1.98 (r(elem!1, s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6909, 6197])).
% 1.74/1.98 tff(6915,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5817, 77, 6914, 118])).
% 1.74/1.98 tff(6916,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[5822, 6915, 6913, 6196])).
% 1.74/1.98 tff(6917,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6918,plain,
% 1.74/1.98 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6917, 66, 6770, 6177, 6651, 6893, 6519, 5696])).
% 1.74/1.98 tff(6919,plain,
% 1.74/1.98 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[319, 6918])).
% 1.74/1.98 tff(6920,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6751, 6919, 6178, 5697, 6893])).
% 1.74/1.98 tff(6921,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[390, 6920])).
% 1.74/1.98 tff(6922,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2055, 192, 6651, 6919, 6921])).
% 1.74/1.98 tff(6923,plain,
% 1.74/1.98 (r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[920, 6922])).
% 1.74/1.98 tff(6924,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[123, 6923, 66])).
% 1.74/1.98 tff(6925,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[133, 6924])).
% 1.74/1.98 tff(6926,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[404, 6925, 6770, 6921])).
% 1.74/1.98 tff(6927,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[406, 6926])).
% 1.74/1.98 tff(6928,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3145, 6927, 6893])).
% 1.74/1.98 tff(6929,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3150, 6928, 6158])).
% 1.74/1.98 tff(6930,plain,
% 1.74/1.98 ((s(elem!1) = elem!1) <=> (s(z) = elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[5696])).
% 1.74/1.98 tff(6931,plain,
% 1.74/1.98 ((s(elem!1) = elem!1) <=> (elem!1 = s(z))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6930, 2186])).
% 1.74/1.98 tff(6932,plain,
% 1.74/1.98 ((~(s(elem!1) = elem!1)) <=> (~(elem!1 = s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6931])).
% 1.74/1.98 tff(6933,plain,
% 1.74/1.98 (elem!1 = z),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2884, 5697])).
% 1.74/1.98 tff(6934,plain,
% 1.74/1.98 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6288, 6933])).
% 1.74/1.98 tff(6935,plain,
% 1.74/1.98 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6788, 6934])).
% 1.74/1.98 tff(6936,plain,
% 1.74/1.98 (~(s(elem!1) = elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6801, 6935])).
% 1.74/1.98 tff(6937,plain,
% 1.74/1.98 (~(elem!1 = s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6936, 6932])).
% 1.74/1.98 tff(6938,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6722])).
% 1.74/1.98 tff(6939,plain,
% 1.74/1.98 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[6938])).
% 1.74/1.98 tff(6940,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6893, 6939])).
% 1.74/1.98 tff(6941,plain,
% 1.74/1.98 (~r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[280, 6923, 66])).
% 1.74/1.98 tff(6942,plain,
% 1.74/1.98 (b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[292, 6941])).
% 1.74/1.98 tff(6943,plain,
% 1.74/1.98 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6722])).
% 1.74/1.98 tff(6944,plain,
% 1.74/1.98 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[6943])).
% 1.74/1.98 tff(6945,plain,
% 1.74/1.98 (b(s(z), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6519, 6944])).
% 1.74/1.98 tff(6946,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6122, 6929, 5697])).
% 1.74/1.98 tff(6947,plain,
% 1.74/1.98 (~b(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2988, 6946, 6945, 6177, 6651, 6942])).
% 1.74/1.98 tff(6948,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1313, 6947])).
% 1.74/1.98 tff(6949,plain,
% 1.74/1.98 (~r(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2565, 6948, 6940])).
% 1.74/1.98 tff(6950,plain,
% 1.74/1.98 (b(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1529, 6949, 6937])).
% 1.74/1.98 tff(6951,plain,
% 1.74/1.98 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6952,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6951])).
% 1.74/1.98 tff(6953,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6952, 6238])).
% 1.74/1.98 tff(6954,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6955,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6954, 6953])).
% 1.74/1.98 tff(6956,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6955, 192, 6178, 6950, 6929, 6651])).
% 1.74/1.98 tff(6957,plain,(b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6958,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2008, 117, 170])).
% 1.74/1.98 tff(6959,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[390, 6958])).
% 1.74/1.98 tff(6960,plain,
% 1.74/1.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6961,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6962,plain,
% 1.74/1.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6961, 6960])).
% 1.74/1.98 tff(6963,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6962, 77, 170, 409, 117])).
% 1.74/1.98 tff(6964,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6965,plain,
% 1.74/1.98 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6964, 117, 170])).
% 1.74/1.98 tff(6966,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[406, 6965])).
% 1.74/1.98 tff(6967,plain,
% 1.74/1.98 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6968,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6967])).
% 1.74/1.98 tff(6969,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6968, 5688])).
% 1.74/1.98 tff(6970,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6971,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6970, 6969])).
% 1.74/1.98 tff(6972,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6971, 192, 38, 395, 394, 3527])).
% 1.74/1.98 tff(6973,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6974,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6973, 6966, 6959, 38, 3527])).
% 1.74/1.98 tff(6975,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6976,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6975, 3527, 38, 170])).
% 1.74/1.98 tff(6977,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[133, 6976])).
% 1.74/1.98 tff(6978,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6979,plain,
% 1.74/1.98 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(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))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(6980,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[6979])).
% 1.74/1.98 tff(6981,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[6980, 6978])).
% 1.74/1.98 tff(6982,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(6983,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[6982, 6981])).
% 1.74/1.98 tff(6984,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6983, 192, 6957, 1408, 3527, 221])).
% 1.74/1.98 tff(6985,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6986,plain,
% 1.74/1.98 (~b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6985, 3527, 6977])).
% 1.74/1.98 tff(6987,plain,
% 1.74/1.98 (r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[920, 6986])).
% 1.74/1.98 tff(6988,plain,
% 1.74/1.98 (b(s(s(s(s(z)))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[526, 303])).
% 1.74/1.98 tff(6989,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[346, 192, 515, 340, 38, 6988])).
% 1.74/1.98 tff(6990,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6991,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6990, 515, 38, 170])).
% 1.74/1.98 tff(6992,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[271, 6991])).
% 1.74/1.98 tff(6993,plain,
% 1.74/1.98 ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2498, 6957])).
% 1.74/1.98 tff(6994,plain,
% 1.74/1.98 (~b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6993, 6992, 515])).
% 1.74/1.98 tff(6995,plain,
% 1.74/1.98 (~r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[262, 6992, 221, 116])).
% 1.74/1.98 tff(6996,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[292, 6995, 6994])).
% 1.74/1.98 tff(6997,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(6998,plain,
% 1.74/1.98 (~b(s(z), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6997, 6977, 6987, 38, 170])).
% 1.74/1.98 tff(6999,plain,
% 1.74/1.98 (r(s(z), z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[351, 6998])).
% 1.74/1.98 tff(7000,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[3484, 77, 170, 383])).
% 1.74/1.98 tff(7001,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[375, 7000])).
% 1.74/1.98 tff(7002,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.98 tff(7003,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[434, 192, 7002, 3527, 221, 440])).
% 1.74/1.98 tff(7004,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(7005,plain,
% 1.74/1.98 (~b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7004, 7001, 3527, 2010])).
% 1.74/1.98 tff(7006,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[438, 60, 5764, 6671, 380])).
% 1.74/1.98 tff(7007,plain,(r(s(z), s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(7008,plain,
% 1.74/1.98 (r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7007, 7005])).
% 1.74/1.98 tff(7009,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[4679, 77, 504, 619, 462])).
% 1.74/1.98 tff(7010,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(7011,plain,
% 1.74/1.98 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7010, 7008, 504])).
% 1.74/1.98 tff(7012,plain,
% 1.74/1.98 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[493, 7011])).
% 1.74/1.98 tff(7013,plain,
% 1.74/1.98 (~r(z, s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2460, 383, 170, 239])).
% 1.74/1.98 tff(7014,plain,
% 1.74/1.98 (b(z, s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[339, 7013])).
% 1.74/1.98 tff(7015,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(7016,plain,
% 1.74/1.98 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(7017,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[7016])).
% 1.74/1.98 tff(7018,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[7017, 7015])).
% 1.74/1.98 tff(7019,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(7020,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[7019, 7018])).
% 1.74/1.98 tff(7021,plain,
% 1.74/1.98 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7020, 192, 7014, 38, 6957, 239])).
% 1.74/1.98 tff(7022,plain,
% 1.74/1.98 (~b(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7021, 7012])).
% 1.74/1.98 tff(7023,plain,
% 1.74/1.98 (r(z, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[292, 7022])).
% 1.74/1.98 tff(7024,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[262, 7023, 239, 2010])).
% 1.74/1.98 tff(7025,plain,
% 1.74/1.98 (b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[920, 7024])).
% 1.74/1.98 tff(7026,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6983, 192, 6957, 7025, 3527, 2010])).
% 1.74/1.98 tff(7027,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(7028,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[7027, 504, 239, 38, 3527, 170])).
% 1.74/1.98 tff(7029,plain,
% 1.74/1.98 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[390, 7028])).
% 1.74/1.98 tff(7030,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6973, 7029, 38, 3527])).
% 1.74/1.98 tff(7031,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[406, 7030])).
% 1.74/1.98 tff(7032,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[6964, 7031, 170])).
% 1.74/1.98 tff(7033,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[133, 7032])).
% 1.74/1.98 tff(7034,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7035,plain,
% 1.74/1.99 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7036,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7035])).
% 1.74/1.99 tff(7037,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7036, 7034])).
% 1.74/1.99 tff(7038,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7039,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7038, 7037])).
% 1.74/1.99 tff(7040,plain,
% 1.74/1.99 (~b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7039, 192, 38, 6957, 7029, 3527, 7033])).
% 1.74/1.99 tff(7041,plain,
% 1.74/1.99 (r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7007, 7040])).
% 1.74/1.99 tff(7042,plain,
% 1.74/1.99 (~r(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7010, 7041, 504])).
% 1.74/1.99 tff(7043,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[493, 7042])).
% 1.74/1.99 tff(7044,plain,
% 1.74/1.99 (~b(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2641, 2638, 239, 221])).
% 1.74/1.99 tff(7045,plain,
% 1.74/1.99 (r(s(s(s(z))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[253, 7044])).
% 1.74/1.99 tff(7046,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[509, 7045, 504])).
% 1.74/1.99 tff(7047,plain,
% 1.74/1.99 (b(s(s(s(z))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[920, 7046])).
% 1.74/1.99 tff(7048,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7049,plain,
% 1.74/1.99 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7050,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7049])).
% 1.74/1.99 tff(7051,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7050, 7048])).
% 1.74/1.99 tff(7052,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7053,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7052, 7051])).
% 1.74/1.99 tff(7054,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7053, 192, 6957, 813, 239, 7047, 2638, 221])).
% 1.74/1.99 tff(7055,plain,((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7056,plain,
% 1.74/1.99 (~b(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7055, 7043, 239, 7033, 504])).
% 1.74/1.99 tff(7057,plain,
% 1.74/1.99 (r(z, s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[237, 7056])).
% 1.74/1.99 tff(7058,plain,
% 1.74/1.99 (~r(z, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[5301, 7057, 7031])).
% 1.74/1.99 tff(7059,plain,
% 1.74/1.99 (b(z, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[339, 7058])).
% 1.74/1.99 tff(7060,plain,
% 1.74/1.99 (~b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7020, 192, 7059, 38, 6957, 7043, 239])).
% 1.74/1.99 tff(7061,plain,
% 1.74/1.99 (r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[292, 7060])).
% 1.74/1.99 tff(7062,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[262, 7061, 239, 7033])).
% 1.74/1.99 tff(7063,plain,
% 1.74/1.99 (b(s(s(s(z))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[920, 7062])).
% 1.74/1.99 tff(7064,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6983, 192, 6957, 7063, 3527, 7033])).
% 1.74/1.99 tff(7065,plain,((~r(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7066,plain,
% 1.74/1.99 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7065, 6999, 3527, 38, 170])).
% 1.74/1.99 tff(7067,plain,
% 1.74/1.99 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[271, 7066])).
% 1.74/1.99 tff(7068,plain,
% 1.74/1.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7069,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7070,plain,
% 1.74/1.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7069, 7068])).
% 1.74/1.99 tff(7071,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7070, 77, 6999, 7067])).
% 1.74/1.99 tff(7072,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7007, 7071])).
% 1.74/1.99 tff(7073,plain,
% 1.74/1.99 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7004, 7072, 3527, 6977])).
% 1.74/1.99 tff(7074,plain,
% 1.74/1.99 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[375, 7073])).
% 1.74/1.99 tff(7075,plain,
% 1.74/1.99 (~r(z, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[329, 7067, 170])).
% 1.74/1.99 tff(7076,plain,
% 1.74/1.99 (b(z, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[339, 7075])).
% 1.74/1.99 tff(7077,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[3484, 77, 170, 383, 4686])).
% 1.74/1.99 tff(7078,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7079,plain,
% 1.74/1.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7078, 7074, 170])).
% 1.74/1.99 tff(7080,plain,
% 1.74/1.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[390, 7079])).
% 1.74/1.99 tff(7081,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7082,plain,
% 1.74/1.99 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7083,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7082])).
% 1.74/1.99 tff(7084,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7083, 7081])).
% 1.74/1.99 tff(7085,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7086,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7085, 7084])).
% 1.74/1.99 tff(7087,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7086, 192, 1242, 395, 394, 2638])).
% 1.74/1.99 tff(7088,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7089,plain,
% 1.74/1.99 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7088, 238, 395, 1242])).
% 1.74/1.99 tff(7090,plain,
% 1.74/1.99 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[406, 7089])).
% 1.74/1.99 tff(7091,plain,
% 1.74/1.99 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[6964, 7090, 170])).
% 1.74/1.99 tff(7092,plain,
% 1.74/1.99 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[133, 7091])).
% 1.74/1.99 tff(7093,plain,
% 1.74/1.99 (~b(s(s(s(s(s(z))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2641, 7092, 254, 238])).
% 1.74/1.99 tff(7094,plain,
% 1.74/1.99 (r(s(s(s(s(s(z))))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[271, 7093])).
% 1.74/1.99 tff(7095,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[302, 7094, 170])).
% 1.74/1.99 tff(7096,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[526, 7095])).
% 1.74/1.99 tff(7097,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7098,plain,
% 1.74/1.99 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7099,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7098])).
% 1.74/1.99 tff(7100,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7099, 7097])).
% 1.74/1.99 tff(7101,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7102,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7101, 7100])).
% 1.74/1.99 tff(7103,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7102, 192, 1242, 254, 395, 7096])).
% 1.74/1.99 tff(7104,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(7105,plain,
% 1.74/1.99 (~r(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7104, 7080, 170, 6987, 7076])).
% 1.74/1.99 tff(7106,plain,
% 1.74/1.99 (b(z, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[292, 7105])).
% 1.74/1.99 tff(7107,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7108,plain,
% 1.74/1.99 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7109,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[7108])).
% 1.74/1.99 tff(7110,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[7109, 7107])).
% 1.74/1.99 tff(7111,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(7112,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[7111, 7110])).
% 1.74/1.99 tff(7113,plain,
% 1.74/1.99 ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7112, 192, 7076, 38, 6957])).
% 1.74/1.99 tff(7114,plain,
% 1.74/1.99 (~b(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[7113, 7106])).
% 1.74/1.99 tff(7115,plain,
% 1.74/1.99 (r(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[493, 7114])).
% 1.74/1.99 tff(7116,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[302, 7067, 170])).
% 1.74/1.99 tff(7117,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), z)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[526, 7116])).
% 1.74/1.99 tff(7118,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7119,plain,
% 1.74/1.99 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(7120,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7119])).
% 1.74/2.00 tff(7121,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7120, 7118])).
% 1.74/2.00 tff(7122,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7123,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7122, 7121])).
% 1.74/2.00 tff(7124,plain,
% 1.74/2.00 (~b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7123, 192, 1242, 512, 38, 395, 1745])).
% 1.74/2.00 tff(7125,plain,
% 1.74/2.00 (r(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[920, 7124])).
% 1.74/2.00 tff(7126,plain,
% 1.74/2.00 (~b(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7102, 192, 1242, 395, 1745])).
% 1.74/2.00 tff(7127,plain,
% 1.74/2.00 (r(s(s(s(z))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[253, 7126])).
% 1.74/2.00 tff(7128,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[507, 77, 504, 7127, 7125])).
% 1.74/2.00 tff(7129,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7130,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7129, 7080, 38, 7117, 6999, 7076])).
% 1.74/2.00 tff(7131,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[217, 7130])).
% 1.74/2.00 tff(7132,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[406, 150])).
% 1.74/2.00 tff(7133,plain,
% 1.74/2.00 (~r(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2505, 67, 170])).
% 1.74/2.00 tff(7134,plain,
% 1.74/2.00 (b(s(s(s(s(z)))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[526, 7133])).
% 1.74/2.00 tff(7135,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7136,plain,
% 1.74/2.00 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7137,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7136])).
% 1.74/2.00 tff(7138,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7137, 7135])).
% 1.74/2.00 tff(7139,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7140,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7139, 7138])).
% 1.74/2.00 tff(7141,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7140, 192, 1242, 395, 7134, 7132, 2638])).
% 1.74/2.00 tff(7142,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7143,plain,
% 1.74/2.00 (~b(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7142, 7131, 6987, 7076, 7080, 170])).
% 1.74/2.00 tff(7144,plain,
% 1.74/2.00 (r(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[237, 7143])).
% 1.74/2.00 tff(7145,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5264, 7144, 7115, 7074])).
% 1.74/2.00 tff(7146,plain,((~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7147,plain,
% 1.74/2.00 (~b(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7146, 170, 38])).
% 1.74/2.00 tff(7148,plain,
% 1.74/2.00 (r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[427, 7147])).
% 1.74/2.00 tff(7149,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[5178, 2650, 117])).
% 1.74/2.00 tff(7150,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[271, 7149])).
% 1.74/2.00 tff(7151,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7152,plain,
% 1.74/2.00 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7153,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7152])).
% 1.74/2.00 tff(7154,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7153, 7151])).
% 1.74/2.00 tff(7155,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7156,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 1.74/2.00 tff(7157,plain,
% 1.74/2.00 (~r(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7156, 77, 408, 2650])).
% 1.74/2.00 tff(7158,plain,
% 1.74/2.00 (b(z, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[292, 7157])).
% 1.74/2.00 tff(7159,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7160,plain,
% 1.74/2.00 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7161,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7160])).
% 1.74/2.00 tff(7162,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7161, 7159])).
% 1.74/2.00 tff(7163,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7164,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 1.74/2.00 tff(7165,plain,
% 1.74/2.00 (~r(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7164, 77, 408, 2650])).
% 1.74/2.00 tff(7166,plain,
% 1.74/2.00 (b(s(z), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[351, 7165])).
% 1.74/2.00 tff(7167,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[6993, 7166, 7158, 7150])).
% 1.74/2.00 tff(7168,plain,((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7169,plain,
% 1.74/2.00 (~r(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7168, 117, 7148])).
% 1.74/2.00 tff(7170,plain,
% 1.74/2.00 (b(z, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[237, 7169])).
% 1.74/2.00 tff(7171,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(7172,plain,
% 1.74/2.00 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7171])).
% 1.74/2.00 tff(7173,plain,
% 1.74/2.00 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[7172])).
% 1.74/2.00 tff(7174,plain,
% 1.74/2.00 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[92, 7173, 722])).
% 1.74/2.00 tff(7175,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2419, 7174])).
% 1.74/2.00 tff(7176,plain,(~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7177,plain,
% 1.74/2.00 (~b(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7088, 7170, 6966, 6959])).
% 1.74/2.00 tff(7178,plain,
% 1.74/2.00 (r(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[339, 7177])).
% 1.74/2.00 tff(7179,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[329, 7178, 170])).
% 1.74/2.00 tff(7180,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[271, 7179])).
% 1.74/2.00 tff(7181,plain,
% 1.74/2.00 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2531, 77, 7148, 117])).
% 1.74/2.00 tff(7182,plain,
% 1.74/2.00 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7007, 7181])).
% 1.74/2.00 tff(7183,plain,
% 1.74/2.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7184,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7185,plain,
% 1.74/2.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7184, 7183])).
% 1.74/2.00 tff(7186,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7185, 77, 170, 4077])).
% 1.74/2.00 tff(7187,plain,
% 1.74/2.00 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[4466, 60, 4424, 7186])).
% 1.74/2.00 tff(7188,plain,
% 1.74/2.00 (b(z, s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[493, 602])).
% 1.74/2.00 tff(7189,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7190,plain,
% 1.74/2.00 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7191,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[7190])).
% 1.74/2.00 tff(7192,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.00 inference(transitivity,[status(thm)],[7191, 7189])).
% 1.74/2.00 tff(7193,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7194,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7193, 7192])).
% 1.74/2.00 tff(7195,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7194, 192, 6957, 7002, 7188, 239, 7187, 4087])).
% 1.74/2.00 tff(7196,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(7197,plain,
% 1.74/2.00 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[7196, 7182, 7180, 7178, 170])).
% 1.74/2.00 tff(7198,plain,
% 1.74/2.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(7199,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(7200,plain,
% 1.74/2.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[7199, 7198])).
% 1.74/2.00 tff(7201,plain,
% 1.74/2.00 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7200, 60])).
% 1.74/2.01 tff(7202,plain,
% 1.74/2.01 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7201, 7197, 7176])).
% 1.74/2.01 tff(7203,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/2.01 tff(7204,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7205,plain,
% 1.74/2.01 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7206,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7205])).
% 1.74/2.01 tff(7207,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7206, 7204])).
% 1.74/2.01 tff(7208,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7209,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7208, 7207])).
% 1.74/2.01 tff(7210,plain,
% 1.74/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7209, 192, 512, 38, 7203])).
% 1.74/2.01 tff(7211,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 1.74/2.01 tff(7212,plain,
% 1.74/2.01 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7211])).
% 1.74/2.01 tff(7213,plain,
% 1.74/2.01 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(symmetry,[status(thm)],[722])).
% 1.74/2.01 tff(7214,plain,
% 1.74/2.01 (s(s(s(s(s(s(z)))))) = z),
% 1.74/2.01 inference(transitivity,[status(thm)],[7213, 7212, 20])).
% 1.74/2.01 tff(7215,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1779, 7214])).
% 1.74/2.01 tff(7216,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7217,plain,
% 1.74/2.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7218,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7219,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = s(z)) | b(s(s(s(s(s(s(s(z))))))), s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7218, 7217])).
% 1.74/2.01 tff(7220,plain,
% 1.74/2.01 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7219, 60, 7216, 7210])).
% 1.74/2.01 tff(7221,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2055, 192, 512, 38, 395])).
% 1.74/2.01 tff(7222,plain,
% 1.74/2.01 (r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[920, 7221])).
% 1.74/2.01 tff(7223,plain,
% 1.74/2.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7224,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7225,plain,
% 1.74/2.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7224, 7223])).
% 1.74/2.01 tff(7226,plain,
% 1.74/2.01 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7225, 77, 7222, 7220])).
% 1.74/2.01 tff(7227,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7228,plain,
% 1.74/2.01 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7229,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7228])).
% 1.74/2.01 tff(7230,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7229, 7227])).
% 1.74/2.01 tff(7231,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7232,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7231, 7230])).
% 1.74/2.01 tff(7233,plain,
% 1.74/2.01 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7232, 192, 512, 38, 395, 394, 7203])).
% 1.74/2.01 tff(7234,plain,
% 1.74/2.01 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[4440, 60, 7233])).
% 1.74/2.01 tff(7235,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7234, 7226, 4432])).
% 1.74/2.01 tff(7236,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7237,plain,
% 1.74/2.01 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7236, 7202, 38, 6966, 6959])).
% 1.74/2.01 tff(7238,plain,
% 1.74/2.01 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[217, 7237])).
% 1.74/2.01 tff(7239,plain,
% 1.74/2.01 (~r(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2505, 7238, 170])).
% 1.74/2.01 tff(7240,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[526, 7239])).
% 1.74/2.01 tff(7241,plain,
% 1.74/2.01 (~r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1572, 7238, 7178])).
% 1.74/2.01 tff(7242,plain,
% 1.74/2.01 (b(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[292, 7241])).
% 1.74/2.01 tff(7243,plain,
% 1.74/2.01 (~b(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6993, 7242, 7180])).
% 1.74/2.01 tff(7244,plain,
% 1.74/2.01 (r(s(z), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[351, 7243])).
% 1.74/2.01 tff(7245,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[3491, 77, 504, 503, 408])).
% 1.74/2.01 tff(7246,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7247,plain,
% 1.74/2.01 (~r(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7246, 7244, 7148])).
% 1.74/2.01 tff(7248,plain,
% 1.74/2.01 (b(s(s(s(z))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[253, 7247])).
% 1.74/2.01 tff(7249,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7250,plain,
% 1.74/2.01 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7251,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7250])).
% 1.74/2.01 tff(7252,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7251, 7249])).
% 1.74/2.01 tff(7253,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7254,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[7253, 7252])).
% 1.74/2.01 tff(7255,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7254, 192, 7248, 6959, 7240, 6966, 7170])).
% 1.74/2.01 tff(7256,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7257,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7256, 170, 38])).
% 1.74/2.01 tff(7258,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[133, 7257])).
% 1.74/2.01 tff(7259,plain,
% 1.74/2.01 (~b(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6993, 515, 239])).
% 1.74/2.01 tff(7260,plain,
% 1.74/2.01 (r(z, s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[292, 7259])).
% 1.74/2.01 tff(7261,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7156, 77, 37, 408, 2650])).
% 1.74/2.01 tff(7262,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(7263,plain,
% 1.74/2.01 (~r(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[7262, 7260, 7148])).
% 1.74/2.01 tff(7264,plain,
% 1.74/2.01 (b(z, s(s(s(z))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[237, 7263])).
% 1.74/2.01 tff(7265,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[6997, 515, 7258, 38, 170])).
% 1.74/2.01 tff(7266,plain,
% 1.74/2.01 (b(s(s(s(z))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[920, 7265])).
% 1.74/2.01 tff(7267,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7268,plain,
% 1.74/2.01 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(7269,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[7268])).
% 1.74/2.01 tff(7270,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[7269, 7267])).
% 1.74/2.01 tff(7271,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(7272,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7271, 7270])).
% 1.74/2.02 tff(7273,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7272, 192, 6957, 239, 7266, 7264, 7258])).
% 1.74/2.02 tff(7274,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7275,plain,
% 1.74/2.02 (~b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7274, 239, 38, 170])).
% 1.74/2.02 tff(7276,plain,
% 1.74/2.02 (r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[351, 7275])).
% 1.74/2.02 tff(7277,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7164, 77, 504, 408, 2650])).
% 1.74/2.02 tff(7278,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7279,plain,
% 1.74/2.02 (~r(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7278, 7276, 7148])).
% 1.74/2.02 tff(7280,plain,
% 1.74/2.02 (b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[237, 7279])).
% 1.74/2.02 tff(7281,plain,
% 1.74/2.02 (~r(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7246, 7276, 7148])).
% 1.74/2.02 tff(7282,plain,
% 1.74/2.02 (b(s(s(s(z))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[253, 7281])).
% 1.74/2.02 tff(7283,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2641, 7282, 7280, 7258, 239])).
% 1.74/2.02 tff(7284,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7285,plain,
% 1.74/2.02 (~b(s(s(s(s(s(z))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7284, 170, 38])).
% 1.74/2.02 tff(7286,plain,
% 1.74/2.02 (r(s(s(s(s(s(z))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[271, 7285])).
% 1.74/2.02 tff(7287,plain,
% 1.74/2.02 (~b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6990, 296, 38, 170])).
% 1.74/2.02 tff(7288,plain,
% 1.74/2.02 (r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[351, 7287])).
% 1.74/2.02 tff(7289,plain,
% 1.74/2.02 (~r(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7278, 7288, 7148])).
% 1.74/2.02 tff(7290,plain,
% 1.74/2.02 (b(z, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[237, 7289])).
% 1.74/2.02 tff(7291,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7088, 7290, 340, 395])).
% 1.74/2.02 tff(7292,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[406, 7291])).
% 1.74/2.02 tff(7293,plain,
% 1.74/2.02 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7129, 6988, 38, 395, 7288, 340])).
% 1.74/2.02 tff(7294,plain,
% 1.74/2.02 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[217, 7293])).
% 1.74/2.02 tff(7295,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[5641, 77, 7294, 7292, 7148])).
% 1.74/2.02 tff(7296,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7297,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7296, 7286, 38, 170])).
% 1.74/2.02 tff(7298,plain,
% 1.74/2.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[390, 7297])).
% 1.74/2.02 tff(7299,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7078, 7298, 170])).
% 1.74/2.02 tff(7300,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[375, 7299])).
% 1.74/2.02 tff(7301,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[302, 7286, 170])).
% 1.74/2.02 tff(7302,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[526, 7301])).
% 1.74/2.02 tff(7303,plain,
% 1.74/2.02 (~b(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[6990, 7286, 38, 170])).
% 1.74/2.02 tff(7304,plain,
% 1.74/2.02 (r(s(z), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[351, 7303])).
% 1.74/2.02 tff(7305,plain,
% 1.74/2.02 (~r(s(z), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7070, 77, 7304, 7286])).
% 1.74/2.02 tff(7306,plain,
% 1.74/2.02 (b(s(z), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7007, 7305])).
% 1.74/2.02 tff(7307,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7308,plain,
% 1.74/2.02 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7309,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7308])).
% 1.74/2.02 tff(7310,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7309, 7307])).
% 1.74/2.02 tff(7311,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7312,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7311, 7310])).
% 1.74/2.02 tff(7313,plain,
% 1.74/2.02 (~b(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7312, 192, 6957, 7306, 7300])).
% 1.74/2.02 tff(7314,plain,
% 1.74/2.02 (r(s(s(s(z))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[920, 7313])).
% 1.74/2.02 tff(7315,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[162, 77, 67, 116, 383])).
% 1.74/2.02 tff(7316,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(7317,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7316, 7314, 7298])).
% 1.74/2.02 tff(7318,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[217, 7317])).
% 1.74/2.02 tff(7319,plain,
% 1.74/2.02 (~r(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[329, 7286, 170])).
% 1.74/2.02 tff(7320,plain,
% 1.74/2.02 (b(z, s(s(s(s(z)))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[339, 7319])).
% 1.74/2.02 tff(7321,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7322,plain,
% 1.74/2.02 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7323,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7322])).
% 1.74/2.02 tff(7324,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7323, 7321])).
% 1.74/2.02 tff(7325,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7326,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7325, 7324])).
% 1.74/2.02 tff(7327,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7326, 192, 1242, 512, 38, 1745, 7203])).
% 1.74/2.02 tff(7328,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7219, 60, 7216, 7327])).
% 1.74/2.02 tff(7329,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7330,plain,
% 1.74/2.02 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7331,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[7330])).
% 1.74/2.02 tff(7332,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[7331, 7329])).
% 1.74/2.02 tff(7333,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(7334,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[7333, 7332])).
% 1.74/2.02 tff(7335,plain,
% 1.74/2.02 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[7334, 192, 1242, 1745, 7203])).
% 1.74/2.02 tff(7336,plain,
% 1.74/2.02 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[4086, 60, 4083, 7335])).
% 1.74/2.02 tff(7337,plain,
% 1.74/2.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(7338,plain,
% 1.74/2.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.87/2.02 inference(quant_inst,[status(thm)],[])).
% 1.87/2.02 tff(7339,plain,
% 1.87/2.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.87/2.02 inference(modus_ponens,[status(thm)],[7338, 7337])).
% 1.87/2.02 tff(7340,plain,
% 1.87/2.02 ($false),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[7339, 77, 504, 7336, 7328])).
% 1.87/2.02 tff(7341,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.02 tff(7342,plain,
% 1.87/2.02 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[7341, 7304, 7320, 7318, 38, 7302])).
% 1.87/2.02 tff(7343,plain,
% 1.87/2.02 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[7201, 7342, 7176])).
% 1.87/2.02 tff(7344,plain,
% 1.87/2.02 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[7185, 77, 170, 7343])).
% 1.87/2.02 tff(7345,plain,
% 1.87/2.02 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.87/2.02 inference(unit_resolution,[status(thm)],[4466, 60, 4424, 7344])).
% 1.87/2.02 tff(7346,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.02 inference(rewrite,[status(thm)],[])).
% 1.87/2.02 tff(7347,plain,
% 1.87/2.02 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.02 inference(rewrite,[status(thm)],[])).
% 1.87/2.02 tff(7348,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.87/2.02 inference(monotonicity,[status(thm)],[7347])).
% 1.87/2.02 tff(7349,plain,
% 1.87/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7348, 7346])).
% 1.87/2.03 tff(7350,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(7351,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[7350, 7349])).
% 1.87/2.03 tff(7352,plain,
% 1.87/2.03 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7351, 192, 6957, 7306, 7345, 7258, 7300])).
% 1.87/2.03 tff(7353,plain,
% 1.87/2.03 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4436, 77, 7298, 7343])).
% 1.87/2.03 tff(7354,plain,
% 1.87/2.03 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4440, 60, 7353])).
% 1.87/2.03 tff(7355,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7354, 7352, 4432])).
% 1.87/2.03 tff(7356,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(7357,plain,
% 1.87/2.03 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7356, 38])).
% 1.87/2.03 tff(7358,plain,
% 1.87/2.03 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[181, 7357])).
% 1.87/2.03 tff(7359,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7360,plain,
% 1.87/2.03 (((~b(s(z), s(s(s(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))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(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))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7361,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[7360])).
% 1.87/2.03 tff(7362,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7361, 7359])).
% 1.87/2.03 tff(7363,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(7364,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[7363, 7362])).
% 1.87/2.03 tff(7365,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7364, 192, 7358, 512, 38, 6957])).
% 1.87/2.03 tff(7366,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(7367,plain,
% 1.87/2.03 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7366, 38])).
% 1.87/2.03 tff(7368,plain,
% 1.87/2.03 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[217, 7367])).
% 1.87/2.03 tff(7369,plain,
% 1.87/2.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7316, 116, 7368])).
% 1.87/2.03 tff(7370,plain,
% 1.87/2.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[390, 7369])).
% 1.87/2.03 tff(7371,plain,
% 1.87/2.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[149, 77, 7368, 116])).
% 1.87/2.03 tff(7372,plain,
% 1.87/2.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[406, 7371])).
% 1.87/2.03 tff(7373,plain,
% 1.87/2.03 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[404, 7372, 7358, 7370])).
% 1.87/2.03 tff(7374,plain,
% 1.87/2.03 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[133, 7373])).
% 1.87/2.03 tff(7375,plain,
% 1.87/2.03 (~b(s(z), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[6973, 7372, 38, 7370])).
% 1.87/2.03 tff(7376,plain,
% 1.87/2.03 (r(s(z), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[427, 7375])).
% 1.87/2.03 tff(7377,plain,
% 1.87/2.03 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[2531, 77, 7376, 7374])).
% 1.87/2.03 tff(7378,plain,
% 1.87/2.03 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7007, 7377])).
% 1.87/2.03 tff(7379,plain,
% 1.87/2.03 (~r(s(s(s(s(z)))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1072, 37, 7368])).
% 1.87/2.03 tff(7380,plain,
% 1.87/2.03 (b(s(s(s(s(z)))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[526, 7379])).
% 1.87/2.03 tff(7381,plain,
% 1.87/2.03 (~r(z, s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1572, 37, 7368])).
% 1.87/2.03 tff(7382,plain,
% 1.87/2.03 (b(z, s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[339, 7381])).
% 1.87/2.03 tff(7383,plain,
% 1.87/2.03 (~r(s(s(s(s(z)))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4660, 504, 7368])).
% 1.87/2.03 tff(7384,plain,
% 1.87/2.03 (b(s(s(s(s(z)))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[526, 7383])).
% 1.87/2.03 tff(7385,plain,
% 1.87/2.03 (~b(z, s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1753, 239, 7358, 1745])).
% 1.87/2.03 tff(7386,plain,
% 1.87/2.03 (r(z, s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[339, 7385])).
% 1.87/2.03 tff(7387,plain,
% 1.87/2.03 (~r(z, s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[1572, 7386, 7368])).
% 1.87/2.03 tff(7388,plain,
% 1.87/2.03 (b(z, s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[292, 7387])).
% 1.87/2.03 tff(7389,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7390,plain,
% 1.87/2.03 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7391,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[7390])).
% 1.87/2.03 tff(7392,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7391, 7389])).
% 1.87/2.03 tff(7393,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(7394,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[7393, 7392])).
% 1.87/2.03 tff(7395,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7394, 192, 7358, 7388, 38, 6957, 239])).
% 1.87/2.03 tff(7396,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(7397,plain,
% 1.87/2.03 (~b(s(s(s(s(s(z))))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7396, 7384, 38])).
% 1.87/2.03 tff(7398,plain,
% 1.87/2.03 (r(s(s(s(s(s(z))))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[271, 7397])).
% 1.87/2.03 tff(7399,plain,
% 1.87/2.03 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7070, 77, 504, 7398])).
% 1.87/2.03 tff(7400,plain,
% 1.87/2.03 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7007, 7399])).
% 1.87/2.03 tff(7401,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7402,plain,
% 1.87/2.03 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7403,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[7402])).
% 1.87/2.03 tff(7404,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7403, 7401])).
% 1.87/2.03 tff(7405,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(7406,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 1.87/2.03 tff(7407,plain,
% 1.87/2.03 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7406, 192, 7358, 7002, 395])).
% 1.87/2.03 tff(7408,plain,
% 1.87/2.03 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7407, 1408])).
% 1.87/2.03 tff(7409,plain,
% 1.87/2.03 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[375, 7408])).
% 1.87/2.03 tff(7410,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7411,plain,
% 1.87/2.03 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7412,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[7411])).
% 1.87/2.03 tff(7413,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7412, 7410])).
% 1.87/2.03 tff(7414,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.87/2.03 inference(quant_inst,[status(thm)],[])).
% 1.87/2.03 tff(7415,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.03 inference(modus_ponens,[status(thm)],[7414, 7413])).
% 1.87/2.03 tff(7416,plain,
% 1.87/2.03 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7415, 192, 465, 38, 395])).
% 1.87/2.03 tff(7417,plain,
% 1.87/2.03 (~b(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7416, 1408])).
% 1.87/2.03 tff(7418,plain,
% 1.87/2.03 (r(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[253, 7417])).
% 1.87/2.03 tff(7419,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[4694, 7418, 7409, 296])).
% 1.87/2.03 tff(7420,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(7421,plain,
% 1.87/2.03 (~b(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7420, 395, 465, 38, 7398, 7400])).
% 1.87/2.03 tff(7422,plain,
% 1.87/2.03 (r(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[920, 7421])).
% 1.87/2.03 tff(7423,plain,
% 1.87/2.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[149, 77, 7368, 7422])).
% 1.87/2.03 tff(7424,plain,
% 1.87/2.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[406, 7423])).
% 1.87/2.03 tff(7425,plain,
% 1.87/2.03 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[404, 7424, 7358, 395])).
% 1.87/2.03 tff(7426,plain,
% 1.87/2.03 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[133, 7425])).
% 1.87/2.03 tff(7427,plain,
% 1.87/2.03 (~r(z, s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[5178, 7426, 7398])).
% 1.87/2.03 tff(7428,plain,
% 1.87/2.03 (b(z, s(s(s(z))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[237, 7427])).
% 1.87/2.03 tff(7429,plain,
% 1.87/2.03 (~r(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[509, 7422, 504])).
% 1.87/2.03 tff(7430,plain,
% 1.87/2.03 (b(s(s(s(z))), z)),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[253, 7429])).
% 1.87/2.03 tff(7431,plain,
% 1.87/2.03 ($false),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7254, 192, 7430, 395, 7384, 7424, 7428])).
% 1.87/2.03 tff(7432,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.03 tff(7433,plain,
% 1.87/2.03 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7432, 465, 504, 38])).
% 1.87/2.03 tff(7434,plain,
% 1.87/2.03 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[390, 7433])).
% 1.87/2.03 tff(7435,plain,
% 1.87/2.03 (~r(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[7316, 7434, 7368])).
% 1.87/2.03 tff(7436,plain,
% 1.87/2.03 (b(s(s(s(z))), s(z))),
% 1.87/2.03 inference(unit_resolution,[status(thm)],[920, 7435])).
% 1.87/2.03 tff(7437,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7438,plain,
% 1.87/2.03 (((~b(s(z), s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(rewrite,[status(thm)],[])).
% 1.87/2.03 tff(7439,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.03 inference(monotonicity,[status(thm)],[7438])).
% 1.87/2.03 tff(7440,plain,
% 1.87/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.03 inference(transitivity,[status(thm)],[7439, 7437])).
% 1.87/2.03 tff(7441,plain,
% 1.87/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(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(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7442,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7441, 7440])).
% 1.87/2.04 tff(7443,plain,
% 1.87/2.04 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7442, 192, 7358, 38, 6957, 7436])).
% 1.87/2.04 tff(7444,plain,
% 1.87/2.04 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[133, 7443])).
% 1.87/2.04 tff(7445,plain,
% 1.87/2.04 (~r(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5178, 7444, 7398])).
% 1.87/2.04 tff(7446,plain,
% 1.87/2.04 (b(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[237, 7445])).
% 1.87/2.04 tff(7447,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7448,plain,
% 1.87/2.04 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7449,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7448])).
% 1.87/2.04 tff(7450,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[7449, 7447])).
% 1.87/2.04 tff(7451,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7452,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7451, 7450])).
% 1.87/2.04 tff(7453,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7452, 192, 465, 6957, 7002, 1408, 3527, 2638])).
% 1.87/2.04 tff(7454,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7455,plain,
% 1.87/2.04 (~b(s(z), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7454, 465, 7400, 7436, 7446])).
% 1.87/2.04 tff(7456,plain,
% 1.87/2.04 (r(s(z), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[427, 7455])).
% 1.87/2.04 tff(7457,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5641, 77, 67, 409, 408])).
% 1.87/2.04 tff(7458,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7459,plain,
% 1.87/2.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7458, 7456, 7368])).
% 1.87/2.04 tff(7460,plain,
% 1.87/2.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[406, 7459])).
% 1.87/2.04 tff(7461,plain,
% 1.87/2.04 (((~b(s(s(s(s(s(z))))), 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))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7462,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7461])).
% 1.87/2.04 tff(7463,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[7462, 7307])).
% 1.87/2.04 tff(7464,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), 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))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7465,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7464, 7463])).
% 1.87/2.04 tff(7466,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7465, 192, 6957, 7400, 7436])).
% 1.87/2.04 tff(7467,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[375, 7466])).
% 1.87/2.04 tff(7468,plain,
% 1.87/2.04 (~r(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4694, 7467, 7398])).
% 1.87/2.04 tff(7469,plain,
% 1.87/2.04 (b(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[253, 7468])).
% 1.87/2.04 tff(7470,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7471,plain,
% 1.87/2.04 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7472,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7471])).
% 1.87/2.04 tff(7473,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.87/2.04 inference(transitivity,[status(thm)],[7472, 7470])).
% 1.87/2.04 tff(7474,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7475,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7474, 7473])).
% 1.87/2.04 tff(7476,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7475, 192, 7469, 7384, 7460, 7446])).
% 1.87/2.04 tff(7477,plain,((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7478,plain,
% 1.87/2.04 (~b(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7477, 504, 38])).
% 1.87/2.04 tff(7479,plain,
% 1.87/2.04 (r(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[292, 7478])).
% 1.87/2.04 tff(7480,plain,
% 1.87/2.04 (~r(z, s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[1572, 7479, 7368])).
% 1.87/2.04 tff(7481,plain,
% 1.87/2.04 (b(z, s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[339, 7480])).
% 1.87/2.04 tff(7482,plain,
% 1.87/2.04 (~r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[507, 77, 504, 7127])).
% 1.87/2.04 tff(7483,plain,
% 1.87/2.04 (b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[920, 7482])).
% 1.87/2.04 tff(7484,plain,
% 1.87/2.04 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4692, 77, 7127, 296])).
% 1.87/2.04 tff(7485,plain,
% 1.87/2.04 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[375, 7484])).
% 1.87/2.04 tff(7486,plain,
% 1.87/2.04 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7070, 77, 504, 296])).
% 1.87/2.04 tff(7487,plain,
% 1.87/2.04 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[438, 60, 7486])).
% 1.87/2.04 tff(7488,plain,
% 1.87/2.04 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7487, 609])).
% 1.87/2.04 tff(7489,plain,
% 1.87/2.04 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7406, 192, 396, 7488, 395])).
% 1.87/2.04 tff(7490,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7489, 7485, 7483])).
% 1.87/2.04 tff(7491,plain,((~b(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))))), z)) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7492,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7491, 7481, 7358, 504, 7384, 7398])).
% 1.87/2.04 tff(7493,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[390, 7492])).
% 1.87/2.04 tff(7494,plain,
% 1.87/2.04 (~r(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7316, 7493, 7368])).
% 1.87/2.04 tff(7495,plain,
% 1.87/2.04 (b(s(s(s(z))), s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[920, 7494])).
% 1.87/2.04 tff(7496,plain,
% 1.87/2.04 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7442, 192, 7358, 38, 6957, 7495])).
% 1.87/2.04 tff(7497,plain,
% 1.87/2.04 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[133, 7496])).
% 1.87/2.04 tff(7498,plain,
% 1.87/2.04 (~r(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5178, 7497, 7398])).
% 1.87/2.04 tff(7499,plain,
% 1.87/2.04 (b(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[237, 7498])).
% 1.87/2.04 tff(7500,plain,
% 1.87/2.04 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7465, 192, 6957, 7400, 7495])).
% 1.87/2.04 tff(7501,plain,
% 1.87/2.04 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[375, 7500])).
% 1.87/2.04 tff(7502,plain,
% 1.87/2.04 (~r(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4694, 7501, 7398])).
% 1.87/2.04 tff(7503,plain,
% 1.87/2.04 (b(s(s(s(z))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[253, 7502])).
% 1.87/2.04 tff(7504,plain,
% 1.87/2.04 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~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)))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7505,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7504])).
% 1.87/2.04 tff(7506,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)))),
% 1.87/2.04 inference(transitivity,[status(thm)],[7505, 7470])).
% 1.87/2.04 tff(7507,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7508,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7507, 7506])).
% 1.87/2.04 tff(7509,plain,
% 1.87/2.04 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7508, 192, 7503, 7384, 7499])).
% 1.87/2.04 tff(7510,plain,
% 1.87/2.04 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[406, 7509])).
% 1.87/2.04 tff(7511,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4187, 77, 2280, 409, 117])).
% 1.87/2.04 tff(7512,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,[]))).
% 1.87/2.04 tff(7513,plain,
% 1.87/2.04 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7512, 7510, 7497])).
% 1.87/2.04 tff(7514,plain,
% 1.87/2.04 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[113, 7513])).
% 1.87/2.04 tff(7515,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4235, 192, 7358, 38, 7400, 7514])).
% 1.87/2.04 tff(7516,plain,((~r(s(z), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7517,plain,
% 1.87/2.04 (~r(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7516, 38])).
% 1.87/2.04 tff(7518,plain,
% 1.87/2.04 (b(s(z), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[351, 7517])).
% 1.87/2.04 tff(7519,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[346, 192, 7518, 7382, 38, 7380])).
% 1.87/2.04 tff(7520,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7521,plain,
% 1.87/2.04 (~r(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7520, 38])).
% 1.87/2.04 tff(7522,plain,
% 1.87/2.04 (b(z, s(z))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[292, 7521])).
% 1.87/2.04 tff(7523,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7524,plain,
% 1.87/2.04 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7525,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7524])).
% 1.87/2.04 tff(7526,plain,
% 1.87/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.87/2.04 inference(transitivity,[status(thm)],[7525, 7523])).
% 1.87/2.04 tff(7527,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 1.87/2.04 inference(quant_inst,[status(thm)],[])).
% 1.87/2.04 tff(7528,plain,
% 1.87/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.87/2.04 inference(modus_ponens,[status(thm)],[7527, 7526])).
% 1.87/2.04 tff(7529,plain,
% 1.87/2.04 (~b(z, s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7528, 192, 7518, 7522, 6957, 7378])).
% 1.87/2.04 tff(7530,plain,
% 1.87/2.04 (r(z, s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[493, 7529])).
% 1.87/2.04 tff(7531,plain,
% 1.87/2.04 ($false),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[4235, 192, 7358, 38, 7002, 441])).
% 1.87/2.04 tff(7532,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.04 tff(7533,plain,
% 1.87/2.04 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7532, 7378, 38])).
% 1.87/2.04 tff(7534,plain,
% 1.87/2.04 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[113, 7533])).
% 1.87/2.04 tff(7535,plain,
% 1.87/2.04 (~b(s(s(s(s(s(z))))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[6993, 7522, 7518])).
% 1.87/2.04 tff(7536,plain,
% 1.87/2.04 (r(s(s(s(s(s(z))))), z)),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[271, 7535])).
% 1.87/2.04 tff(7537,plain,
% 1.87/2.04 (~r(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[5178, 7374, 7536])).
% 1.87/2.04 tff(7538,plain,
% 1.87/2.04 (b(z, s(s(s(z))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[237, 7537])).
% 1.87/2.04 tff(7539,plain,
% 1.87/2.04 (~b(z, s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[7088, 7538, 7370, 7372])).
% 1.87/2.04 tff(7540,plain,
% 1.87/2.04 (r(z, s(s(s(s(z)))))),
% 1.87/2.04 inference(unit_resolution,[status(thm)],[339, 7539])).
% 1.87/2.04 tff(7541,plain,
% 1.87/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7542,plain,
% 1.87/2.04 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.87/2.04 inference(rewrite,[status(thm)],[])).
% 1.87/2.04 tff(7543,plain,
% 1.87/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.87/2.04 inference(monotonicity,[status(thm)],[7542])).
% 1.87/2.04 tff(7544,plain,
% 1.87/2.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7543, 7541])).
% 1.87/2.05 tff(7545,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7546,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 1.87/2.05 tff(7547,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7546, 77, 7540, 7534, 7530])).
% 1.87/2.05 tff(7548,plain,((~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7549,plain,
% 1.87/2.05 (~r(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7548, 38])).
% 1.87/2.05 tff(7550,plain,
% 1.87/2.05 (b(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[920, 7549])).
% 1.87/2.05 tff(7551,plain,
% 1.87/2.05 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7442, 192, 7358, 38, 6957, 7550])).
% 1.87/2.05 tff(7552,plain,
% 1.87/2.05 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[133, 7551])).
% 1.87/2.05 tff(7553,plain,
% 1.87/2.05 (~b(s(s(s(z))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[935, 192, 7518, 7522, 7550])).
% 1.87/2.05 tff(7554,plain,
% 1.87/2.05 (r(s(s(s(z))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[253, 7553])).
% 1.87/2.05 tff(7555,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4755, 77, 7554, 7536, 7552])).
% 1.87/2.05 tff(7556,plain,(~b(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7557,plain,
% 1.87/2.05 (r(s(z), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[319, 7556])).
% 1.87/2.05 tff(7558,plain,
% 1.87/2.05 ((~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4038, 7557])).
% 1.87/2.05 tff(7559,plain,
% 1.87/2.05 (~r(z, s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7558, 37])).
% 1.87/2.05 tff(7560,plain,
% 1.87/2.05 (b(z, s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[339, 7559])).
% 1.87/2.05 tff(7561,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7562,plain,
% 1.87/2.05 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7563,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[7562])).
% 1.87/2.05 tff(7564,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7563, 7561])).
% 1.87/2.05 tff(7565,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7566,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7565, 7564])).
% 1.87/2.05 tff(7567,plain,
% 1.87/2.05 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7566, 77, 7557, 4077])).
% 1.87/2.05 tff(7568,plain,
% 1.87/2.05 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7219, 60, 7216, 7567])).
% 1.87/2.05 tff(7569,plain,
% 1.87/2.05 ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[627, 7557])).
% 1.87/2.05 tff(7570,plain,
% 1.87/2.05 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7569, 170])).
% 1.87/2.05 tff(7571,plain,
% 1.87/2.05 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7007, 7570])).
% 1.87/2.05 tff(7572,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7573,plain,
% 1.87/2.05 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7574,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[7573])).
% 1.87/2.05 tff(7575,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7574, 7572])).
% 1.87/2.05 tff(7576,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7577,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7576, 7575])).
% 1.87/2.05 tff(7578,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7577, 192, 6957, 7571, 7187, 7568])).
% 1.87/2.05 tff(7579,plain,((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7580,plain,
% 1.87/2.05 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7579, 170])).
% 1.87/2.05 tff(7581,plain,
% 1.87/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7201, 7176])).
% 1.87/2.05 tff(7582,plain,
% 1.87/2.05 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7581, 7580])).
% 1.87/2.05 tff(7583,plain,
% 1.87/2.05 (~r(s(z), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4718, 383, 308])).
% 1.87/2.05 tff(7584,plain,
% 1.87/2.05 (b(s(z), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[427, 7583])).
% 1.87/2.05 tff(7585,plain,
% 1.87/2.05 (~r(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[388, 383, 308])).
% 1.87/2.05 tff(7586,plain,
% 1.87/2.05 (b(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[920, 7585])).
% 1.87/2.05 tff(7587,plain,
% 1.87/2.05 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[627, 170, 308])).
% 1.87/2.05 tff(7588,plain,
% 1.87/2.05 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[438, 60, 7587, 380])).
% 1.87/2.05 tff(7589,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7590,plain,
% 1.87/2.05 (((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7591,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(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(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[7590])).
% 1.87/2.05 tff(7592,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(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(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7591, 7589])).
% 1.87/2.05 tff(7593,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7594,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 1.87/2.05 tff(7595,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7594, 192, 6957, 7588, 7586, 7584, 2010])).
% 1.87/2.05 tff(7596,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7597,plain,
% 1.87/2.05 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7596, 7557])).
% 1.87/2.05 tff(7598,plain,
% 1.87/2.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7597, 170])).
% 1.87/2.05 tff(7599,plain,
% 1.87/2.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[390, 7598])).
% 1.87/2.05 tff(7600,plain,
% 1.87/2.05 (~b(z, s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7088, 5227, 395, 1242])).
% 1.87/2.05 tff(7601,plain,
% 1.87/2.05 (r(z, s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[237, 7600])).
% 1.87/2.05 tff(7602,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7156, 77, 37, 408, 7601])).
% 1.87/2.05 tff(7603,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7604,plain,
% 1.87/2.05 ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7603, 7557])).
% 1.87/2.05 tff(7605,plain,
% 1.87/2.05 (~r(s(z), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7604, 7599, 37, 7560])).
% 1.87/2.05 tff(7606,plain,
% 1.87/2.05 (b(s(z), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[427, 7605])).
% 1.87/2.05 tff(7607,plain,
% 1.87/2.05 (~r(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7104, 7599, 37, 170, 7560])).
% 1.87/2.05 tff(7608,plain,
% 1.87/2.05 (b(s(s(s(z))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[920, 7607])).
% 1.87/2.05 tff(7609,plain,
% 1.87/2.05 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6985, 7606, 7608])).
% 1.87/2.05 tff(7610,plain,
% 1.87/2.05 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[133, 7609])).
% 1.87/2.05 tff(7611,plain,
% 1.87/2.05 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[6964, 7610, 170])).
% 1.87/2.05 tff(7612,plain,
% 1.87/2.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[406, 7611])).
% 1.87/2.05 tff(7613,plain,
% 1.87/2.05 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7614,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[7613])).
% 1.87/2.05 tff(7615,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7614, 6894])).
% 1.87/2.05 tff(7616,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7617,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(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)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7616, 7615])).
% 1.87/2.05 tff(7618,plain,
% 1.87/2.05 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7617, 192, 7608, 7612, 7606])).
% 1.87/2.05 tff(7619,plain,
% 1.87/2.05 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[217, 7618])).
% 1.87/2.05 tff(7620,plain,
% 1.87/2.05 (~r(s(s(s(s(z)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[2505, 7619, 170])).
% 1.87/2.05 tff(7621,plain,
% 1.87/2.05 (b(s(s(s(s(z)))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[526, 7620])).
% 1.87/2.05 tff(7622,plain,
% 1.87/2.05 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7334, 192, 7560, 7621, 7582])).
% 1.87/2.05 tff(7623,plain,
% 1.87/2.05 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4086, 60, 4083, 7622])).
% 1.87/2.05 tff(7624,plain,
% 1.87/2.05 (~b(s(s(s(z))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7102, 192, 7560, 7599, 7621])).
% 1.87/2.05 tff(7625,plain,
% 1.87/2.05 (r(s(s(s(z))), z)),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[253, 7624])).
% 1.87/2.05 tff(7626,plain,
% 1.87/2.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7627,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7628,plain,
% 1.87/2.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7627, 7626])).
% 1.87/2.05 tff(7629,plain,
% 1.87/2.05 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7628, 77, 7625, 7623])).
% 1.87/2.05 tff(7630,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7631,plain,
% 1.87/2.05 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.05 inference(rewrite,[status(thm)],[])).
% 1.87/2.05 tff(7632,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.87/2.05 inference(monotonicity,[status(thm)],[7631])).
% 1.87/2.05 tff(7633,plain,
% 1.87/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.87/2.05 inference(transitivity,[status(thm)],[7632, 7630])).
% 1.87/2.05 tff(7634,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.87/2.05 inference(quant_inst,[status(thm)],[])).
% 1.87/2.05 tff(7635,plain,
% 1.87/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.87/2.05 inference(modus_ponens,[status(thm)],[7634, 7633])).
% 1.87/2.05 tff(7636,plain,
% 1.87/2.05 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7635, 192, 7560, 7599, 7621, 7612, 7582])).
% 1.87/2.05 tff(7637,plain,
% 1.87/2.05 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[4440, 60, 7636])).
% 1.87/2.05 tff(7638,plain,
% 1.87/2.05 ($false),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7637, 7629, 4432])).
% 1.87/2.05 tff(7639,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.05 tff(7640,plain,
% 1.87/2.05 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.05 inference(unit_resolution,[status(thm)],[7639, 37])).
% 1.87/2.06 tff(7641,plain,
% 1.87/2.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[181, 7640])).
% 1.87/2.06 tff(7642,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.87/2.06 tff(7643,plain,
% 1.87/2.06 (b(s(s(s(s(z)))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[217, 7642])).
% 1.87/2.06 tff(7644,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7645,plain,
% 1.87/2.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7646,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7645])).
% 1.87/2.06 tff(7647,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[7646, 7644])).
% 1.87/2.06 tff(7648,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(7649,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), 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(z)))), s(z)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 1.87/2.06 tff(7650,plain,
% 1.87/2.06 (~b(s(s(s(s(s(z))))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7649, 192, 7641, 7560, 7643, 6957])).
% 1.87/2.06 tff(7651,plain,
% 1.87/2.06 (r(s(s(s(s(s(z))))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[271, 7650])).
% 1.87/2.06 tff(7652,plain,
% 1.87/2.06 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[388, 7557])).
% 1.87/2.06 tff(7653,plain,
% 1.87/2.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7652, 116])).
% 1.87/2.06 tff(7654,plain,
% 1.87/2.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[390, 7653])).
% 1.87/2.06 tff(7655,plain,
% 1.87/2.06 (~r(s(z), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7604, 7654, 37, 7560])).
% 1.87/2.06 tff(7656,plain,
% 1.87/2.06 (b(s(z), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[427, 7655])).
% 1.87/2.06 tff(7657,plain,
% 1.87/2.06 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7658,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7657])).
% 1.87/2.06 tff(7659,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[7658, 2518])).
% 1.87/2.06 tff(7660,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(7661,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[7660, 7659])).
% 1.87/2.06 tff(7662,plain,
% 1.87/2.06 ($false),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7661, 192, 515, 2639, 3527, 2638])).
% 1.87/2.06 tff(7663,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.06 tff(7664,plain,
% 1.87/2.06 (~b(s(z), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7663, 254, 7656, 238])).
% 1.87/2.06 tff(7665,plain,
% 1.87/2.06 (r(s(z), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[351, 7664])).
% 1.87/2.06 tff(7666,plain,
% 1.87/2.06 (~b(s(s(s(s(s(z))))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[4029, 504, 308, 396])).
% 1.87/2.06 tff(7667,plain,
% 1.87/2.06 (r(s(s(s(s(s(z))))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[271, 7666])).
% 1.87/2.06 tff(7668,plain,
% 1.87/2.06 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(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))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7669,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7668])).
% 1.87/2.06 tff(7670,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[7669, 6978])).
% 1.87/2.06 tff(7671,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(7672,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(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)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[7671, 7670])).
% 1.87/2.06 tff(7673,plain,
% 1.87/2.06 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7672, 192, 6957, 7586, 7584])).
% 1.87/2.06 tff(7674,plain,
% 1.87/2.06 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[133, 7673])).
% 1.87/2.06 tff(7675,plain,
% 1.87/2.06 (~r(z, s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5178, 7674, 7667])).
% 1.87/2.06 tff(7676,plain,
% 1.87/2.06 (b(z, s(s(s(z))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[237, 7675])).
% 1.87/2.06 tff(7677,plain,
% 1.87/2.06 (~b(z, s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[4048, 441, 396, 1242])).
% 1.87/2.06 tff(7678,plain,
% 1.87/2.06 (r(z, s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[493, 7677])).
% 1.87/2.06 tff(7679,plain,
% 1.87/2.06 (~r(s(z), s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7010, 7678, 504])).
% 1.87/2.06 tff(7680,plain,
% 1.87/2.06 (b(s(z), s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7007, 7679])).
% 1.87/2.06 tff(7681,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7682,plain,
% 1.87/2.06 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7683,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7682])).
% 1.87/2.06 tff(7684,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[7683, 7681])).
% 1.87/2.06 tff(7685,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(7686,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[7685, 7684])).
% 1.87/2.06 tff(7687,plain,
% 1.87/2.06 (~b(s(s(s(s(z)))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7686, 192, 6957, 7680, 441])).
% 1.87/2.06 tff(7688,plain,
% 1.87/2.06 (~b(z, s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[4652, 192, 7586, 7584, 7676])).
% 1.87/2.06 tff(7689,plain,
% 1.87/2.06 (r(z, s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[292, 7688])).
% 1.87/2.06 tff(7690,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.87/2.06 tff(7691,plain,
% 1.87/2.06 (~r(s(s(s(s(s(z))))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[2633, 504, 296])).
% 1.87/2.06 tff(7692,plain,
% 1.87/2.06 (b(s(s(s(s(s(z))))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[65, 7691])).
% 1.87/2.06 tff(7693,plain,
% 1.87/2.06 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[7465, 192, 7692, 7488, 7586])).
% 1.87/2.06 tff(7694,plain,
% 1.87/2.06 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[375, 7693])).
% 1.87/2.06 tff(7695,plain,
% 1.87/2.06 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[217, 7690])).
% 1.87/2.06 tff(7696,plain,
% 1.87/2.06 (~r(s(s(s(s(z)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1072, 7695, 37])).
% 1.87/2.06 tff(7697,plain,
% 1.87/2.06 (b(s(s(s(s(z)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[526, 7696])).
% 1.87/2.06 tff(7698,plain,
% 1.87/2.06 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.87/2.06 inference(commutativity,[status(thm)],[])).
% 1.87/2.06 tff(7699,plain,
% 1.87/2.06 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[7698])).
% 1.87/2.06 tff(7700,plain,
% 1.87/2.06 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7699])).
% 1.87/2.06 tff(7701,plain,
% 1.87/2.06 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[1159])).
% 1.87/2.06 tff(7702,plain,
% 1.87/2.06 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(s(s(s(z)))))) = s(z)))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7701])).
% 1.87/2.06 tff(7703,plain,
% 1.87/2.06 (~(s(s(s(s(s(s(z)))))) = s(z))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[1307, 7702])).
% 1.87/2.06 tff(7704,plain,
% 1.87/2.06 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[7703, 7700])).
% 1.87/2.06 tff(7705,plain,
% 1.87/2.06 (~r(z, s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[3745, 1146, 3742])).
% 1.87/2.06 tff(7706,plain,
% 1.87/2.06 (b(z, s(elem!1))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[580, 7705])).
% 1.87/2.06 tff(7707,plain,
% 1.87/2.06 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[2472])).
% 1.87/2.06 tff(7708,plain,
% 1.87/2.06 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[2474])).
% 1.87/2.06 tff(7709,plain,
% 1.87/2.06 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.87/2.06 inference(symmetry,[status(thm)],[7708])).
% 1.87/2.06 tff(7710,plain,
% 1.87/2.06 (b(elem!1, s(z))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[1408, 7709])).
% 1.87/2.06 tff(7711,plain,
% 1.87/2.06 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[2474])).
% 1.87/2.06 tff(7712,plain,
% 1.87/2.06 (b(s(z), s(s(s(z)))) <=> b(s(z), elem!1)),
% 1.87/2.06 inference(symmetry,[status(thm)],[7711])).
% 1.87/2.06 tff(7713,plain,
% 1.87/2.06 (b(s(z), elem!1)),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[3527, 7712])).
% 1.87/2.06 tff(7714,plain,
% 1.87/2.06 (b(z, s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[339, 3742])).
% 1.87/2.06 tff(7715,plain,
% 1.87/2.06 ((s(s(s(elem!1))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[1345])).
% 1.87/2.06 tff(7716,plain,
% 1.87/2.06 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.87/2.06 inference(symmetry,[status(thm)],[7715])).
% 1.87/2.06 tff(7717,plain,
% 1.87/2.06 ((~(s(s(s(elem!1))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(s(z))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7716])).
% 1.87/2.06 tff(7718,plain,
% 1.87/2.06 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.87/2.06 inference(modus_ponens,[status(thm)],[2548, 7717])).
% 1.87/2.06 tff(7719,plain,
% 1.87/2.06 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[5564, 77, 67, 667])).
% 1.87/2.06 tff(7720,assumption,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.06 tff(7721,plain,
% 1.87/2.06 (~r(s(s(s(s(z)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[1072, 37, 67])).
% 1.87/2.06 tff(7722,plain,
% 1.87/2.06 (b(s(s(s(s(z)))), z)),
% 1.87/2.06 inference(unit_resolution,[status(thm)],[526, 7721])).
% 1.87/2.06 tff(7723,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7724,plain,
% 1.87/2.06 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.06 inference(rewrite,[status(thm)],[])).
% 1.87/2.06 tff(7725,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.87/2.06 inference(monotonicity,[status(thm)],[7724])).
% 1.87/2.06 tff(7726,plain,
% 1.87/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.06 inference(transitivity,[status(thm)],[7725, 7723])).
% 1.87/2.06 tff(7727,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)))),
% 1.87/2.06 inference(quant_inst,[status(thm)],[])).
% 1.87/2.06 tff(7728,plain,
% 1.87/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7727, 7726])).
% 1.87/2.07 tff(7729,plain,
% 1.87/2.07 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7728, 192, 4273, 1242, 7722])).
% 1.87/2.07 tff(7730,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1396, 60, 7729, 7720, 7719])).
% 1.87/2.07 tff(7731,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(7732,plain,
% 1.87/2.07 (~r(s(s(s(elem!1))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7731, 7718, 7714, 37, 67])).
% 1.87/2.07 tff(7733,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1313, 7732])).
% 1.87/2.07 tff(7734,plain,
% 1.87/2.07 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2294, 7733, 7713, 7710])).
% 1.87/2.07 tff(7735,plain,
% 1.87/2.07 (r(s(s(s(elem!1))), elem!1)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1628, 7734, 2471])).
% 1.87/2.07 tff(7736,plain,
% 1.87/2.07 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7735, 7707])).
% 1.87/2.07 tff(7737,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 1.87/2.07 tff(7738,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7739,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7740,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7739, 7738])).
% 1.87/2.07 tff(7741,plain,
% 1.87/2.07 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7740, 77, 383, 7737])).
% 1.87/2.07 tff(7742,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7741, 1348])).
% 1.87/2.07 tff(7743,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(7744,plain,
% 1.87/2.07 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7743, 1146, 383, 7736])).
% 1.87/2.07 tff(7745,plain,
% 1.87/2.07 (b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[679, 7744, 2548])).
% 1.87/2.07 tff(7746,plain,
% 1.87/2.07 (~b(s(s(s(elem!1))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1931, 7745, 583, 7706])).
% 1.87/2.07 tff(7747,plain,
% 1.87/2.07 (~b(s(s(s(s(s(s(z)))))), z)),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7746, 3980])).
% 1.87/2.07 tff(7748,plain,
% 1.87/2.07 (r(s(s(s(s(s(s(z)))))), z)),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[1782, 60, 1779, 7747])).
% 1.87/2.07 tff(7749,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7750,plain,
% 1.87/2.07 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7751,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7750])).
% 1.87/2.07 tff(7752,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[7751, 7749])).
% 1.87/2.07 tff(7753,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7754,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7753, 7752])).
% 1.87/2.07 tff(7755,plain,
% 1.87/2.07 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7754, 77, 504, 7748])).
% 1.87/2.07 tff(7756,plain,
% 1.87/2.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7757,plain,
% 1.87/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7758,plain,
% 1.87/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7757, 7756])).
% 1.87/2.07 tff(7759,plain,
% 1.87/2.07 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7758, 60, 7755])).
% 1.87/2.07 tff(7760,plain,
% 1.87/2.07 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7759, 7704])).
% 1.87/2.07 tff(7761,plain,
% 1.87/2.07 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7733, 3378])).
% 1.87/2.07 tff(7762,plain,
% 1.87/2.07 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7672, 192, 2490, 1408, 3527])).
% 1.87/2.07 tff(7763,plain,
% 1.87/2.07 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[133, 7762])).
% 1.87/2.07 tff(7764,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7765,plain,
% 1.87/2.07 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7766,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7765])).
% 1.87/2.07 tff(7767,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[7766, 7764])).
% 1.87/2.07 tff(7768,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7769,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 1.87/2.07 tff(7770,plain,
% 1.87/2.07 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7769, 77, 7763])).
% 1.87/2.07 tff(7771,plain,
% 1.87/2.07 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7770, 7736])).
% 1.87/2.07 tff(7772,plain,
% 1.87/2.07 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[5120, 60, 7771])).
% 1.87/2.07 tff(7773,plain,
% 1.87/2.07 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7772, 5110])).
% 1.87/2.07 tff(7774,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7775,plain,
% 1.87/2.07 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(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(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7776,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7775])).
% 1.87/2.07 tff(7777,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[7776, 7774])).
% 1.87/2.07 tff(7778,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7779,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7778, 7777])).
% 1.87/2.07 tff(7780,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7779, 192, 2490, 7773, 7761, 7760])).
% 1.87/2.07 tff(7781,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(s(elem!1), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(7782,plain,
% 1.87/2.07 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7781, 383, 504, 583, 7692, 37, 7695, 7586, 7584, 5723])).
% 1.87/2.07 tff(7783,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7784,plain,
% 1.87/2.07 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7785,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7784])).
% 1.87/2.07 tff(7786,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.07 inference(transitivity,[status(thm)],[7785, 7783])).
% 1.87/2.07 tff(7787,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(elem!1), z)))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7788,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7787, 7786])).
% 1.87/2.07 tff(7789,plain,
% 1.87/2.07 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7788, 192, 583, 5724, 1745])).
% 1.87/2.07 tff(7790,plain,
% 1.87/2.07 (r(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[535, 528, 7789])).
% 1.87/2.07 tff(7791,plain,
% 1.87/2.07 (~r(s(elem!1), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[3506, 77, 7790, 383])).
% 1.87/2.07 tff(7792,plain,
% 1.87/2.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7793,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7794,plain,
% 1.87/2.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z)))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7793, 7792])).
% 1.87/2.07 tff(7795,plain,
% 1.87/2.07 ($false),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7794, 77, 537, 668, 308])).
% 1.87/2.07 tff(7796,plain,((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.07 tff(7797,plain,
% 1.87/2.07 (~r(s(elem!1), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7796, 7790, 308])).
% 1.87/2.07 tff(7798,plain,
% 1.87/2.07 (b(s(elem!1), s(z))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[950, 7797, 115])).
% 1.87/2.07 tff(7799,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7800,plain,
% 1.87/2.07 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.87/2.07 inference(rewrite,[status(thm)],[])).
% 1.87/2.07 tff(7801,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7800])).
% 1.87/2.07 tff(7802,plain,
% 1.87/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.87/2.07 inference(transitivity,[status(thm)],[7801, 7799])).
% 1.87/2.07 tff(7803,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))))),
% 1.87/2.07 inference(quant_inst,[status(thm)],[])).
% 1.87/2.07 tff(7804,plain,
% 1.87/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.87/2.07 inference(modus_ponens,[status(thm)],[7803, 7802])).
% 1.87/2.07 tff(7805,plain,
% 1.87/2.07 ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7804, 192, 583, 2639, 7584])).
% 1.87/2.07 tff(7806,plain,
% 1.87/2.07 (~b(s(elem!1), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7805, 7798])).
% 1.87/2.07 tff(7807,plain,
% 1.87/2.07 (s(elem!1) = s(s(s(z)))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[2148, 60, 7806, 7791])).
% 1.87/2.07 tff(7808,plain,
% 1.87/2.07 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7807])).
% 1.87/2.07 tff(7809,plain,
% 1.87/2.07 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.87/2.07 inference(symmetry,[status(thm)],[7808])).
% 1.87/2.07 tff(7810,plain,
% 1.87/2.07 (s(s(z)) = elem!1),
% 1.87/2.07 inference(transitivity,[status(thm)],[16, 7809, 682])).
% 1.87/2.07 tff(7811,plain,
% 1.87/2.07 (b(s(s(z)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7810])).
% 1.87/2.07 tff(7812,plain,
% 1.87/2.07 (b(elem!1, s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.87/2.07 inference(symmetry,[status(thm)],[7811])).
% 1.87/2.07 tff(7813,plain,
% 1.87/2.07 (r(s(s(z)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7810])).
% 1.87/2.07 tff(7814,plain,
% 1.87/2.07 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7813])).
% 1.87/2.07 tff(7815,plain,
% 1.87/2.07 (elem!1 = s(s(z))),
% 1.87/2.07 inference(transitivity,[status(thm)],[695, 7808, 15])).
% 1.87/2.07 tff(7816,plain,
% 1.87/2.07 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7815])).
% 1.87/2.07 tff(7817,plain,
% 1.87/2.07 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7815])).
% 1.87/2.07 tff(7818,plain,
% 1.87/2.07 (b(s(s(z)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.87/2.07 inference(symmetry,[status(thm)],[7817])).
% 1.87/2.07 tff(7819,plain,
% 1.87/2.07 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.87/2.07 inference(monotonicity,[status(thm)],[7818])).
% 1.87/2.07 tff(7820,plain,
% 1.87/2.07 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[7672, 192, 7692, 7586, 7584])).
% 1.87/2.07 tff(7821,plain,
% 1.87/2.07 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.87/2.07 inference(unit_resolution,[status(thm)],[133, 7820])).
% 1.87/2.07 tff(7822,plain,
% 1.87/2.07 (b(s(s(s(s(z)))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7807])).
% 1.87/2.08 tff(7823,plain,
% 1.87/2.08 ((~b(s(s(s(s(z)))), s(elem!1))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7822])).
% 1.87/2.08 tff(7824,plain,
% 1.87/2.08 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[3745, 562, 3742])).
% 1.87/2.08 tff(7825,plain,
% 1.87/2.08 (r(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[535, 7824, 531])).
% 1.87/2.08 tff(7826,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7827,plain,
% 1.87/2.08 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7828,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7827])).
% 1.87/2.08 tff(7829,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7828, 7826])).
% 1.87/2.08 tff(7830,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7831,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7830, 7829])).
% 1.87/2.08 tff(7832,plain,
% 1.87/2.08 (~r(s(z), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7831, 77, 7825, 308])).
% 1.87/2.08 tff(7833,plain,
% 1.87/2.08 (b(s(z), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[658, 7832, 651])).
% 1.87/2.08 tff(7834,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7835,plain,
% 1.87/2.08 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7836,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7835])).
% 1.87/2.08 tff(7837,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7836, 7834])).
% 1.87/2.08 tff(7838,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~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(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7839,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7838, 7837])).
% 1.87/2.08 tff(7840,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7839, 192, 953, 582, 2490, 641])).
% 1.87/2.08 tff(7841,plain,((~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(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(7842,plain,
% 1.87/2.08 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7841, 7833, 2490, 953])).
% 1.87/2.08 tff(7843,plain,
% 1.87/2.08 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[597, 7842, 815])).
% 1.87/2.08 tff(7844,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7845,plain,
% 1.87/2.08 (((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7846,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7845])).
% 1.87/2.08 tff(7847,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7846, 7844])).
% 1.87/2.08 tff(7848,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7849,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7848, 7847])).
% 1.87/2.08 tff(7850,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7849, 77, 562, 7843, 296])).
% 1.87/2.08 tff(7851,plain,((~r(z, s(elem!1))) | (~r(s(s(s(s(s(z))))), z)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (s(z) = s(elem!1)) | (~r(s(z), s(s(s(s(z)))))) | b(s(elem!1), s(s(s(s(z))))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(7852,plain,
% 1.87/2.08 (~r(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7851, 7798, 7692, 815, 296, 639, 308, 7789, 5723])).
% 1.87/2.08 tff(7853,plain,
% 1.87/2.08 (b(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[580, 7852])).
% 1.87/2.08 tff(7854,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7855,plain,
% 1.87/2.08 (((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7856,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7855])).
% 1.87/2.08 tff(7857,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7856, 7854])).
% 1.87/2.08 tff(7858,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7859,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 1.87/2.08 tff(7860,plain,
% 1.87/2.08 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7859, 192, 7853, 583, 1745])).
% 1.87/2.08 tff(7861,plain,
% 1.87/2.08 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7860, 7823])).
% 1.87/2.08 tff(7862,plain,
% 1.87/2.08 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[406, 7861])).
% 1.87/2.08 tff(7863,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[4187, 77, 7862, 7821])).
% 1.87/2.08 tff(7864,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[111, 60, 7863, 106])).
% 1.87/2.08 tff(7865,plain,
% 1.87/2.08 (~r(s(s(s(s(s(z))))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[2633, 296, 504])).
% 1.87/2.08 tff(7866,plain,
% 1.87/2.08 (b(s(s(s(s(s(z))))), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[65, 7865])).
% 1.87/2.08 tff(7867,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 1.87/2.08 tff(7868,plain,
% 1.87/2.08 (b(s(elem!1), s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[950, 7867, 115])).
% 1.87/2.08 tff(7869,plain,
% 1.87/2.08 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[1985])).
% 1.87/2.08 tff(7870,plain,
% 1.87/2.08 (~b(s(elem!1), s(z))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7690, 7869])).
% 1.87/2.08 tff(7871,plain,
% 1.87/2.08 ($false),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[953, 7870])).
% 1.87/2.08 tff(7872,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~b(s(elem!1), s(z))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.08 tff(7873,plain,
% 1.87/2.08 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7872, 7868, 7690])).
% 1.87/2.08 tff(7874,plain,
% 1.87/2.08 (r(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[535, 7873, 531])).
% 1.87/2.08 tff(7875,plain,
% 1.87/2.08 (~r(s(z), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7831, 77, 7874, 308])).
% 1.87/2.08 tff(7876,plain,
% 1.87/2.08 (b(s(z), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[658, 7875, 639])).
% 1.87/2.08 tff(7877,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7878,plain,
% 1.87/2.08 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7879,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7878])).
% 1.87/2.08 tff(7880,plain,
% 1.87/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7879, 7877])).
% 1.87/2.08 tff(7881,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7882,plain,
% 1.87/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7881, 7880])).
% 1.87/2.08 tff(7883,plain,
% 1.87/2.08 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7882, 192, 7868, 7866, 7488, 7876])).
% 1.87/2.08 tff(7884,plain,
% 1.87/2.08 (~r(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7851, 7868, 815, 7866, 296, 639, 308, 531, 4018])).
% 1.87/2.08 tff(7885,plain,
% 1.87/2.08 (b(z, s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[580, 7884])).
% 1.87/2.08 tff(7886,plain,
% 1.87/2.08 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1931, 7885, 583, 1005])).
% 1.87/2.08 tff(7887,plain,
% 1.87/2.08 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7841, 7876, 7866, 7868])).
% 1.87/2.08 tff(7888,plain,
% 1.87/2.08 (r(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[597, 7887, 815])).
% 1.87/2.08 tff(7889,plain,
% 1.87/2.08 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[543, 7888, 7874])).
% 1.87/2.08 tff(7890,plain,
% 1.87/2.08 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[181, 7889])).
% 1.87/2.08 tff(7891,plain,
% 1.87/2.08 (~b(z, s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[971, 192, 7885, 7868, 7876])).
% 1.87/2.08 tff(7892,plain,
% 1.87/2.08 (r(z, s(z))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[292, 7891])).
% 1.87/2.08 tff(7893,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[1072, 7892, 7695])).
% 1.87/2.08 tff(7894,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), z)),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[526, 7893])).
% 1.87/2.08 tff(7895,plain,
% 1.87/2.08 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7859, 192, 7885, 583, 7894])).
% 1.87/2.08 tff(7896,plain,
% 1.87/2.08 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7873, 1341])).
% 1.87/2.08 tff(7897,plain,
% 1.87/2.08 (r(s(s(s(s(z)))), s(elem!1))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[772, 60, 7896, 7895])).
% 1.87/2.08 tff(7898,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7899,plain,
% 1.87/2.08 (((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(rewrite,[status(thm)],[])).
% 1.87/2.08 tff(7900,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7899])).
% 1.87/2.08 tff(7901,plain,
% 1.87/2.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7900, 7898])).
% 1.87/2.08 tff(7902,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.87/2.08 inference(quant_inst,[status(thm)],[])).
% 1.87/2.08 tff(7903,plain,
% 1.87/2.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[7902, 7901])).
% 1.87/2.08 tff(7904,plain,
% 1.87/2.08 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[7903, 77, 7888, 7897])).
% 1.87/2.08 tff(7905,plain,
% 1.87/2.08 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(unit_resolution,[status(thm)],[111, 60, 7904, 106])).
% 1.87/2.08 tff(7906,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 1.87/2.08 tff(7907,plain,
% 1.87/2.08 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7906])).
% 1.87/2.08 tff(7908,plain,
% 1.87/2.08 (s(s(elem!1)) = s(s(s(z)))),
% 1.87/2.08 inference(transitivity,[status(thm)],[1035, 7907, 91])).
% 1.87/2.08 tff(7909,plain,
% 1.87/2.08 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7908])).
% 1.87/2.08 tff(7910,plain,
% 1.87/2.08 (s(elem!1) = s(s(z))),
% 1.87/2.08 inference(transitivity,[status(thm)],[1047, 7909, 15])).
% 1.87/2.08 tff(7911,plain,
% 1.87/2.08 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7910])).
% 1.87/2.08 tff(7912,plain,
% 1.87/2.08 (b(s(s(z)), z)),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[583, 7911])).
% 1.87/2.08 tff(7913,plain,
% 1.87/2.08 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.87/2.08 inference(symmetry,[status(thm)],[7909])).
% 1.87/2.08 tff(7914,plain,
% 1.87/2.08 (s(s(z)) = s(elem!1)),
% 1.87/2.08 inference(transitivity,[status(thm)],[16, 7913, 1046])).
% 1.87/2.08 tff(7915,plain,
% 1.87/2.08 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7914])).
% 1.87/2.08 tff(7916,plain,
% 1.87/2.08 (b(s(elem!1), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(symmetry,[status(thm)],[7915])).
% 1.87/2.08 tff(7917,plain,
% 1.87/2.08 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7906])).
% 1.87/2.08 tff(7918,plain,
% 1.87/2.08 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7917])).
% 1.87/2.08 tff(7919,plain,
% 1.87/2.08 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7918, 7916])).
% 1.87/2.08 tff(7920,plain,
% 1.87/2.08 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7917])).
% 1.87/2.08 tff(7921,plain,
% 1.87/2.08 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(symmetry,[status(thm)],[7920])).
% 1.87/2.08 tff(7922,plain,
% 1.87/2.08 ((~r(s(elem!1), s(s(s(s(s(z))))))) <=> (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7921])).
% 1.87/2.08 tff(7923,plain,
% 1.87/2.08 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.08 inference(modus_ponens,[status(thm)],[806, 7922])).
% 1.87/2.08 tff(7924,plain,
% 1.87/2.08 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7906])).
% 1.87/2.08 tff(7925,plain,
% 1.87/2.08 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7924, 3030])).
% 1.87/2.08 tff(7926,plain,
% 1.87/2.08 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.87/2.08 inference(symmetry,[status(thm)],[7925])).
% 1.87/2.08 tff(7927,plain,
% 1.87/2.08 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7910])).
% 1.87/2.08 tff(7928,plain,
% 1.87/2.08 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.87/2.08 inference(symmetry,[status(thm)],[7927])).
% 1.87/2.08 tff(7929,plain,
% 1.87/2.08 (s(z) = elem!1),
% 1.87/2.08 inference(transitivity,[status(thm)],[1507, 7928, 682])).
% 1.87/2.08 tff(7930,plain,
% 1.87/2.08 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(s(z)))) = elem!1)),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7929])).
% 1.87/2.08 tff(7931,plain,
% 1.87/2.08 ((s(s(s(s(z)))) = s(z)) <=> (elem!1 = s(s(s(s(z)))))),
% 1.87/2.08 inference(transitivity,[status(thm)],[7930, 3030])).
% 1.87/2.08 tff(7932,plain,
% 1.87/2.08 ((s(s(s(s(z)))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 1.87/2.08 inference(transitivity,[status(thm)],[7931, 7926])).
% 1.87/2.08 tff(7933,plain,
% 1.87/2.08 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.87/2.08 inference(monotonicity,[status(thm)],[7932])).
% 1.87/2.09 tff(7934,plain,
% 1.87/2.09 (~(s(s(s(elem!1))) = elem!1)),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[212, 7933])).
% 1.87/2.09 tff(7935,plain,
% 1.87/2.09 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4956, 7934])).
% 1.87/2.09 tff(7936,plain,
% 1.87/2.09 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4961, 7935])).
% 1.87/2.09 tff(7937,plain,
% 1.87/2.09 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4973, 7936, 7923])).
% 1.87/2.09 tff(7938,plain,
% 1.87/2.09 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7937, 7919])).
% 1.87/2.09 tff(7939,plain,
% 1.87/2.09 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7910])).
% 1.87/2.09 tff(7940,plain,
% 1.87/2.09 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 1.87/2.09 inference(commutativity,[status(thm)],[])).
% 1.87/2.09 tff(7941,plain,
% 1.87/2.09 ((s(z) = s(s(z))) <=> (s(z) = s(elem!1))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7914])).
% 1.87/2.09 tff(7942,plain,
% 1.87/2.09 ((s(z) = s(s(z))) <=> (s(elem!1) = s(z))),
% 1.87/2.09 inference(transitivity,[status(thm)],[7941, 7940])).
% 1.87/2.09 tff(7943,plain,
% 1.87/2.09 ((~(s(z) = s(s(z)))) <=> (~(s(elem!1) = s(z)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7942])).
% 1.87/2.09 tff(7944,plain,
% 1.87/2.09 (~(s(elem!1) = s(z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[2196, 7943])).
% 1.87/2.09 tff(7945,plain,
% 1.87/2.09 (b(s(elem!1), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[950, 7944, 7867])).
% 1.87/2.09 tff(7946,plain,
% 1.87/2.09 (b(s(s(z)), s(z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7945, 7939])).
% 1.87/2.09 tff(7947,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(7948,plain,
% 1.87/2.09 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(7949,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7948])).
% 1.87/2.09 tff(7950,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[7949, 7947])).
% 1.87/2.09 tff(7951,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(7952,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7951, 7950])).
% 1.87/2.09 tff(7953,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[7952, 192, 2490, 7002, 7946, 7938])).
% 1.87/2.09 tff(7954,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(elem!1), s(z)) | r(s(elem!1), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(7955,plain,
% 1.87/2.09 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[7954, 7906, 7002, 7867, 2490])).
% 1.87/2.09 tff(7956,plain,
% 1.87/2.09 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7914])).
% 1.87/2.09 tff(7957,plain,
% 1.87/2.09 (r(s(elem!1), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7956])).
% 1.87/2.09 tff(7958,plain,
% 1.87/2.09 (r(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[537, 7957])).
% 1.87/2.09 tff(7959,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.09 tff(7960,plain,
% 1.87/2.09 (~(s(s(s(z))) = s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1553, 1535])).
% 1.87/2.09 tff(7961,plain,
% 1.87/2.09 (s(s(z)) = s(elem!1)),
% 1.87/2.09 inference(symmetry,[status(thm)],[1536])).
% 1.87/2.09 tff(7962,plain,
% 1.87/2.09 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7963,plain,
% 1.87/2.09 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7962])).
% 1.87/2.09 tff(7964,plain,
% 1.87/2.09 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7965,plain,
% 1.87/2.09 ((~r(s(s(z)), s(z))) <=> (~r(s(elem!1), s(z)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7964])).
% 1.87/2.09 tff(7966,plain,
% 1.87/2.09 (~r(s(s(z)), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6619, 77, 308, 5916])).
% 1.87/2.09 tff(7967,plain,
% 1.87/2.09 (~r(s(elem!1), s(z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7966, 7965])).
% 1.87/2.09 tff(7968,plain,
% 1.87/2.09 (b(s(elem!1), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[950, 7967, 1551])).
% 1.87/2.09 tff(7969,plain,
% 1.87/2.09 (b(s(s(z)), s(z))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7968, 7963])).
% 1.87/2.09 tff(7970,plain,
% 1.87/2.09 ((s(z) = s(s(z))) <=> (s(z) = s(elem!1))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7971,plain,
% 1.87/2.09 ((s(z) = s(s(z))) <=> (s(elem!1) = s(z))),
% 1.87/2.09 inference(transitivity,[status(thm)],[7970, 7940])).
% 1.87/2.09 tff(7972,plain,
% 1.87/2.09 ((s(elem!1) = s(z)) <=> (s(z) = s(s(z)))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7971])).
% 1.87/2.09 tff(7973,plain,
% 1.87/2.09 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7972])).
% 1.87/2.09 tff(7974,plain,
% 1.87/2.09 (~(s(z) = s(s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[1551, 7973])).
% 1.87/2.09 tff(7975,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(7976,plain,
% 1.87/2.09 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(7977,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7976])).
% 1.87/2.09 tff(7978,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[7977, 7975])).
% 1.87/2.09 tff(7979,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(7980,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7979, 7978])).
% 1.87/2.09 tff(7981,plain,
% 1.87/2.09 (~r(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[7980, 77, 308, 5916])).
% 1.87/2.09 tff(7982,plain,
% 1.87/2.09 ((s(z) = s(s(z))) | b(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[6092, 60, 7981])).
% 1.87/2.09 tff(7983,plain,
% 1.87/2.09 (b(s(z), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[7982, 7974])).
% 1.87/2.09 tff(7984,plain,
% 1.87/2.09 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7985,plain,
% 1.87/2.09 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7984])).
% 1.87/2.09 tff(7986,plain,
% 1.87/2.09 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7987,plain,
% 1.87/2.09 ((~r(z, s(s(z)))) <=> (~r(z, s(elem!1)))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7986])).
% 1.87/2.09 tff(7988,plain,
% 1.87/2.09 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7961])).
% 1.87/2.09 tff(7989,plain,
% 1.87/2.09 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7988])).
% 1.87/2.09 tff(7990,plain,
% 1.87/2.09 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[795, 7989])).
% 1.87/2.09 tff(7991,plain,
% 1.87/2.09 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[4201])).
% 1.87/2.09 tff(7992,plain,
% 1.87/2.09 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7991])).
% 1.87/2.09 tff(7993,plain,
% 1.87/2.09 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7992])).
% 1.87/2.09 tff(7994,plain,
% 1.87/2.09 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7993])).
% 1.87/2.09 tff(7995,plain,
% 1.87/2.09 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7991])).
% 1.87/2.09 tff(7996,plain,
% 1.87/2.09 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[7995])).
% 1.87/2.09 tff(7997,plain,
% 1.87/2.09 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(z, s(s(s(s(elem!1))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[7996])).
% 1.87/2.09 tff(7998,plain,
% 1.87/2.09 (~b(z, s(s(s(s(s(z))))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[4046, 192, 396, 1242, 441])).
% 1.87/2.09 tff(7999,plain,
% 1.87/2.09 (~b(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[7998, 7997])).
% 1.87/2.09 tff(8000,plain,
% 1.87/2.09 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.87/2.09 inference(commutativity,[status(thm)],[])).
% 1.87/2.09 tff(8001,plain,
% 1.87/2.09 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(symmetry,[status(thm)],[8000])).
% 1.87/2.09 tff(8002,plain,
% 1.87/2.09 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[8001])).
% 1.87/2.09 tff(8003,plain,
% 1.87/2.09 (~(z = s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[4914, 8002])).
% 1.87/2.09 tff(8004,plain,
% 1.87/2.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8005,plain,
% 1.87/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(8006,plain,
% 1.87/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8005, 8004])).
% 1.87/2.09 tff(8007,plain,
% 1.87/2.09 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8006, 60])).
% 1.87/2.09 tff(8008,plain,
% 1.87/2.09 (b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8007, 8003])).
% 1.87/2.09 tff(8009,plain,
% 1.87/2.09 (r(z, s(s(s(s(elem!1)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8008, 7999])).
% 1.87/2.09 tff(8010,plain,
% 1.87/2.09 (r(z, s(s(s(s(s(z))))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8009, 7994])).
% 1.87/2.09 tff(8011,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8012,plain,
% 1.87/2.09 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8013,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[8012])).
% 1.87/2.09 tff(8014,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[8013, 8011])).
% 1.87/2.09 tff(8015,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(8016,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8015, 8014])).
% 1.87/2.09 tff(8017,plain,
% 1.87/2.09 ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8016, 77, 8010])).
% 1.87/2.09 tff(8018,plain,
% 1.87/2.09 (~r(z, s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8017, 7990])).
% 1.87/2.09 tff(8019,plain,
% 1.87/2.09 (~r(z, s(elem!1))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8018, 7987])).
% 1.87/2.09 tff(8020,plain,
% 1.87/2.09 (b(z, s(elem!1))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[580, 8019])).
% 1.87/2.09 tff(8021,plain,
% 1.87/2.09 (b(z, s(s(z)))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8020, 7985])).
% 1.87/2.09 tff(8022,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 1.87/2.09 tff(8023,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8024,plain,
% 1.87/2.09 (((~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))))) <=> ((~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)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8025,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[8024])).
% 1.87/2.09 tff(8026,plain,
% 1.87/2.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[8025, 8023])).
% 1.87/2.09 tff(8027,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(8028,plain,
% 1.87/2.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 1.87/2.09 tff(8029,plain,
% 1.87/2.09 (~r(s(s(s(z))), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8028, 77, 383, 5916])).
% 1.87/2.09 tff(8030,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.87/2.09 tff(8031,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[1557, 60, 8022, 8030, 8029])).
% 1.87/2.09 tff(8032,plain,(b(s(s(s(z))), s(s(z))) | (s(s(s(z))) = s(s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(8033,plain,
% 1.87/2.09 (b(s(s(s(z))), s(s(z)))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8032, 383, 8022, 5916])).
% 1.87/2.09 tff(8034,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.87/2.09 tff(8035,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.87/2.09 tff(8036,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.87/2.09 tff(8037,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8038,plain,
% 1.87/2.09 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8039,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 1.87/2.09 inference(monotonicity,[status(thm)],[8038])).
% 1.87/2.09 tff(8040,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.09 inference(transitivity,[status(thm)],[8039, 8037])).
% 1.87/2.09 tff(8041,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.09 inference(quant_inst,[status(thm)],[])).
% 1.87/2.09 tff(8042,plain,
% 1.87/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 1.87/2.09 inference(modus_ponens,[status(thm)],[8041, 8040])).
% 1.87/2.09 tff(8043,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(z))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8042, 192, 6128, 8036, 8035, 8034, 8033])).
% 1.87/2.09 tff(8044,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[919, 60, 7585, 34, 8043])).
% 1.87/2.09 tff(8045,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (s(s(s(z))) = s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(8046,plain,
% 1.87/2.09 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8045, 8021, 6128, 7983, 7969, 7960, 5916, 308])).
% 1.87/2.09 tff(8047,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.09 tff(8048,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.09 tff(8049,plain,
% 1.87/2.09 ($false),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[166, 60, 8048, 8047, 7959])).
% 1.87/2.09 tff(8050,plain,(b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.09 tff(8051,plain,
% 1.87/2.09 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[8050, 8046, 7959])).
% 1.87/2.09 tff(8052,plain,
% 1.87/2.09 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[447, 192, 396, 8051, 441])).
% 1.87/2.09 tff(8053,plain,
% 1.87/2.09 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.09 inference(unit_resolution,[status(thm)],[373, 60, 102, 8052])).
% 1.87/2.09 tff(8054,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8055,plain,
% 1.87/2.09 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.09 inference(rewrite,[status(thm)],[])).
% 1.87/2.09 tff(8056,plain,
% 1.87/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8055])).
% 1.87/2.10 tff(8057,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8056, 8054])).
% 1.87/2.10 tff(8058,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8059,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8058, 8057])).
% 1.87/2.10 tff(8060,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8059, 192, 396, 1242, 2639, 395, 1745, 441])).
% 1.87/2.10 tff(8061,plain,((~b(s(s(s(z))), 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(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8062,plain,
% 1.87/2.10 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8061, 2639, 1242, 396, 1745, 441])).
% 1.87/2.10 tff(8063,plain,
% 1.87/2.10 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8050, 8062, 7959])).
% 1.87/2.10 tff(8064,plain,
% 1.87/2.10 (~r(s(s(s(z))), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8028, 77, 8063, 5916])).
% 1.87/2.10 tff(8065,plain,
% 1.87/2.10 (b(s(s(s(z))), s(s(z)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1557, 60, 8022, 8064])).
% 1.87/2.10 tff(8066,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8067,plain,
% 1.87/2.10 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8068,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8067])).
% 1.87/2.10 tff(8069,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8068, 8066])).
% 1.87/2.10 tff(8070,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8071,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8070, 8069])).
% 1.87/2.10 tff(8072,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8071, 192, 2639, 6128, 8036, 8065])).
% 1.87/2.10 tff(8073,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (s(s(s(z))) = s(s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (s(s(s(z))) = 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8074,plain,
% 1.87/2.10 (~b(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8073, 8021, 6128, 7960, 5916, 7959, 1242, 396, 1745, 441])).
% 1.87/2.10 tff(8075,plain,
% 1.87/2.10 (r(s(s(s(z))), z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[253, 8074])).
% 1.87/2.10 tff(8076,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8077,plain,
% 1.87/2.10 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8078,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8077])).
% 1.87/2.10 tff(8079,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8078, 8076])).
% 1.87/2.10 tff(8080,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8081,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8080, 8079])).
% 1.87/2.10 tff(8082,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8081, 77, 8075, 8010, 8053])).
% 1.87/2.10 tff(8083,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8084,plain,
% 1.87/2.10 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~r(s(elem!1), s(s(s(s(s(z)))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8083, 145])).
% 1.87/2.10 tff(8085,plain,
% 1.87/2.10 (~(elem!1 = s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8084, 7958, 441, 7955, 308, 1242, 1745, 7912, 396])).
% 1.87/2.10 tff(8086,plain,
% 1.87/2.10 (elem!1 = s(z)),
% 1.87/2.10 inference(transitivity,[status(thm)],[695, 7927, 10])).
% 1.87/2.10 tff(8087,plain,
% 1.87/2.10 (b(elem!1, s(z)) <=> b(s(z), s(z))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8086])).
% 1.87/2.10 tff(8088,plain,
% 1.87/2.10 (b(s(z), s(z)) <=> b(elem!1, s(z))),
% 1.87/2.10 inference(symmetry,[status(thm)],[8087])).
% 1.87/2.10 tff(8089,plain,
% 1.87/2.10 ((~b(s(z), s(z))) <=> (~b(elem!1, s(z)))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8088])).
% 1.87/2.10 tff(8090,plain,
% 1.87/2.10 (~b(elem!1, s(z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[1504, 8089])).
% 1.87/2.10 tff(8091,plain,
% 1.87/2.10 (r(elem!1, s(z)) <=> r(s(z), s(z))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8086])).
% 1.87/2.10 tff(8092,plain,
% 1.87/2.10 (r(s(z), s(z)) <=> r(elem!1, s(z))),
% 1.87/2.10 inference(symmetry,[status(thm)],[8091])).
% 1.87/2.10 tff(8093,plain,
% 1.87/2.10 ((~r(s(z), s(z))) <=> (~r(elem!1, s(z)))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8092])).
% 1.87/2.10 tff(8094,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8095,plain,
% 1.87/2.10 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8096,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8095])).
% 1.87/2.10 tff(8097,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8096, 8094])).
% 1.87/2.10 tff(8098,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8099,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(z)))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8098, 8097])).
% 1.87/2.10 tff(8100,plain,
% 1.87/2.10 (~r(s(z), s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8099, 77, 308])).
% 1.87/2.10 tff(8101,plain,
% 1.87/2.10 (~r(elem!1, s(z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8100, 8093])).
% 1.87/2.10 tff(8102,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1529, 8101, 8090, 8085])).
% 1.87/2.10 tff(8103,plain,((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(elem!1), s(z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8104,plain,
% 1.87/2.10 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8103, 7905, 308, 4019, 7894, 7890, 7874, 583, 7488, 7867, 7866])).
% 1.87/2.10 tff(8105,plain,
% 1.87/2.10 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[7728, 192, 1005, 4019, 7894])).
% 1.87/2.10 tff(8106,plain,
% 1.87/2.10 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[1396, 60, 8105])).
% 1.87/2.10 tff(8107,plain,
% 1.87/2.10 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8106, 8104])).
% 1.87/2.10 tff(8108,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8109,plain,
% 1.87/2.10 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8110,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8109])).
% 1.87/2.10 tff(8111,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8110, 8108])).
% 1.87/2.10 tff(8112,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8113,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8112, 8111])).
% 1.87/2.10 tff(8114,plain,
% 1.87/2.10 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8113, 77, 7874, 8107])).
% 1.87/2.10 tff(8115,plain,
% 1.87/2.10 (s(s(s(elem!1))) = s(elem!1)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[679, 8114, 7886])).
% 1.87/2.10 tff(8116,plain,
% 1.87/2.10 (s(elem!1) = s(s(s(elem!1)))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[708, 8115])).
% 1.87/2.10 tff(8117,plain,
% 1.87/2.10 (elem!1 = s(s(s(s(elem!1))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[718, 8116])).
% 1.87/2.10 tff(8118,plain,
% 1.87/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8117, 702])).
% 1.87/2.10 tff(8119,plain,
% 1.87/2.10 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[744, 8118])).
% 1.87/2.10 tff(8120,plain,
% 1.87/2.10 (r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[811, 8119, 7883])).
% 1.87/2.10 tff(8121,plain,
% 1.87/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.10 inference(symmetry,[status(thm)],[8117])).
% 1.87/2.10 tff(8122,plain,
% 1.87/2.10 (b(s(s(s(s(elem!1)))), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8121])).
% 1.87/2.10 tff(8123,plain,
% 1.87/2.10 ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8122])).
% 1.87/2.10 tff(8124,plain,
% 1.87/2.10 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8121])).
% 1.87/2.10 tff(8125,plain,
% 1.87/2.10 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.10 inference(symmetry,[status(thm)],[8124])).
% 1.87/2.10 tff(8126,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.87/2.10 tff(8127,plain,
% 1.87/2.10 (s(z) = s(s(elem!1))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8126, 695, 694, 691])).
% 1.87/2.10 tff(8128,plain,
% 1.87/2.10 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8127])).
% 1.87/2.10 tff(8129,plain,
% 1.87/2.10 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.87/2.10 inference(symmetry,[status(thm)],[8128])).
% 1.87/2.10 tff(8130,plain,
% 1.87/2.10 (s(elem!1) = z),
% 1.87/2.10 inference(transitivity,[status(thm)],[1047, 8129, 20])).
% 1.87/2.10 tff(8131,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[556, 8130])).
% 1.87/2.10 tff(8132,plain,((~(s(z) = elem!1)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8133,plain,
% 1.87/2.10 (~(s(z) = elem!1)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8132, 8115])).
% 1.87/2.10 tff(8134,plain,
% 1.87/2.10 (s(z) = elem!1),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[1535, 2185])).
% 1.87/2.10 tff(8135,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.87/2.10 tff(8136,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8135, 8134])).
% 1.87/2.10 tff(8137,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8138,plain,
% 1.87/2.10 (~(elem!1 = s(z))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8137, 8133])).
% 1.87/2.10 tff(8139,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.87/2.10 tff(8140,plain,
% 1.87/2.10 (s(s(s(s(elem!1)))) = elem!1),
% 1.87/2.10 inference(symmetry,[status(thm)],[8139])).
% 1.87/2.10 tff(8141,plain,
% 1.87/2.10 (r(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.10 tff(8142,plain,
% 1.87/2.10 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.87/2.10 inference(symmetry,[status(thm)],[8141])).
% 1.87/2.10 tff(8143,plain,
% 1.87/2.10 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.10 tff(8144,plain,
% 1.87/2.10 ((~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8143])).
% 1.87/2.10 tff(8145,plain,
% 1.87/2.10 (b(elem!1, z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8139])).
% 1.87/2.10 tff(8146,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8147,plain,
% 1.87/2.10 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8148,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8147])).
% 1.87/2.10 tff(8149,plain,
% 1.87/2.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8148, 8146])).
% 1.87/2.10 tff(8150,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8151,plain,
% 1.87/2.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8150, 8149])).
% 1.87/2.10 tff(8152,plain,
% 1.87/2.10 ($false),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8151, 77, 3199, 504, 2554])).
% 1.87/2.10 tff(8153,plain,((~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.10 tff(8154,plain,
% 1.87/2.10 (~r(elem!1, z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8153, 2554, 504])).
% 1.87/2.10 tff(8155,plain,
% 1.87/2.10 (b(elem!1, z)),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[2354, 8154, 2184])).
% 1.87/2.10 tff(8156,plain,
% 1.87/2.10 (b(s(s(s(s(elem!1)))), z)),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8155, 8145])).
% 1.87/2.10 tff(8157,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8158,plain,
% 1.87/2.10 (((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(rewrite,[status(thm)],[])).
% 1.87/2.10 tff(8159,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))))),
% 1.87/2.10 inference(monotonicity,[status(thm)],[8158])).
% 1.87/2.10 tff(8160,plain,
% 1.87/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))))),
% 1.87/2.10 inference(transitivity,[status(thm)],[8159, 8157])).
% 1.87/2.10 tff(8161,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.87/2.10 inference(quant_inst,[status(thm)],[])).
% 1.87/2.10 tff(8162,plain,
% 1.87/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z))))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8161, 8160])).
% 1.87/2.10 tff(8163,plain,
% 1.87/2.10 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.87/2.10 inference(unit_resolution,[status(thm)],[8162, 192, 584, 8156, 583, 1242, 1745])).
% 1.87/2.10 tff(8164,plain,
% 1.87/2.10 (~b(elem!1, s(s(s(s(z)))))),
% 1.87/2.10 inference(modus_ponens,[status(thm)],[8163, 8144])).
% 1.87/2.11 tff(8165,plain,
% 1.87/2.11 (r(elem!1, s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2385, 8164, 3528])).
% 1.87/2.11 tff(8166,plain,
% 1.87/2.11 (r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8165, 8142])).
% 1.87/2.11 tff(8167,plain,
% 1.87/2.11 (r(s(s(s(s(elem!1)))), s(z)) <=> r(elem!1, s(z))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8168,plain,
% 1.87/2.11 (r(elem!1, s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8167])).
% 1.87/2.11 tff(8169,plain,
% 1.87/2.11 (r(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[2554, 8168])).
% 1.87/2.11 tff(8170,plain,
% 1.87/2.11 (~r(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4908, 77, 67, 8169])).
% 1.87/2.11 tff(8171,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8170, 8166])).
% 1.87/2.11 tff(8172,plain,((~r(elem!1, s(z))) | (~(elem!1 = s(s(s(s(elem!1)))))) | (~r(s(s(s(s(z)))), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (elem!1 = z) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(8173,plain,
% 1.87/2.11 (~r(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8172, 8117, 7695, 4803, 7885, 583, 4019, 7894, 2779, 504])).
% 1.87/2.11 tff(8174,plain,
% 1.87/2.11 (b(elem!1, s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1529, 8173, 8138])).
% 1.87/2.11 tff(8175,plain,
% 1.87/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8174, 8125])).
% 1.87/2.11 tff(8176,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8177,plain,
% 1.87/2.11 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8178,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8177])).
% 1.87/2.11 tff(8179,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8178, 8176])).
% 1.87/2.11 tff(8180,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(8181,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8180, 8179])).
% 1.87/2.11 tff(8182,plain,
% 1.87/2.11 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8181, 192, 7868, 7866, 7488, 7876, 8175])).
% 1.87/2.11 tff(8183,plain,
% 1.87/2.11 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8182, 8123])).
% 1.87/2.11 tff(8184,plain,
% 1.87/2.11 ((s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8121])).
% 1.87/2.11 tff(8185,plain,
% 1.87/2.11 ((~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8184])).
% 1.87/2.11 tff(8186,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.87/2.11 tff(8187,plain,
% 1.87/2.11 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8186])).
% 1.87/2.11 tff(8188,plain,
% 1.87/2.11 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8187])).
% 1.87/2.11 tff(8189,plain,
% 1.87/2.11 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(z))))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8188])).
% 1.87/2.11 tff(8190,plain,
% 1.87/2.11 (s(elem!1) = s(s(s(elem!1)))),
% 1.87/2.11 inference(symmetry,[status(thm)],[692])).
% 1.87/2.11 tff(8191,plain,
% 1.87/2.11 (s(elem!1) = s(s(s(s(z))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8190, 4894, 8189, 44])).
% 1.87/2.11 tff(8192,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[528, 8191])).
% 1.87/2.11 tff(8193,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))) | (s(elem!1) = s(s(s(s(z))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(8194,plain,
% 1.87/2.11 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8193, 7873, 8115])).
% 1.87/2.11 tff(8195,plain,
% 1.87/2.11 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8194, 8185])).
% 1.87/2.11 tff(8196,plain,
% 1.87/2.11 (r(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2227, 8195, 8183])).
% 1.87/2.11 tff(8197,plain,
% 1.87/2.11 (~r(s(elem!1), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[5758, 8196, 8120])).
% 1.87/2.11 tff(8198,plain,
% 1.87/2.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(elem!1), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8115])).
% 1.87/2.11 tff(8199,plain,
% 1.87/2.11 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8198])).
% 1.87/2.11 tff(8200,plain,
% 1.87/2.11 (~b(z, s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4046, 192, 7890, 4019, 7905])).
% 1.87/2.11 tff(8201,plain,
% 1.87/2.11 (r(z, s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[491, 60, 8200, 486])).
% 1.87/2.11 tff(8202,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8203,plain,
% 1.87/2.11 (((~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8204,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8203])).
% 1.87/2.11 tff(8205,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8204, 8202])).
% 1.87/2.11 tff(8206,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, z)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(8207,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 1.87/2.11 tff(8208,plain,
% 1.87/2.11 (~r(elem!1, z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8207, 77, 5750, 462])).
% 1.87/2.11 tff(8209,plain,
% 1.87/2.11 (b(elem!1, z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2354, 8208, 2184])).
% 1.87/2.11 tff(8210,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8211,plain,
% 1.87/2.11 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8212,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8211])).
% 1.87/2.11 tff(8213,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8212, 8210])).
% 1.87/2.11 tff(8214,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, elem!1)))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(8215,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8214, 8213])).
% 1.87/2.11 tff(8216,plain,
% 1.87/2.11 (~r(z, elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8215, 77, 5750, 462])).
% 1.87/2.11 tff(8217,plain,
% 1.87/2.11 (b(z, elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2911, 8216, 4355])).
% 1.87/2.11 tff(8218,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[4380, 192, 8217, 8209, 6804, 1005])).
% 1.87/2.11 tff(8219,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)) | (elem!1 = z) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(8220,plain,
% 1.87/2.11 (~b(s(s(s(elem!1))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8219, 8196, 2779, 1005, 8201])).
% 1.87/2.11 tff(8221,plain,
% 1.87/2.11 (~b(s(elem!1), elem!1)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8220, 8199])).
% 1.87/2.11 tff(8222,plain,
% 1.87/2.11 (s(elem!1) = elem!1),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[3123, 8221, 8197])).
% 1.87/2.11 tff(8223,plain,
% 1.87/2.11 (b(s(z), s(elem!1)) <=> b(s(z), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8222])).
% 1.87/2.11 tff(8224,plain,
% 1.87/2.11 (b(s(z), elem!1)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[7876, 8223])).
% 1.87/2.11 tff(8225,plain,
% 1.87/2.11 (~(elem!1 = s(s(s(z))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[1993, 7873])).
% 1.87/2.11 tff(8226,plain,
% 1.87/2.11 (~(s(s(s(z))) = elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2015, 8225])).
% 1.87/2.11 tff(8227,plain,
% 1.87/2.11 (elem!1 = s(elem!1)),
% 1.87/2.11 inference(symmetry,[status(thm)],[8222])).
% 1.87/2.11 tff(8228,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8227])).
% 1.87/2.11 tff(8229,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), s(elem!1)) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.87/2.11 inference(symmetry,[status(thm)],[8228])).
% 1.87/2.11 tff(8230,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), elem!1)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[7888, 8229])).
% 1.87/2.11 tff(8231,plain,
% 1.87/2.11 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8232,plain,
% 1.87/2.11 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8231])).
% 1.87/2.11 tff(8233,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.87/2.11 tff(8234,plain,
% 1.87/2.11 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8235,plain,
% 1.87/2.11 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), elem!1))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8234])).
% 1.87/2.11 tff(8236,plain,
% 1.87/2.11 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8237,plain,
% 1.87/2.11 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8236])).
% 1.87/2.11 tff(8238,plain,
% 1.87/2.11 (b(s(z), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[2268, 8237])).
% 1.87/2.11 tff(8239,plain,
% 1.87/2.11 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8240,plain,
% 1.87/2.11 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8239])).
% 1.87/2.11 tff(8241,plain,
% 1.87/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[2237, 8240])).
% 1.87/2.11 tff(8242,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8243,plain,
% 1.87/2.11 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8244,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8243])).
% 1.87/2.11 tff(8245,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8244, 8242])).
% 1.87/2.11 tff(8246,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(z))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(8247,plain,
% 1.87/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8246, 8245])).
% 1.87/2.11 tff(8248,plain,
% 1.87/2.11 ((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8247, 192, 1408])).
% 1.87/2.11 tff(8249,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8248, 8241, 8238])).
% 1.87/2.11 tff(8250,plain,
% 1.87/2.11 (~b(s(s(s(z))), elem!1)),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8249, 8235])).
% 1.87/2.11 tff(8251,plain,
% 1.87/2.11 (r(s(s(s(z))), elem!1)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[2025, 8250, 8233])).
% 1.87/2.11 tff(8252,plain,
% 1.87/2.11 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8251, 8232])).
% 1.87/2.11 tff(8253,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8140])).
% 1.87/2.11 tff(8254,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8253])).
% 1.87/2.11 tff(8255,plain,
% 1.87/2.11 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[6597, 8254])).
% 1.87/2.11 tff(8256,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[7465, 192, 2490, 7002, 1408])).
% 1.87/2.11 tff(8257,plain,
% 1.87/2.11 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[373, 60, 102, 8256])).
% 1.87/2.11 tff(8258,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8259,plain,
% 1.87/2.11 (((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(rewrite,[status(thm)],[])).
% 1.87/2.11 tff(8260,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8259])).
% 1.87/2.11 tff(8261,plain,
% 1.87/2.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[8260, 8258])).
% 1.87/2.11 tff(8262,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.87/2.11 inference(quant_inst,[status(thm)],[])).
% 1.87/2.11 tff(8263,plain,
% 1.87/2.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(modus_ponens,[status(thm)],[8262, 8261])).
% 1.87/2.11 tff(8264,plain,
% 1.87/2.11 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8263, 77, 8257])).
% 1.87/2.11 tff(8265,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8264, 8255, 8252])).
% 1.87/2.11 tff(8266,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(z))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(8267,plain,
% 1.87/2.11 (~b(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8266, 8230, 8117, 8226, 8174, 8224, 7866, 7488])).
% 1.87/2.11 tff(8268,plain,
% 1.87/2.11 (r(s(s(s(z))), s(z))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[920, 8267])).
% 1.87/2.11 tff(8269,plain,
% 1.87/2.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[388, 8268, 308])).
% 1.87/2.11 tff(8270,plain,
% 1.87/2.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[390, 8269])).
% 1.87/2.11 tff(8271,plain,
% 1.87/2.11 (~b(s(s(s(z))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8061, 8270, 4019, 7905, 7894, 7890])).
% 1.87/2.11 tff(8272,plain,
% 1.87/2.11 (r(s(s(s(z))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[253, 8271])).
% 1.87/2.11 tff(8273,plain,
% 1.87/2.11 ($false),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[245, 77, 7892, 8272, 8268])).
% 1.87/2.11 tff(8274,plain,(r(s(elem!1), s(z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (s(s(s(s(s(z))))) = s(elem!1)) | b(s(elem!1), s(s(s(s(z))))) | b(s(s(s(s(z)))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.11 tff(8275,plain,
% 1.87/2.11 (~b(s(s(s(elem!1))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[8274, 7797, 296, 583, 504, 308, 815, 7789, 7690, 115])).
% 1.87/2.11 tff(8276,plain,
% 1.87/2.11 (r(s(s(s(elem!1))), z)),
% 1.87/2.11 inference(unit_resolution,[status(thm)],[992, 8275])).
% 1.87/2.11 tff(8277,plain,
% 1.87/2.11 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[3522, 3838])).
% 1.87/2.11 tff(8278,plain,
% 1.87/2.11 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8277])).
% 1.87/2.11 tff(8279,plain,
% 1.87/2.11 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.87/2.11 inference(transitivity,[status(thm)],[5433, 8278])).
% 1.87/2.11 tff(8280,plain,
% 1.87/2.11 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[3522])).
% 1.87/2.11 tff(8281,plain,
% 1.87/2.11 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.11 inference(symmetry,[status(thm)],[8280])).
% 1.87/2.11 tff(8282,plain,
% 1.87/2.11 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.87/2.11 inference(monotonicity,[status(thm)],[8281])).
% 1.87/2.11 tff(8283,plain,
% 1.87/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8284,plain,
% 1.87/2.12 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8285,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(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(z)), s(s(s(s(z))))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8284])).
% 1.87/2.12 tff(8286,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[8285, 8283])).
% 1.87/2.12 tff(8287,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(8288,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(z)), s(s(s(s(z))))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8287, 8286])).
% 1.87/2.12 tff(8289,plain,
% 1.87/2.12 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8288, 192, 396, 441, 6127])).
% 1.87/2.12 tff(8290,plain,
% 1.87/2.12 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8289, 8282])).
% 1.87/2.12 tff(8291,plain,
% 1.87/2.12 (r(elem!1, s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2227, 8290, 5450])).
% 1.87/2.12 tff(8292,plain,
% 1.87/2.12 (r(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8291, 8279])).
% 1.87/2.12 tff(8293,plain,
% 1.87/2.12 (b(s(s(z)), z) <=> b(elem!1, z)),
% 1.87/2.12 inference(symmetry,[status(thm)],[5413])).
% 1.87/2.12 tff(8294,plain,
% 1.87/2.12 ((~b(s(s(z)), z)) <=> (~b(elem!1, z))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8293])).
% 1.87/2.12 tff(8295,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8296,plain,
% 1.87/2.12 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8297,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8296])).
% 1.87/2.12 tff(8298,plain,
% 1.87/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[8297, 8295])).
% 1.87/2.12 tff(8299,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(8300,plain,
% 1.87/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8299, 8298])).
% 1.87/2.12 tff(8301,plain,
% 1.87/2.12 (~b(s(s(z)), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8300, 192, 396, 1242, 1745, 441, 6127])).
% 1.87/2.12 tff(8302,plain,
% 1.87/2.12 (~b(elem!1, z)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8301, 8294])).
% 1.87/2.12 tff(8303,plain,
% 1.87/2.12 (r(elem!1, z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2354, 8302, 2184])).
% 1.87/2.12 tff(8304,plain,
% 1.87/2.12 (~r(elem!1, s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2819, 8303, 974])).
% 1.87/2.12 tff(8305,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8304, 8292])).
% 1.87/2.12 tff(8306,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~(s(elem!1) = s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (elem!1 = 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(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8307,plain,
% 1.87/2.12 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8306, 7807, 8276, 2779, 396, 5724, 1745, 7864])).
% 1.87/2.12 tff(8308,plain,
% 1.87/2.12 (~b(elem!1, s(s(s(s(z)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8307, 7819])).
% 1.87/2.12 tff(8309,plain,
% 1.87/2.12 (r(elem!1, s(s(s(s(z)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2385, 8308, 4803])).
% 1.87/2.12 tff(8310,plain,
% 1.87/2.12 (r(s(s(z)), s(s(s(s(z)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8309, 7816])).
% 1.87/2.12 tff(8311,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(z))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8312,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(z))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(8313,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(z)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8312, 8311])).
% 1.87/2.12 tff(8314,plain,
% 1.87/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8313, 77, 383, 8310])).
% 1.87/2.12 tff(8315,plain,
% 1.87/2.12 (~r(elem!1, s(s(s(z))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8314, 7814])).
% 1.87/2.12 tff(8316,plain,
% 1.87/2.12 (b(elem!1, s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2037, 8315, 3053])).
% 1.87/2.12 tff(8317,plain,
% 1.87/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8316, 7812])).
% 1.87/2.12 tff(8318,plain,
% 1.87/2.12 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7810])).
% 1.87/2.12 tff(8319,plain,
% 1.87/2.12 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(s(z))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[8318, 2011])).
% 1.87/2.12 tff(8320,plain,
% 1.87/2.12 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.87/2.12 inference(symmetry,[status(thm)],[8319])).
% 1.87/2.12 tff(8321,plain,
% 1.87/2.12 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8320])).
% 1.87/2.12 tff(8322,plain,
% 1.87/2.12 (~(s(s(s(z))) = s(s(z)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[3053, 8321])).
% 1.87/2.12 tff(8323,plain,
% 1.87/2.12 (b(s(s(s(z))), s(s(z)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8032, 8310, 383, 8322])).
% 1.87/2.12 tff(8324,plain,
% 1.87/2.12 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7815])).
% 1.87/2.12 tff(8325,plain,
% 1.87/2.12 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7810])).
% 1.87/2.12 tff(8326,plain,
% 1.87/2.12 ((~(s(z) = s(s(z)))) <=> (~(s(z) = elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8325])).
% 1.87/2.12 tff(8327,plain,
% 1.87/2.12 (~(s(z) = elem!1)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[2196, 8326])).
% 1.87/2.12 tff(8328,plain,
% 1.87/2.12 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 1.87/2.12 inference(monotonicity,[status(thm)],[7810])).
% 1.87/2.12 tff(8329,plain,
% 1.87/2.12 ((~r(s(z), s(s(z)))) <=> (~r(s(z), elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8328])).
% 1.87/2.12 tff(8330,plain,
% 1.87/2.12 (~r(s(z), s(s(z)))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7980, 77, 308, 8310])).
% 1.87/2.12 tff(8331,plain,
% 1.87/2.12 (~r(s(z), elem!1)),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8330, 8329])).
% 1.87/2.12 tff(8332,plain,
% 1.87/2.12 (b(s(z), elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5427, 8331, 8327])).
% 1.87/2.12 tff(8333,plain,
% 1.87/2.12 (b(s(z), s(s(z)))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8332, 8324])).
% 1.87/2.12 tff(8334,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[6099, 192, 8333, 8323, 7584, 8317])).
% 1.87/2.12 tff(8335,plain,((s(elem!1) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(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)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | b(s(s(s(s(z)))), s(z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8336,plain,
% 1.87/2.12 (~b(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8335, 7782, 308, 396, 7697, 583, 383, 815, 296, 504, 7690, 115])).
% 1.87/2.12 tff(8337,plain,
% 1.87/2.12 (r(s(s(s(z))), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[253, 8336])).
% 1.87/2.12 tff(8338,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4692, 77, 8337, 296, 7694])).
% 1.87/2.12 tff(8339,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(elem!1), z)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~r(s(z), z)) | b(s(s(s(s(z)))), s(z)) | (s(elem!1) = s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8340,plain,
% 1.87/2.12 (~b(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8339, 815, 308, 396, 504, 7667, 383, 7690, 115, 7689])).
% 1.87/2.12 tff(8341,plain,
% 1.87/2.12 (r(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[560, 8340])).
% 1.87/2.12 tff(8342,plain,
% 1.87/2.12 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4784, 8341, 7667])).
% 1.87/2.12 tff(8343,plain,
% 1.87/2.12 (~r(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2109, 504, 545])).
% 1.87/2.12 tff(8344,plain,
% 1.87/2.12 (b(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[950, 8343, 115])).
% 1.87/2.12 tff(8345,plain,
% 1.87/2.12 (~b(s(z), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7841, 8344, 2490, 582])).
% 1.87/2.12 tff(8346,plain,
% 1.87/2.12 (r(s(z), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[658, 8345, 639])).
% 1.87/2.12 tff(8347,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[4341, 77, 545, 504, 8346])).
% 1.87/2.12 tff(8348,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8349,plain,
% 1.87/2.12 ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(elem!1) = s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8348, 6957])).
% 1.87/2.12 tff(8350,plain,
% 1.87/2.12 (~b(s(s(s(s(s(z))))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8349, 8341, 115, 504])).
% 1.87/2.12 tff(8351,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[597, 8350, 8342, 815])).
% 1.87/2.12 tff(8352,plain,((s(s(s(s(s(z))))) = s(elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8353,plain,
% 1.87/2.12 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8352, 7687, 504, 308, 396, 383, 115])).
% 1.87/2.12 tff(8354,plain,
% 1.87/2.12 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), s(elem!1))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8353])).
% 1.87/2.12 tff(8355,plain,
% 1.87/2.12 (b(s(z), s(elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[7680, 8354])).
% 1.87/2.12 tff(8356,plain,
% 1.87/2.12 (~b(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[3263, 8353, 7666])).
% 1.87/2.12 tff(8357,plain,
% 1.87/2.12 (r(s(elem!1), z)),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[560, 8356])).
% 1.87/2.12 tff(8358,plain,
% 1.87/2.12 (~r(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2109, 8357, 504])).
% 1.87/2.12 tff(8359,plain,
% 1.87/2.12 (b(s(elem!1), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[950, 8358, 115])).
% 1.87/2.12 tff(8360,plain,
% 1.87/2.12 (r(s(s(s(s(z)))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[217, 7687])).
% 1.87/2.12 tff(8361,plain,
% 1.87/2.12 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1294, 8357, 7667])).
% 1.87/2.12 tff(8362,plain,
% 1.87/2.12 ((~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(elem!1), s(z)) | r(s(elem!1), s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7954, 6957])).
% 1.87/2.12 tff(8363,plain,
% 1.87/2.12 (~(s(s(s(elem!1))) = s(s(s(s(z)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8362, 8358, 7680, 8361])).
% 1.87/2.12 tff(8364,plain,
% 1.87/2.12 (~r(s(s(s(elem!1))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7731, 8363, 7689, 1242, 8360])).
% 1.87/2.12 tff(8365,plain,
% 1.87/2.12 (b(s(s(s(elem!1))), s(z))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1313, 8364])).
% 1.87/2.12 tff(8366,plain,
% 1.87/2.12 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[7465, 192, 6957, 7680, 7586])).
% 1.87/2.12 tff(8367,plain,
% 1.87/2.12 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[375, 8366])).
% 1.87/2.12 tff(8368,plain,
% 1.87/2.12 (r(s(s(s(z))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5541, 8353, 8367])).
% 1.87/2.12 tff(8369,plain,
% 1.87/2.12 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[5277, 8365, 7586, 7584])).
% 1.87/2.12 tff(8370,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.87/2.12 tff(8371,plain,
% 1.87/2.12 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[1958, 60, 8370, 5268])).
% 1.87/2.12 tff(8372,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 1.87/2.12 tff(8373,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8374,plain,
% 1.87/2.12 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.12 inference(rewrite,[status(thm)],[])).
% 1.87/2.12 tff(8375,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8374])).
% 1.87/2.12 tff(8376,plain,
% 1.87/2.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.12 inference(transitivity,[status(thm)],[8375, 8373])).
% 1.87/2.12 tff(8377,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 1.87/2.12 inference(quant_inst,[status(thm)],[])).
% 1.87/2.12 tff(8378,plain,
% 1.87/2.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8377, 8376])).
% 1.87/2.12 tff(8379,plain,
% 1.87/2.12 ($false),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8378, 77, 1342, 8372, 8371])).
% 1.87/2.12 tff(8380,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.87/2.12 tff(8381,plain,
% 1.87/2.12 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[8380, 8369, 5253, 8368])).
% 1.87/2.12 tff(8382,plain,
% 1.87/2.12 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8353])).
% 1.87/2.12 tff(8383,plain,
% 1.87/2.12 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.87/2.12 inference(transitivity,[status(thm)],[8382, 703])).
% 1.87/2.12 tff(8384,plain,
% 1.87/2.12 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.87/2.12 inference(monotonicity,[status(thm)],[8383])).
% 1.87/2.12 tff(8385,plain,
% 1.87/2.12 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[752, 8353])).
% 1.87/2.12 tff(8386,plain,
% 1.87/2.12 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.87/2.12 inference(unit_resolution,[status(thm)],[2314, 8385])).
% 1.87/2.12 tff(8387,plain,
% 1.87/2.12 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.87/2.12 inference(modus_ponens,[status(thm)],[8386, 8384])).
% 1.87/2.12 tff(8388,plain,
% 1.87/2.12 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[679, 8387, 8381])).
% 1.97/2.12 tff(8389,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8390,plain,
% 1.97/2.12 (((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(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(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.12 inference(rewrite,[status(thm)],[])).
% 1.97/2.12 tff(8391,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.97/2.12 inference(monotonicity,[status(thm)],[8390])).
% 1.97/2.12 tff(8392,plain,
% 1.97/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.97/2.12 inference(transitivity,[status(thm)],[8391, 8389])).
% 1.97/2.12 tff(8393,plain,
% 1.97/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.97/2.12 inference(quant_inst,[status(thm)],[])).
% 1.97/2.12 tff(8394,plain,
% 1.97/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.97/2.12 inference(modus_ponens,[status(thm)],[8393, 8392])).
% 1.97/2.12 tff(8395,plain,
% 1.97/2.12 ($false),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8394, 192, 8388, 8365, 8359, 8355])).
% 1.97/2.12 tff(8396,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.12 tff(8397,plain,
% 1.97/2.12 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[8396, 383, 115, 504, 308, 396, 1242])).
% 1.97/2.12 tff(8398,plain,
% 1.97/2.12 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[113, 8397])).
% 1.97/2.12 tff(8399,plain,
% 1.97/2.12 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[7512, 8398, 7674])).
% 1.97/2.12 tff(8400,plain,
% 1.97/2.12 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.12 inference(unit_resolution,[status(thm)],[406, 8399])).
% 1.97/2.13 tff(8401,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[883, 77, 296, 2280, 297])).
% 1.97/2.13 tff(8402,plain,((~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)))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8403,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8402, 8398, 7667])).
% 1.97/2.13 tff(8404,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[526, 8403])).
% 1.97/2.13 tff(8405,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7617, 192, 7586, 8400, 7584])).
% 1.97/2.13 tff(8406,plain,
% 1.97/2.13 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8352, 8405, 504, 308, 396, 383, 115])).
% 1.97/2.13 tff(8407,plain,
% 1.97/2.13 (~b(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3263, 8406, 7666])).
% 1.97/2.13 tff(8408,plain,
% 1.97/2.13 (r(s(elem!1), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[560, 8407])).
% 1.97/2.13 tff(8409,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8410,plain,
% 1.97/2.13 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(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(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8411,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8410])).
% 1.97/2.13 tff(8412,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8411, 8409])).
% 1.97/2.13 tff(8413,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(z, s(s(s(s(s(z))))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8414,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8413, 8412])).
% 1.97/2.13 tff(8415,plain,
% 1.97/2.13 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8414, 192, 396, 1242, 8400, 7676])).
% 1.97/2.13 tff(8416,plain,
% 1.97/2.13 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[493, 8415])).
% 1.97/2.13 tff(8417,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7010, 8416, 504])).
% 1.97/2.13 tff(8418,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7007, 8417])).
% 1.97/2.13 tff(8419,plain,
% 1.97/2.13 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = s(elem!1))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8406])).
% 1.97/2.13 tff(8420,plain,
% 1.97/2.13 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8419, 2700])).
% 1.97/2.13 tff(8421,plain,
% 1.97/2.13 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8420])).
% 1.97/2.13 tff(8422,plain,
% 1.97/2.13 (~(s(elem!1) = s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[102, 8421])).
% 1.97/2.13 tff(8423,plain,
% 1.97/2.13 (b(s(elem!1), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[950, 3822, 115])).
% 1.97/2.13 tff(8424,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8425,plain,
% 1.97/2.13 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8426,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8425])).
% 1.97/2.13 tff(8427,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8426, 8424])).
% 1.97/2.13 tff(8428,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(elem!1), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8429,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8428, 8427])).
% 1.97/2.13 tff(8430,plain,
% 1.97/2.13 (~b(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8429, 192, 8423, 6957, 7002, 1408, 3527])).
% 1.97/2.13 tff(8431,plain,
% 1.97/2.13 (~r(s(elem!1), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[3944, 77, 545, 503])).
% 1.97/2.13 tff(8432,assumption,(~(s(elem!1) = s(s(s(z))))), introduced(assumption)).
% 1.97/2.13 tff(8433,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2148, 60, 8432, 8431, 8430])).
% 1.97/2.13 tff(8434,plain,((~r(s(elem!1), z)) | (s(elem!1) = s(s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (s(elem!1) = s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8435,plain,
% 1.97/2.13 (~r(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8434, 8422, 7586, 8418, 7584, 8408, 115, 7689])).
% 1.97/2.13 tff(8436,plain,
% 1.97/2.13 (b(s(s(s(z))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[253, 8435])).
% 1.97/2.13 tff(8437,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8438,plain,
% 1.97/2.13 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8439,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8438])).
% 1.97/2.13 tff(8440,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8439, 8437])).
% 1.97/2.13 tff(8441,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8442,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8441, 8440])).
% 1.97/2.13 tff(8443,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8442, 192, 8436, 8404, 7586, 8400, 7584, 7676])).
% 1.97/2.13 tff(8444,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8445,plain,
% 1.97/2.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8444, 504, 115, 308, 396, 1242])).
% 1.97/2.13 tff(8446,plain,
% 1.97/2.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[390, 8445])).
% 1.97/2.13 tff(8447,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7491, 8446, 396, 504, 1242, 7667])).
% 1.97/2.13 tff(8448,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[526, 8447])).
% 1.97/2.13 tff(8449,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8402, 8448, 7667])).
% 1.97/2.13 tff(8450,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[113, 8449])).
% 1.97/2.13 tff(8451,plain,
% 1.97/2.13 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4048, 8450, 396, 1242])).
% 1.97/2.13 tff(8452,plain,
% 1.97/2.13 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[493, 8451])).
% 1.97/2.13 tff(8453,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7010, 8452, 504])).
% 1.97/2.13 tff(8454,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7007, 8453])).
% 1.97/2.13 tff(8455,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4660, 8448, 504])).
% 1.97/2.13 tff(8456,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[217, 8455])).
% 1.97/2.13 tff(8457,plain,
% 1.97/2.13 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8458,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(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))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8457])).
% 1.97/2.13 tff(8459,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(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))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8458, 7681])).
% 1.97/2.13 tff(8460,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(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))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8461,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8460, 8459])).
% 1.97/2.13 tff(8462,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8461, 192, 8456, 6957, 8454, 8450])).
% 1.97/2.13 tff(8463,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.13 tff(8464,plain,
% 1.97/2.13 ((~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (s(elem!1) = s(z))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8463, 7557])).
% 1.97/2.13 tff(8465,plain,
% 1.97/2.13 (s(elem!1) = s(z)),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8464, 7665, 7641, 7560])).
% 1.97/2.13 tff(8466,plain,
% 1.97/2.13 (s(s(elem!1)) = s(s(z))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8465])).
% 1.97/2.13 tff(8467,plain,
% 1.97/2.13 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8466])).
% 1.97/2.13 tff(8468,plain,
% 1.97/2.13 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8467])).
% 1.97/2.13 tff(8469,plain,
% 1.97/2.13 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.97/2.13 inference(symmetry,[status(thm)],[8468])).
% 1.97/2.13 tff(8470,plain,
% 1.97/2.13 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8469])).
% 1.97/2.13 tff(8471,plain,
% 1.97/2.13 (z = elem!1),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[1550, 8465])).
% 1.97/2.13 tff(8472,plain,
% 1.97/2.13 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8471])).
% 1.97/2.13 tff(8473,plain,
% 1.97/2.13 ((~r(z, s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8472])).
% 1.97/2.13 tff(8474,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(z))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[228, 8473])).
% 1.97/2.13 tff(8475,plain,
% 1.97/2.13 (~r(elem!1, s(s(s(elem!1))))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8474, 8470])).
% 1.97/2.13 tff(8476,plain,
% 1.97/2.13 (elem!1 = z),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[2884, 8471])).
% 1.97/2.13 tff(8477,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8478,plain,
% 1.97/2.13 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.13 inference(rewrite,[status(thm)],[])).
% 1.97/2.13 tff(8479,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z)))), s(z)))))),
% 1.97/2.13 inference(monotonicity,[status(thm)],[8478])).
% 1.97/2.13 tff(8480,plain,
% 1.97/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z)))), s(z))))),
% 1.97/2.13 inference(transitivity,[status(thm)],[8479, 8477])).
% 1.97/2.13 tff(8481,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.97/2.13 inference(quant_inst,[status(thm)],[])).
% 1.97/2.13 tff(8482,plain,
% 1.97/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[8481, 8480])).
% 1.97/2.13 tff(8483,plain,
% 1.97/2.13 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8482, 192, 7641, 7643, 6957, 7654])).
% 1.97/2.13 tff(8484,plain,
% 1.97/2.13 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[133, 8483])).
% 1.97/2.13 tff(8485,plain,
% 1.97/2.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7088, 238, 7560, 7654])).
% 1.97/2.13 tff(8486,plain,
% 1.97/2.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[406, 8485])).
% 1.97/2.13 tff(8487,plain,
% 1.97/2.13 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7512, 8486, 8484])).
% 1.97/2.13 tff(8488,plain,
% 1.97/2.13 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[113, 8487])).
% 1.97/2.13 tff(8489,plain,
% 1.97/2.13 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[4048, 8488, 7641, 7560])).
% 1.97/2.13 tff(8490,plain,
% 1.97/2.13 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[493, 8489])).
% 1.97/2.13 tff(8491,plain,
% 1.97/2.13 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7010, 8490, 7665])).
% 1.97/2.13 tff(8492,plain,
% 1.97/2.13 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[7007, 8491])).
% 1.97/2.13 tff(8493,assumption,(~(s(s(s(s(z)))) = s(z))), introduced(assumption)).
% 1.97/2.13 tff(8494,plain,
% 1.97/2.13 (s(s(s(s(z)))) = s(z)),
% 1.97/2.13 inference(modus_ponens,[status(thm)],[204, 202])).
% 1.97/2.13 tff(8495,plain,
% 1.97/2.13 ($false),
% 1.97/2.13 inference(unit_resolution,[status(thm)],[8493, 8494])).
% 1.97/2.13 tff(8496,plain,((~(s(z) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8497,plain,
% 1.97/2.14 (~(s(z) = s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8496, 8493])).
% 1.97/2.14 tff(8498,plain,
% 1.97/2.14 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6288, 2167])).
% 1.97/2.14 tff(8499,plain,
% 1.97/2.14 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6272])).
% 1.97/2.14 tff(8500,plain,
% 1.97/2.14 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8499])).
% 1.97/2.14 tff(8501,plain,
% 1.97/2.14 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8500])).
% 1.97/2.14 tff(8502,plain,
% 1.97/2.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8499])).
% 1.97/2.14 tff(8503,plain,
% 1.97/2.14 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8502, 8501])).
% 1.97/2.14 tff(8504,plain,
% 1.97/2.14 ((~b(s(s(s(z))), s(s(s(s(z)))))) <=> (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8503])).
% 1.97/2.14 tff(8505,plain,
% 1.97/2.14 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[952])).
% 1.97/2.14 tff(8506,plain,
% 1.97/2.14 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8505])).
% 1.97/2.14 tff(8507,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.97/2.14 tff(8508,plain,
% 1.97/2.14 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8507, 8506])).
% 1.97/2.14 tff(8509,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[216, 8493, 7642])).
% 1.97/2.14 tff(8510,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8461, 192, 8509, 7002, 2490])).
% 1.97/2.14 tff(8511,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[111, 60, 8510])).
% 1.97/2.14 tff(8512,plain,
% 1.97/2.14 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8511, 8508])).
% 1.97/2.14 tff(8513,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6246])).
% 1.97/2.14 tff(8514,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(symmetry,[status(thm)],[8513])).
% 1.97/2.14 tff(8515,plain,
% 1.97/2.14 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[2167])).
% 1.97/2.14 tff(8516,plain,
% 1.97/2.14 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.97/2.14 inference(transitivity,[status(thm)],[8515, 331])).
% 1.97/2.14 tff(8517,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8516])).
% 1.97/2.14 tff(8518,plain,
% 1.97/2.14 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.97/2.14 inference(transitivity,[status(thm)],[8517, 3031])).
% 1.97/2.14 tff(8519,plain,
% 1.97/2.14 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8518])).
% 1.97/2.14 tff(8520,plain,
% 1.97/2.14 (~(s(s(s(s(z)))) = elem!1)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[48, 8519])).
% 1.97/2.14 tff(8521,plain,
% 1.97/2.14 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6247])).
% 1.97/2.14 tff(8522,plain,
% 1.97/2.14 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6246])).
% 1.97/2.14 tff(8523,plain,
% 1.97/2.14 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8522])).
% 1.97/2.14 tff(8524,plain,
% 1.97/2.14 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6246])).
% 1.97/2.14 tff(8525,plain,
% 1.97/2.14 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8524, 1978])).
% 1.97/2.14 tff(8526,plain,
% 1.97/2.14 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8525])).
% 1.97/2.14 tff(8527,plain,
% 1.97/2.14 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[266, 8526])).
% 1.97/2.14 tff(8528,plain,
% 1.97/2.14 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[6246])).
% 1.97/2.14 tff(8529,plain,
% 1.97/2.14 ((~b(z, s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8528])).
% 1.97/2.14 tff(8530,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8501, 8502])).
% 1.97/2.14 tff(8531,plain,
% 1.97/2.14 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8530])).
% 1.97/2.14 tff(8532,plain,
% 1.97/2.14 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6788, 8498])).
% 1.97/2.14 tff(8533,plain,
% 1.97/2.14 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8501, 8502])).
% 1.97/2.14 tff(8534,plain,
% 1.97/2.14 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8533])).
% 1.97/2.14 tff(8535,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8536,plain,
% 1.97/2.14 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8537,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8536])).
% 1.97/2.14 tff(8538,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8537, 8535])).
% 1.97/2.14 tff(8539,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8540,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8539, 8538])).
% 1.97/2.14 tff(8541,plain,
% 1.97/2.14 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8540, 192, 396, 2639, 395])).
% 1.97/2.14 tff(8542,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8541, 813])).
% 1.97/2.14 tff(8543,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[373, 60, 102, 8542])).
% 1.97/2.14 tff(8544,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8545,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8546,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8545, 8544])).
% 1.97/2.14 tff(8547,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8546, 77, 2280, 8543])).
% 1.97/2.14 tff(8548,plain,
% 1.97/2.14 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8547, 8534])).
% 1.97/2.14 tff(8549,plain,
% 1.97/2.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8550,plain,
% 1.97/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8551,plain,
% 1.97/2.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8550, 8549])).
% 1.97/2.14 tff(8552,plain,
% 1.97/2.14 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8551, 60])).
% 1.97/2.14 tff(8553,plain,
% 1.97/2.14 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8552, 8548, 8532])).
% 1.97/2.14 tff(8554,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8553, 8531])).
% 1.97/2.14 tff(8555,plain,
% 1.97/2.14 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8502])).
% 1.97/2.14 tff(8556,plain,
% 1.97/2.14 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8555])).
% 1.97/2.14 tff(8557,plain,
% 1.97/2.14 (b(z, s(s(s(z))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[4314, 8556])).
% 1.97/2.14 tff(8558,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7086, 192, 1242, 395, 8557])).
% 1.97/2.14 tff(8559,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8558, 8554])).
% 1.97/2.14 tff(8560,plain,((~b(z, s(s(s(s(s(z))))))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8561,plain,
% 1.97/2.14 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8560, 395, 1242, 2167, 2280, 396, 2639, 4314])).
% 1.97/2.14 tff(8562,plain,
% 1.97/2.14 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8561, 8529])).
% 1.97/2.14 tff(8563,plain,
% 1.97/2.14 (r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[2227, 8562, 8527])).
% 1.97/2.14 tff(8564,plain,
% 1.97/2.14 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8563, 8523])).
% 1.97/2.14 tff(8565,plain,
% 1.97/2.14 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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)))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8566,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8567,plain,
% 1.97/2.14 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8566, 8565])).
% 1.97/2.14 tff(8568,plain,
% 1.97/2.14 ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8567, 77, 2280])).
% 1.97/2.14 tff(8569,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8568, 8564])).
% 1.97/2.14 tff(8570,plain,
% 1.97/2.14 (~r(s(s(s(s(z)))), elem!1)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8569, 8521])).
% 1.97/2.14 tff(8571,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), elem!1)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[3150, 8570, 8520])).
% 1.97/2.14 tff(8572,plain,
% 1.97/2.14 (b(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8571, 8514])).
% 1.97/2.14 tff(8573,plain,
% 1.97/2.14 (~b(s(s(s(s(z)))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7102, 192, 1242, 2639, 395])).
% 1.97/2.14 tff(8574,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8573, 8572])).
% 1.97/2.14 tff(8575,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8576,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8575, 8512, 1242, 2639, 2167, 396, 4314])).
% 1.97/2.14 tff(8577,plain,
% 1.97/2.14 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8576, 8504])).
% 1.97/2.14 tff(8578,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[5001, 8577, 8498])).
% 1.97/2.14 tff(8579,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8502, 8501])).
% 1.97/2.14 tff(8580,plain,
% 1.97/2.14 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(symmetry,[status(thm)],[8579])).
% 1.97/2.14 tff(8581,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[6298, 8580])).
% 1.97/2.14 tff(8582,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8047, 8581])).
% 1.97/2.14 tff(8583,plain,(r(s(s(s(z))), s(s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8584,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8583, 8578, 2167])).
% 1.97/2.14 tff(8585,plain,
% 1.97/2.14 (~r(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[388, 8584, 116])).
% 1.97/2.14 tff(8586,plain,
% 1.97/2.14 (b(s(z), s(s(s(s(z)))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[318, 8585, 8497])).
% 1.97/2.14 tff(8587,plain,
% 1.97/2.14 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8588,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8587])).
% 1.97/2.14 tff(8589,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8588, 7359])).
% 1.97/2.14 tff(8590,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8591,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.97/2.14 inference(modus_ponens,[status(thm)],[8590, 8589])).
% 1.97/2.14 tff(8592,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8591, 192, 396, 8509, 8586, 2490])).
% 1.97/2.14 tff(8593,plain,((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))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8594,plain,
% 1.97/2.14 ((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))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8593, 104])).
% 1.97/2.14 tff(8595,plain,
% 1.97/2.14 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8594, 212])).
% 1.97/2.14 tff(8596,plain,
% 1.97/2.14 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8595, 6957])).
% 1.97/2.14 tff(8597,plain,
% 1.97/2.14 (~b(z, s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8596, 8492, 7641, 7560, 254, 116, 8476, 7642])).
% 1.97/2.14 tff(8598,plain,
% 1.97/2.14 (r(z, s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[1021, 8597])).
% 1.97/2.14 tff(8599,plain,
% 1.97/2.14 (r(elem!1, s(s(s(elem!1))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[6296, 8598, 8476])).
% 1.97/2.14 tff(8600,plain,
% 1.97/2.14 ($false),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8599, 8475])).
% 1.97/2.14 tff(8601,plain,((~r(s(s(s(z))), s(z))) | r(s(s(s(s(z)))), s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.14 tff(8602,plain,
% 1.97/2.14 (~r(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8601, 7642, 37])).
% 1.97/2.14 tff(8603,plain,
% 1.97/2.14 (b(s(s(s(z))), s(z))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[920, 8602])).
% 1.97/2.14 tff(8604,plain,
% 1.97/2.14 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[7649, 192, 396, 1242, 512, 6957])).
% 1.97/2.14 tff(8605,plain,
% 1.97/2.14 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[271, 8604])).
% 1.97/2.14 tff(8606,plain,
% 1.97/2.14 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[4708, 192, 396, 512, 1408])).
% 1.97/2.14 tff(8607,plain,
% 1.97/2.14 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[8606, 395])).
% 1.97/2.14 tff(8608,plain,
% 1.97/2.14 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.14 inference(unit_resolution,[status(thm)],[375, 8607])).
% 1.97/2.14 tff(8609,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8610,plain,
% 1.97/2.14 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.14 inference(rewrite,[status(thm)],[])).
% 1.97/2.14 tff(8611,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.14 inference(monotonicity,[status(thm)],[8610])).
% 1.97/2.14 tff(8612,plain,
% 1.97/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.14 inference(transitivity,[status(thm)],[8611, 8609])).
% 1.97/2.14 tff(8613,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.97/2.14 inference(quant_inst,[status(thm)],[])).
% 1.97/2.14 tff(8614,plain,
% 1.97/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8613, 8612])).
% 1.97/2.15 tff(8615,plain,
% 1.97/2.15 ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8614, 192, 1242, 512, 1408])).
% 1.97/2.15 tff(8616,plain,
% 1.97/2.15 (~b(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8615, 395])).
% 1.97/2.15 tff(8617,plain,
% 1.97/2.15 (r(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[253, 8616])).
% 1.97/2.15 tff(8618,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4694, 8617, 8608, 8605])).
% 1.97/2.15 tff(8619,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8620,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8619, 7643, 7560, 8603, 7641])).
% 1.97/2.15 tff(8621,plain,
% 1.97/2.15 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[390, 8620])).
% 1.97/2.15 tff(8622,plain,
% 1.97/2.15 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4718, 7557])).
% 1.97/2.15 tff(8623,plain,
% 1.97/2.15 (~r(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8622, 8621])).
% 1.97/2.15 tff(8624,plain,
% 1.97/2.15 (b(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[427, 8623])).
% 1.97/2.15 tff(8625,plain,
% 1.97/2.15 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6985, 8624, 8603])).
% 1.97/2.15 tff(8626,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[133, 8625])).
% 1.97/2.15 tff(8627,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8402, 2280, 296])).
% 1.97/2.15 tff(8628,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[526, 8627])).
% 1.97/2.15 tff(8629,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7512, 2280, 117])).
% 1.97/2.15 tff(8630,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[406, 8629])).
% 1.97/2.15 tff(8631,plain,
% 1.97/2.15 (~r(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5178, 117, 296])).
% 1.97/2.15 tff(8632,plain,
% 1.97/2.15 (b(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[237, 8631])).
% 1.97/2.15 tff(8633,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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)))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(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)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8634,plain,
% 1.97/2.15 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(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)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8635,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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)))), z)) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8634])).
% 1.97/2.15 tff(8636,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(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)))), z)) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8635, 8633])).
% 1.97/2.15 tff(8637,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8638,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8637, 8636])).
% 1.97/2.15 tff(8639,plain,
% 1.97/2.15 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8638, 192, 1242, 512, 1408, 8632])).
% 1.97/2.15 tff(8640,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8639, 8630, 8628])).
% 1.97/2.15 tff(8641,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8642,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8641, 8626, 7643, 8603, 7560, 7651])).
% 1.97/2.15 tff(8643,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[113, 8642])).
% 1.97/2.15 tff(8644,plain,
% 1.97/2.15 (~r(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5178, 7674, 296])).
% 1.97/2.15 tff(8645,plain,
% 1.97/2.15 (b(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[237, 8644])).
% 1.97/2.15 tff(8646,plain,
% 1.97/2.15 (~b(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7663, 8645, 515, 7584])).
% 1.97/2.15 tff(8647,plain,
% 1.97/2.15 (r(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[253, 8646])).
% 1.97/2.15 tff(8648,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4755, 77, 8647, 296, 7674])).
% 1.97/2.15 tff(8649,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8650,plain,
% 1.97/2.15 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8649, 7557])).
% 1.97/2.15 tff(8651,plain,
% 1.97/2.15 (~b(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8650, 8621, 7651])).
% 1.97/2.15 tff(8652,plain,
% 1.97/2.15 (r(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[351, 8651])).
% 1.97/2.15 tff(8653,plain,
% 1.97/2.15 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4048, 8643, 7641, 7560])).
% 1.97/2.15 tff(8654,plain,
% 1.97/2.15 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[493, 8653])).
% 1.97/2.15 tff(8655,plain,
% 1.97/2.15 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7010, 8654, 8652])).
% 1.97/2.15 tff(8656,plain,
% 1.97/2.15 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7007, 8655])).
% 1.97/2.15 tff(8657,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8461, 192, 7643, 6957, 8656, 8643])).
% 1.97/2.15 tff(8658,plain,(r(s(s(s(s(z)))), s(z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8659,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8658, 37])).
% 1.97/2.15 tff(8660,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1072, 8659, 37])).
% 1.97/2.15 tff(8661,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[526, 8660])).
% 1.97/2.15 tff(8662,plain,
% 1.97/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1753, 8661, 7560, 7641])).
% 1.97/2.15 tff(8663,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[271, 8662])).
% 1.97/2.15 tff(8664,plain,
% 1.97/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1753, 1745, 1242, 396])).
% 1.97/2.15 tff(8665,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[271, 8664])).
% 1.97/2.15 tff(8666,plain,
% 1.97/2.15 (~r(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7491, 395, 396, 1242, 1745, 8665])).
% 1.97/2.15 tff(8667,plain,
% 1.97/2.15 (b(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[351, 8666])).
% 1.97/2.15 tff(8668,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8669,plain,
% 1.97/2.15 (((~b(z, 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(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8670,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8669])).
% 1.97/2.15 tff(8671,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8670, 8668])).
% 1.97/2.15 tff(8672,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8673,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8672, 8671])).
% 1.97/2.15 tff(8674,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8673, 192, 396, 515, 1242, 2490, 239])).
% 1.97/2.15 tff(8675,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8676,plain,
% 1.97/2.15 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8675, 6957])).
% 1.97/2.15 tff(8677,plain,
% 1.97/2.15 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8676, 515, 396, 1242])).
% 1.97/2.15 tff(8678,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[271, 8677])).
% 1.97/2.15 tff(8679,plain,
% 1.97/2.15 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8649, 8678, 515, 308])).
% 1.97/2.15 tff(8680,plain,
% 1.97/2.15 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[390, 8679])).
% 1.97/2.15 tff(8681,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[404, 221, 396, 8680])).
% 1.97/2.15 tff(8682,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[406, 8681])).
% 1.97/2.15 tff(8683,plain,
% 1.97/2.15 (~r(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[417, 8682, 308])).
% 1.97/2.15 tff(8684,plain,
% 1.97/2.15 (b(s(z), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[427, 8683])).
% 1.97/2.15 tff(8685,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8686,plain,
% 1.97/2.15 (((~b(s(s(s(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z))))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8687,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z)))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8686])).
% 1.97/2.15 tff(8688,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(z), s(s(s(z))))))),
% 1.97/2.15 inference(transitivity,[status(thm)],[8687, 8685])).
% 1.97/2.15 tff(8689,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.15 inference(quant_inst,[status(thm)],[])).
% 1.97/2.15 tff(8690,plain,
% 1.97/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8689, 8688])).
% 1.97/2.15 tff(8691,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8690, 192, 396, 515, 1242, 6957, 8680, 8684, 221])).
% 1.97/2.15 tff(8692,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8693,plain,
% 1.97/2.15 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8692, 7557])).
% 1.97/2.15 tff(8694,plain,
% 1.97/2.15 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8693, 8667, 396, 1242])).
% 1.97/2.15 tff(8695,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[133, 8694])).
% 1.97/2.15 tff(8696,plain,
% 1.97/2.15 (~r(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[5178, 8695, 8665])).
% 1.97/2.15 tff(8697,plain,
% 1.97/2.15 (b(z, s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[237, 8696])).
% 1.97/2.15 tff(8698,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[447, 192, 396, 395, 441])).
% 1.97/2.15 tff(8699,plain,
% 1.97/2.15 (~b(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8061, 395, 1242, 441, 1745, 396])).
% 1.97/2.15 tff(8700,plain,
% 1.97/2.15 (r(s(s(s(z))), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[253, 8699])).
% 1.97/2.15 tff(8701,plain,
% 1.97/2.15 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[4692, 77, 8700, 296])).
% 1.97/2.15 tff(8702,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[375, 8701, 8698])).
% 1.97/2.15 tff(8703,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8704,plain,
% 1.97/2.15 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8703, 395, 396, 1745, 1242, 8665])).
% 1.97/2.15 tff(8705,plain,
% 1.97/2.15 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[113, 8704])).
% 1.97/2.15 tff(8706,plain,
% 1.97/2.15 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7512, 8695, 8705])).
% 1.97/2.15 tff(8707,plain,
% 1.97/2.15 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[406, 8706])).
% 1.97/2.15 tff(8708,plain,
% 1.97/2.15 ($false),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[7088, 8707, 8697, 1242, 395])).
% 1.97/2.15 tff(8709,plain,((~b(s(s(s(z))), 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(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.15 tff(8710,plain,
% 1.97/2.15 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8709, 7560, 7641, 8661])).
% 1.97/2.15 tff(8711,plain,
% 1.97/2.15 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[390, 8710])).
% 1.97/2.15 tff(8712,plain,
% 1.97/2.15 (~b(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8650, 8711, 8663])).
% 1.97/2.15 tff(8713,plain,
% 1.97/2.15 (r(s(z), z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[351, 8712])).
% 1.97/2.15 tff(8714,plain,
% 1.97/2.15 (s(elem!1) = s(z)),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8464, 8713, 7641, 7560])).
% 1.97/2.15 tff(8715,plain,
% 1.97/2.15 (z = elem!1),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[1550, 8714])).
% 1.97/2.15 tff(8716,plain,
% 1.97/2.15 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8715])).
% 1.97/2.15 tff(8717,plain,
% 1.97/2.15 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8716])).
% 1.97/2.15 tff(8718,plain,
% 1.97/2.15 (~(s(s(elem!1)) = elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[1076, 8717])).
% 1.97/2.15 tff(8719,plain,
% 1.97/2.15 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8715])).
% 1.97/2.15 tff(8720,plain,
% 1.97/2.15 (r(s(z), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8713, 8719])).
% 1.97/2.15 tff(8721,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8715])).
% 1.97/2.15 tff(8722,plain,
% 1.97/2.15 (r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.15 inference(modus_ponens,[status(thm)],[8663, 8721])).
% 1.97/2.15 tff(8723,plain,
% 1.97/2.15 ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6356, 77, 6597])).
% 1.97/2.15 tff(8724,plain,
% 1.97/2.15 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8723, 5917])).
% 1.97/2.15 tff(8725,plain,
% 1.97/2.15 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6360, 60, 3070, 8724])).
% 1.97/2.15 tff(8726,plain,
% 1.97/2.15 ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6029, 77, 5431])).
% 1.97/2.15 tff(8727,plain,
% 1.97/2.15 (~r(s(s(z)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8726, 5917])).
% 1.97/2.15 tff(8728,plain,
% 1.97/2.15 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6033, 60, 8727])).
% 1.97/2.15 tff(8729,plain,
% 1.97/2.15 (b(s(s(z)), s(z))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8728, 5847])).
% 1.97/2.15 tff(8730,plain,
% 1.97/2.15 ((~r(s(z), s(s(z)))) | (~r(s(s(z)), elem!1))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6088, 77, 5431])).
% 1.97/2.15 tff(8731,plain,
% 1.97/2.15 (~r(s(z), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[8730, 5917])).
% 1.97/2.15 tff(8732,plain,
% 1.97/2.15 (b(s(z), s(s(z)))),
% 1.97/2.15 inference(unit_resolution,[status(thm)],[6092, 60, 2196, 8731])).
% 1.97/2.15 tff(8733,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8734,plain,
% 1.97/2.15 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.97/2.15 inference(rewrite,[status(thm)],[])).
% 1.97/2.15 tff(8735,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 1.97/2.15 inference(monotonicity,[status(thm)],[8734])).
% 1.97/2.15 tff(8736,plain,
% 1.97/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8735, 8733])).
% 1.97/2.16 tff(8737,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8738,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8737, 8736])).
% 1.97/2.16 tff(8739,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8738, 192, 2490, 8732, 8729, 8725])).
% 1.97/2.16 tff(8740,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8741,plain,
% 1.97/2.16 ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8740, 6957])).
% 1.97/2.16 tff(8742,plain,
% 1.97/2.16 (~r(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8741, 8722, 8720])).
% 1.97/2.16 tff(8743,plain,
% 1.97/2.16 (~r(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6025, 8742, 8714])).
% 1.97/2.16 tff(8744,plain,
% 1.97/2.16 (b(s(s(elem!1)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5931, 8743, 8718])).
% 1.97/2.16 tff(8745,plain,
% 1.97/2.16 (b(s(s(z)), elem!1)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6417, 8744, 8714])).
% 1.97/2.16 tff(8746,plain,
% 1.97/2.16 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8715])).
% 1.97/2.16 tff(8747,plain,
% 1.97/2.16 (elem!1 = z),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[2884, 8715])).
% 1.97/2.16 tff(8748,plain,
% 1.97/2.16 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8714])).
% 1.97/2.16 tff(8749,plain,
% 1.97/2.16 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8748])).
% 1.97/2.16 tff(8750,plain,
% 1.97/2.16 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8749])).
% 1.97/2.16 tff(8751,plain,
% 1.97/2.16 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[1307, 8750])).
% 1.97/2.16 tff(8752,plain,
% 1.97/2.16 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8502])).
% 1.97/2.16 tff(8753,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8752])).
% 1.97/2.16 tff(8754,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2168])).
% 1.97/2.16 tff(8755,plain,
% 1.97/2.16 (s(z) = s(elem!1)),
% 1.97/2.16 inference(symmetry,[status(thm)],[2168])).
% 1.97/2.16 tff(8756,plain,
% 1.97/2.16 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8502, 8755])).
% 1.97/2.16 tff(8757,plain,
% 1.97/2.16 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(elem!1))), s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8756])).
% 1.97/2.16 tff(8758,plain,
% 1.97/2.16 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[507, 77, 504])).
% 1.97/2.16 tff(8759,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8758, 503])).
% 1.97/2.16 tff(8760,plain,
% 1.97/2.16 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8759, 8757])).
% 1.97/2.16 tff(8761,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[679, 8760, 3104])).
% 1.97/2.16 tff(8762,plain,
% 1.97/2.16 (b(s(s(s(elem!1))), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8761, 8754])).
% 1.97/2.16 tff(8763,plain,
% 1.97/2.16 (b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8762, 8753])).
% 1.97/2.16 tff(8764,plain,
% 1.97/2.16 ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4692, 77, 296])).
% 1.97/2.16 tff(8765,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8764, 503])).
% 1.97/2.16 tff(8766,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[373, 60, 102, 8765])).
% 1.97/2.16 tff(8767,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8755])).
% 1.97/2.16 tff(8768,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8767])).
% 1.97/2.16 tff(8769,plain,
% 1.97/2.16 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[2168])).
% 1.97/2.16 tff(8770,plain,
% 1.97/2.16 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 1.97/2.16 inference(symmetry,[status(thm)],[8769])).
% 1.97/2.16 tff(8771,plain,
% 1.97/2.16 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(s(s(s(s(z))))) = s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8770])).
% 1.97/2.16 tff(8772,plain,
% 1.97/2.16 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[50, 8771])).
% 1.97/2.16 tff(8773,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8755])).
% 1.97/2.16 tff(8774,plain,
% 1.97/2.16 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(s(z))))), s(elem!1)))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8773])).
% 1.97/2.16 tff(8775,plain,
% 1.97/2.16 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[355, 77, 504])).
% 1.97/2.16 tff(8776,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8775, 296])).
% 1.97/2.16 tff(8777,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8776, 8774])).
% 1.97/2.16 tff(8778,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[597, 8777, 8772])).
% 1.97/2.16 tff(8779,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8778, 8768])).
% 1.97/2.16 tff(8780,plain,
% 1.97/2.16 ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7070, 77, 504])).
% 1.97/2.16 tff(8781,plain,
% 1.97/2.16 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8780, 296])).
% 1.97/2.16 tff(8782,plain,
% 1.97/2.16 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[438, 60, 8781])).
% 1.97/2.16 tff(8783,plain,
% 1.97/2.16 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8782, 609])).
% 1.97/2.16 tff(8784,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7312, 192, 8783, 8779, 8766])).
% 1.97/2.16 tff(8785,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8784, 8763])).
% 1.97/2.16 tff(8786,plain,((~r(s(s(s(z))), z)) | (~(elem!1 = z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8787,plain,
% 1.97/2.16 (~r(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8786, 8751, 8663, 8713, 8747])).
% 1.97/2.16 tff(8788,plain,
% 1.97/2.16 (b(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[253, 8787])).
% 1.97/2.16 tff(8789,plain,
% 1.97/2.16 (b(s(s(s(z))), elem!1)),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8788, 8746])).
% 1.97/2.16 tff(8790,plain,
% 1.97/2.16 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8715])).
% 1.97/2.16 tff(8791,plain,
% 1.97/2.16 (~r(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8622, 8711])).
% 1.97/2.16 tff(8792,plain,
% 1.97/2.16 (b(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[427, 8791])).
% 1.97/2.16 tff(8793,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7316, 8711, 8659])).
% 1.97/2.16 tff(8794,plain,
% 1.97/2.16 (b(s(s(s(z))), s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[920, 8793])).
% 1.97/2.16 tff(8795,plain,
% 1.97/2.16 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6985, 8794, 8792])).
% 1.97/2.16 tff(8796,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[133, 8795])).
% 1.97/2.16 tff(8797,plain,
% 1.97/2.16 (~r(z, s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5178, 8796, 8663])).
% 1.97/2.16 tff(8798,plain,
% 1.97/2.16 (b(z, s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[237, 8797])).
% 1.97/2.16 tff(8799,plain,
% 1.97/2.16 (b(elem!1, s(s(s(z))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8798, 8790])).
% 1.97/2.16 tff(8800,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8801,plain,
% 1.97/2.16 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8802,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8801])).
% 1.97/2.16 tff(8803,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8802, 8800])).
% 1.97/2.16 tff(8804,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8805,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8804, 8803])).
% 1.97/2.16 tff(8806,plain,
% 1.97/2.16 (~b(s(s(z)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8805, 192, 8799, 8789, 8745])).
% 1.97/2.16 tff(8807,plain,
% 1.97/2.16 (r(s(s(z)), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5965, 60, 8806, 36])).
% 1.97/2.16 tff(8808,plain,
% 1.97/2.16 (b(s(s(z)), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5938, 8744, 8714])).
% 1.97/2.16 tff(8809,plain,
% 1.97/2.16 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6135, 8808, 8661, 7560])).
% 1.97/2.16 tff(8810,plain,
% 1.97/2.16 (r(s(s(z)), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5381, 8809])).
% 1.97/2.16 tff(8811,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8313, 77, 8711, 8810, 8807])).
% 1.97/2.16 tff(8812,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8813,plain,
% 1.97/2.16 (b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[292, 8812])).
% 1.97/2.16 tff(8814,plain,
% 1.97/2.16 ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4017, 7557])).
% 1.97/2.16 tff(8815,plain,
% 1.97/2.16 (~r(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8814, 321])).
% 1.97/2.16 tff(8816,plain,
% 1.97/2.16 (b(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[351, 8815])).
% 1.97/2.16 tff(8817,plain,
% 1.97/2.16 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6993, 8816, 8813])).
% 1.97/2.16 tff(8818,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[271, 8817])).
% 1.97/2.16 tff(8819,plain,
% 1.97/2.16 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8650, 8818, 8816])).
% 1.97/2.16 tff(8820,plain,
% 1.97/2.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[390, 8819])).
% 1.97/2.16 tff(8821,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[329, 321, 170])).
% 1.97/2.16 tff(8822,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[271, 8821])).
% 1.97/2.16 tff(8823,plain,
% 1.97/2.16 (~r(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4038, 321, 308])).
% 1.97/2.16 tff(8824,plain,
% 1.97/2.16 (b(z, s(z))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[292, 8823])).
% 1.97/2.16 tff(8825,plain,
% 1.97/2.16 (~r(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4017, 321, 308])).
% 1.97/2.16 tff(8826,plain,
% 1.97/2.16 (b(s(z), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[351, 8825])).
% 1.97/2.16 tff(8827,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[6993, 8826, 8824, 8822])).
% 1.97/2.16 tff(8828,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8829,plain,
% 1.97/2.16 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8828, 7557])).
% 1.97/2.16 tff(8830,plain,
% 1.97/2.16 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8829, 321])).
% 1.97/2.16 tff(8831,plain,
% 1.97/2.16 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[181, 8830])).
% 1.97/2.16 tff(8832,plain,
% 1.97/2.16 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[404, 221, 396, 395])).
% 1.97/2.16 tff(8833,plain,
% 1.97/2.16 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[406, 8832])).
% 1.97/2.16 tff(8834,plain,
% 1.97/2.16 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[417, 7557])).
% 1.97/2.16 tff(8835,plain,
% 1.97/2.16 (~r(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8834, 8833])).
% 1.97/2.16 tff(8836,plain,
% 1.97/2.16 (b(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[427, 8835])).
% 1.97/2.16 tff(8837,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8838,plain,
% 1.97/2.16 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8839,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z), s(s(s(z)))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8838])).
% 1.97/2.16 tff(8840,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(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(z), s(s(s(z))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8839, 8837])).
% 1.97/2.16 tff(8841,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8842,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8841, 8840])).
% 1.97/2.16 tff(8843,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8842, 192, 396, 6957, 395, 8836, 221])).
% 1.97/2.16 tff(8844,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8845,plain,
% 1.97/2.16 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8844, 8831, 8820])).
% 1.97/2.16 tff(8846,plain,
% 1.97/2.16 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[133, 8845])).
% 1.97/2.16 tff(8847,plain,
% 1.97/2.16 (~r(z, s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[5178, 8846, 8818])).
% 1.97/2.16 tff(8848,plain,
% 1.97/2.16 (b(z, s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[237, 8847])).
% 1.97/2.16 tff(8849,plain,
% 1.97/2.16 ($false),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4755, 77, 503, 296, 117])).
% 1.97/2.16 tff(8850,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.16 tff(8851,plain,
% 1.97/2.16 (~r(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8850, 8818, 8846])).
% 1.97/2.16 tff(8852,plain,
% 1.97/2.16 (b(s(s(s(z))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[253, 8851])).
% 1.97/2.16 tff(8853,plain,
% 1.97/2.16 (~b(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7663, 8852, 8816, 8848])).
% 1.97/2.16 tff(8854,plain,
% 1.97/2.16 (r(s(z), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[427, 8853])).
% 1.97/2.16 tff(8855,plain,
% 1.97/2.16 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8834, 8854])).
% 1.97/2.16 tff(8856,plain,
% 1.97/2.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[406, 8855])).
% 1.97/2.16 tff(8857,plain,
% 1.97/2.16 (~b(s(s(s(s(z)))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[7254, 192, 8852, 8820, 8856, 8848])).
% 1.97/2.16 tff(8858,plain,
% 1.97/2.16 (r(s(s(s(s(z)))), z)),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[526, 8857])).
% 1.97/2.16 tff(8859,plain,
% 1.97/2.16 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8402, 8858, 8818])).
% 1.97/2.16 tff(8860,plain,
% 1.97/2.16 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[113, 8859])).
% 1.97/2.16 tff(8861,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8862,plain,
% 1.97/2.16 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.16 tff(8863,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.97/2.16 inference(monotonicity,[status(thm)],[8862])).
% 1.97/2.16 tff(8864,plain,
% 1.97/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.16 inference(transitivity,[status(thm)],[8863, 8861])).
% 1.97/2.16 tff(8865,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.16 inference(quant_inst,[status(thm)],[])).
% 1.97/2.16 tff(8866,plain,
% 1.97/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.97/2.16 inference(modus_ponens,[status(thm)],[8865, 8864])).
% 1.97/2.16 tff(8867,plain,
% 1.97/2.16 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[8866, 192, 396, 441, 7203])).
% 1.97/2.16 tff(8868,plain,
% 1.97/2.16 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[4466, 60, 8867, 4424])).
% 1.97/2.16 tff(8869,plain,
% 1.97/2.16 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[449, 441, 396, 395])).
% 1.97/2.16 tff(8870,plain,
% 1.97/2.16 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.16 inference(unit_resolution,[status(thm)],[375, 8869])).
% 1.97/2.16 tff(8871,plain,
% 1.97/2.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.16 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8872,plain,
% 1.97/2.17 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8873,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8872])).
% 1.97/2.17 tff(8874,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8873, 8871])).
% 1.97/2.17 tff(8875,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8876,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8875, 8874])).
% 1.97/2.17 tff(8877,plain,
% 1.97/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8876, 77, 8870, 8868])).
% 1.97/2.17 tff(8878,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8879,plain,
% 1.97/2.17 (((~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(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8880,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8879])).
% 1.97/2.17 tff(8881,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8880, 8878])).
% 1.97/2.17 tff(8882,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8883,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8882, 8881])).
% 1.97/2.17 tff(8884,plain,
% 1.97/2.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8883, 192, 396, 395, 441, 394, 7203])).
% 1.97/2.17 tff(8885,plain,
% 1.97/2.17 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4440, 60, 8884])).
% 1.97/2.17 tff(8886,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8885, 8877, 4432])).
% 1.97/2.17 tff(8887,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8888,plain,
% 1.97/2.17 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8887, 8831, 8820, 8860, 8856])).
% 1.97/2.17 tff(8889,plain,
% 1.97/2.17 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7581, 8888])).
% 1.97/2.17 tff(8890,plain,
% 1.97/2.17 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4080, 77, 321, 8889])).
% 1.97/2.17 tff(8891,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4086, 60, 4083, 8890])).
% 1.97/2.17 tff(8892,plain,
% 1.97/2.17 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7566, 77, 7557, 8889])).
% 1.97/2.17 tff(8893,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7219, 60, 7216, 8892])).
% 1.97/2.17 tff(8894,plain,
% 1.97/2.17 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4093, 77, 321, 8889])).
% 1.97/2.17 tff(8895,plain,
% 1.97/2.17 (b(z, s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[4103, 8894])).
% 1.97/2.17 tff(8896,assumption,(r(s(z), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.97/2.17 tff(8897,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8898,plain,
% 1.97/2.17 (((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8899,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8898])).
% 1.97/2.17 tff(8900,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8899, 8897])).
% 1.97/2.17 tff(8901,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8902,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8901, 8900])).
% 1.97/2.17 tff(8903,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8902, 77, 308, 8896, 4077])).
% 1.97/2.17 tff(8904,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8905,plain,
% 1.97/2.17 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8904, 7557])).
% 1.97/2.17 tff(8906,plain,
% 1.97/2.17 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8905, 8889])).
% 1.97/2.17 tff(8907,plain,
% 1.97/2.17 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(commutativity,[status(thm)],[])).
% 1.97/2.17 tff(8908,plain,
% 1.97/2.17 ((~(s(s(s(s(s(s(s(z))))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8907])).
% 1.97/2.17 tff(8909,plain,
% 1.97/2.17 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[7216, 8908])).
% 1.97/2.17 tff(8910,plain,
% 1.97/2.17 (b(s(z), s(s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2762, 8909])).
% 1.97/2.17 tff(8911,plain,
% 1.97/2.17 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8910, 8906])).
% 1.97/2.17 tff(8912,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8913,plain,
% 1.97/2.17 (((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8914,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8913])).
% 1.97/2.17 tff(8915,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8914, 8912])).
% 1.97/2.17 tff(8916,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8917,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8916, 8915])).
% 1.97/2.17 tff(8918,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8917, 192, 8816, 8911, 8895, 8893, 8891])).
% 1.97/2.17 tff(8919,plain,(~r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8920,plain,
% 1.97/2.17 (b(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[339, 8919])).
% 1.97/2.17 tff(8921,plain,
% 1.97/2.17 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7569, 295])).
% 1.97/2.17 tff(8922,plain,
% 1.97/2.17 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7007, 8921])).
% 1.97/2.17 tff(8923,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8924,plain,
% 1.97/2.17 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8925,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8924])).
% 1.97/2.17 tff(8926,plain,
% 1.97/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[8925, 8923])).
% 1.97/2.17 tff(8927,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8928,plain,
% 1.97/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8927, 8926])).
% 1.97/2.17 tff(8929,plain,
% 1.97/2.17 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8928, 192, 8813, 6957, 8922])).
% 1.97/2.17 tff(8930,plain,
% 1.97/2.17 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[493, 8929])).
% 1.97/2.17 tff(8931,plain,
% 1.97/2.17 (~b(z, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7088, 6966, 8920, 7599])).
% 1.97/2.17 tff(8932,plain,
% 1.97/2.17 (r(z, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[237, 8931])).
% 1.97/2.17 tff(8933,plain,
% 1.97/2.17 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8928, 192, 8813, 6957, 7571])).
% 1.97/2.17 tff(8934,plain,
% 1.97/2.17 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[493, 8933])).
% 1.97/2.17 tff(8935,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5313, 77, 8934, 8932, 117])).
% 1.97/2.17 tff(8936,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8937,plain,
% 1.97/2.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8936, 295])).
% 1.97/2.17 tff(8938,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[133, 8937])).
% 1.97/2.17 tff(8939,plain,
% 1.97/2.17 ((s(s(s(s(s(s(s(z))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(commutativity,[status(thm)],[])).
% 1.97/2.17 tff(8940,plain,
% 1.97/2.17 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 1.97/2.17 inference(symmetry,[status(thm)],[8939])).
% 1.97/2.17 tff(8941,plain,
% 1.97/2.17 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[627, 295, 308])).
% 1.97/2.17 tff(8942,plain,
% 1.97/2.17 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[438, 60, 8941, 380])).
% 1.97/2.17 tff(8943,plain,
% 1.97/2.17 (~b(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8928, 192, 465, 6957, 8942])).
% 1.97/2.17 tff(8944,plain,
% 1.97/2.17 (r(z, s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[493, 8943])).
% 1.97/2.17 tff(8945,plain,
% 1.97/2.17 (~r(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8828, 295, 308])).
% 1.97/2.17 tff(8946,plain,
% 1.97/2.17 (b(z, s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[339, 8945])).
% 1.97/2.17 tff(8947,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7596, 295, 308])).
% 1.97/2.17 tff(8948,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[390, 8947])).
% 1.97/2.17 tff(8949,plain,
% 1.97/2.17 (~b(z, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7088, 5227, 8948, 8946])).
% 1.97/2.17 tff(8950,plain,
% 1.97/2.17 (r(z, s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[237, 8949])).
% 1.97/2.17 tff(8951,plain,
% 1.97/2.17 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[5264, 8950, 8944])).
% 1.97/2.17 tff(8952,plain,
% 1.97/2.17 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[375, 8951])).
% 1.97/2.17 tff(8953,plain,
% 1.97/2.17 (~r(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7164, 77, 408, 8950])).
% 1.97/2.17 tff(8954,plain,
% 1.97/2.17 (b(s(z), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[351, 8953])).
% 1.97/2.17 tff(8955,plain,
% 1.97/2.17 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6993, 8954, 465])).
% 1.97/2.17 tff(8956,plain,
% 1.97/2.17 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[271, 8955])).
% 1.97/2.17 tff(8957,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[302, 8956, 295])).
% 1.97/2.17 tff(8958,plain,
% 1.97/2.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[7168, 8950, 408])).
% 1.97/2.17 tff(8959,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[133, 8958])).
% 1.97/2.17 tff(8960,plain,
% 1.97/2.17 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[853, 849])).
% 1.97/2.17 tff(8961,plain,
% 1.97/2.17 (s(elem!1) = s(s(s(s(s(z)))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[752, 8960])).
% 1.97/2.17 tff(8962,plain,
% 1.97/2.17 (~b(s(s(s(s(s(z))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[6993, 515, 465])).
% 1.97/2.17 tff(8963,plain,
% 1.97/2.17 (r(s(s(s(s(s(z))))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[271, 8962])).
% 1.97/2.17 tff(8964,plain,
% 1.97/2.17 (~b(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3263, 8960, 8962])).
% 1.97/2.17 tff(8965,plain,
% 1.97/2.17 (r(s(elem!1), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[560, 8964])).
% 1.97/2.17 tff(8966,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[2301, 4425])).
% 1.97/2.17 tff(8967,plain,
% 1.97/2.17 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[8966])).
% 1.97/2.17 tff(8968,plain,
% 1.97/2.17 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.97/2.17 inference(transitivity,[status(thm)],[2317, 704])).
% 1.97/2.17 tff(8969,plain,
% 1.97/2.17 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8968])).
% 1.97/2.17 tff(8970,plain,
% 1.97/2.17 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[4133, 8969])).
% 1.97/2.17 tff(8971,plain,
% 1.97/2.17 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.97/2.17 inference(rewrite,[status(thm)],[])).
% 1.97/2.17 tff(8972,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.97/2.17 inference(quant_inst,[status(thm)],[])).
% 1.97/2.17 tff(8973,plain,
% 1.97/2.17 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8972, 8971])).
% 1.97/2.17 tff(8974,plain,
% 1.97/2.17 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8973, 77, 545, 974])).
% 1.97/2.17 tff(8975,plain,
% 1.97/2.17 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[3232, 60, 8974])).
% 1.97/2.17 tff(8976,plain,
% 1.97/2.17 (b(s(elem!1), s(s(s(elem!1))))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8975, 8970])).
% 1.97/2.17 tff(8977,plain,
% 1.97/2.17 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8976, 8967])).
% 1.97/2.17 tff(8978,plain,
% 1.97/2.17 ((z = elem!1) <=> (z = s(s(s(s(z)))))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[1433])).
% 1.97/2.17 tff(8979,plain,
% 1.97/2.17 ((z = elem!1) <=> (s(s(s(s(z)))) = z)),
% 1.97/2.17 inference(transitivity,[status(thm)],[8978, 331])).
% 1.97/2.17 tff(8980,plain,
% 1.97/2.17 ((s(s(s(s(z)))) = z) <=> (z = elem!1)),
% 1.97/2.17 inference(symmetry,[status(thm)],[8979])).
% 1.97/2.17 tff(8981,plain,
% 1.97/2.17 ((s(s(s(s(z)))) = z) <=> (elem!1 = z)),
% 1.97/2.17 inference(transitivity,[status(thm)],[8980, 2880])).
% 1.97/2.17 tff(8982,plain,
% 1.97/2.17 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8981])).
% 1.97/2.17 tff(8983,plain,
% 1.97/2.17 (~(elem!1 = z)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[48, 8982])).
% 1.97/2.17 tff(8984,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), z) <=> r(elem!1, z)),
% 1.97/2.17 inference(monotonicity,[status(thm)],[2277])).
% 1.97/2.17 tff(8985,plain,
% 1.97/2.17 (r(elem!1, z) <=> r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(symmetry,[status(thm)],[8984])).
% 1.97/2.17 tff(8986,plain,
% 1.97/2.17 (r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[3199, 8985])).
% 1.97/2.17 tff(8987,plain,
% 1.97/2.17 (~r(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[300, 77, 170, 296])).
% 1.97/2.17 tff(8988,plain,
% 1.97/2.17 ($false),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8987, 8986])).
% 1.97/2.17 tff(8989,plain,((~r(elem!1, z)) | (~(s(elem!1) = 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))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.17 tff(8990,plain,
% 1.97/2.17 (~r(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[8989, 723, 295, 296])).
% 1.97/2.17 tff(8991,plain,
% 1.97/2.17 (b(elem!1, z)),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[2354, 8990, 8983])).
% 1.97/2.17 tff(8992,plain,
% 1.97/2.17 (b(s(s(s(s(z)))), z)),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[8991, 1434])).
% 1.97/2.17 tff(8993,plain,
% 1.97/2.17 (r(s(s(s(s(s(s(s(z))))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.17 tff(8994,plain,
% 1.97/2.17 ((s(s(s(s(s(s(s(z))))))) = s(z)) <=> (s(s(s(elem!1))) = s(z))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.17 tff(8995,plain,
% 1.97/2.17 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.97/2.17 inference(symmetry,[status(thm)],[8994])).
% 1.97/2.17 tff(8996,plain,
% 1.97/2.17 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(s(s(s(s(z))))))) = s(z)))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[8995])).
% 1.97/2.17 tff(8997,plain,
% 1.97/2.17 (~(s(s(s(s(s(s(s(z))))))) = s(z))),
% 1.97/2.17 inference(modus_ponens,[status(thm)],[1307, 8996])).
% 1.97/2.17 tff(8998,plain,
% 1.97/2.17 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.17 inference(monotonicity,[status(thm)],[4425, 2301])).
% 1.97/2.17 tff(8999,plain,
% 1.97/2.17 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.17 inference(symmetry,[status(thm)],[8998])).
% 1.97/2.17 tff(9000,plain,
% 1.97/2.17 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.17 inference(unit_resolution,[status(thm)],[1683, 77, 545, 974])).
% 1.97/2.17 tff(9001,plain,
% 1.97/2.17 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[2317])).
% 1.97/2.18 tff(9002,plain,
% 1.97/2.18 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[4133, 9001])).
% 1.97/2.18 tff(9003,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[679, 9002, 9000])).
% 1.97/2.18 tff(9004,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9003, 8999])).
% 1.97/2.18 tff(9005,plain,
% 1.97/2.18 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[1433])).
% 1.97/2.18 tff(9006,plain,
% 1.97/2.18 ((s(z) = elem!1) <=> (s(z) = s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[1433])).
% 1.97/2.18 tff(9007,plain,
% 1.97/2.18 ((s(z) = elem!1) <=> (s(s(s(s(z)))) = s(z))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9006, 202])).
% 1.97/2.18 tff(9008,plain,
% 1.97/2.18 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9007])).
% 1.97/2.18 tff(9009,plain,
% 1.97/2.18 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9008])).
% 1.97/2.18 tff(9010,plain,
% 1.97/2.18 (~(s(z) = elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[212, 9009])).
% 1.97/2.18 tff(9011,plain,
% 1.97/2.18 (b(z, elem!1) <=> b(z, s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[1433])).
% 1.97/2.18 tff(9012,plain,
% 1.97/2.18 (b(z, s(s(s(s(z))))) <=> b(z, elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9011])).
% 1.97/2.18 tff(9013,plain,
% 1.97/2.18 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2125, 723, 294])).
% 1.97/2.18 tff(9014,plain,
% 1.97/2.18 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[1613, 723])).
% 1.97/2.18 tff(9015,plain,
% 1.97/2.18 (r(s(elem!1), s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[535, 9014, 9013])).
% 1.97/2.18 tff(9016,plain,
% 1.97/2.18 (~r(z, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[553, 9015, 545])).
% 1.97/2.18 tff(9017,plain,
% 1.97/2.18 (b(z, s(s(s(s(z)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[339, 9016])).
% 1.97/2.18 tff(9018,plain,
% 1.97/2.18 (b(z, elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9017, 9012])).
% 1.97/2.18 tff(9019,plain,
% 1.97/2.18 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[723])).
% 1.97/2.18 tff(9020,plain,
% 1.97/2.18 ((s(s(s(s(s(z))))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9019])).
% 1.97/2.18 tff(9021,plain,
% 1.97/2.18 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9020])).
% 1.97/2.18 tff(9022,plain,
% 1.97/2.18 (~(s(elem!1) = s(z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[50, 9021])).
% 1.97/2.18 tff(9023,plain,
% 1.97/2.18 (r(s(elem!1), elem!1) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[723])).
% 1.97/2.18 tff(9024,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(elem!1), elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9023])).
% 1.97/2.18 tff(9025,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[1433])).
% 1.97/2.18 tff(9026,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9025])).
% 1.97/2.18 tff(9027,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(elem!1), elem!1)),
% 1.97/2.18 inference(transitivity,[status(thm)],[9026, 9024])).
% 1.97/2.18 tff(9028,plain,
% 1.97/2.18 (r(s(elem!1), elem!1)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[295, 9027])).
% 1.97/2.18 tff(9029,plain,
% 1.97/2.18 (~b(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3887, 2199, 2898, 1435])).
% 1.97/2.18 tff(9030,plain,
% 1.97/2.18 (r(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5427, 9029, 8135])).
% 1.97/2.18 tff(9031,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9032,plain,
% 1.97/2.18 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9033,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9032])).
% 1.97/2.18 tff(9034,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9033, 9031])).
% 1.97/2.18 tff(9035,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9036,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9035, 9034])).
% 1.97/2.18 tff(9037,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9036, 77, 1618, 9030, 668])).
% 1.97/2.18 tff(9038,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(9039,plain,
% 1.97/2.18 (~r(s(elem!1), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9038, 8991, 9028, 9010, 545, 9018])).
% 1.97/2.18 tff(9040,plain,
% 1.97/2.18 (b(s(elem!1), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[950, 9039, 9022])).
% 1.97/2.18 tff(9041,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[959, 9040, 723])).
% 1.97/2.18 tff(9042,plain,
% 1.97/2.18 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(z) = s(s(s(elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9043,plain,
% 1.97/2.18 ((s(z) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(elem!1))) = s(z))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9042, 1657])).
% 1.97/2.18 tff(9044,plain,
% 1.97/2.18 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9043])).
% 1.97/2.18 tff(9045,plain,
% 1.97/2.18 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9044])).
% 1.97/2.18 tff(9046,plain,
% 1.97/2.18 (~(s(z) = s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[1307, 9045])).
% 1.97/2.18 tff(9047,assumption,(b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.97/2.18 tff(9048,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.97/2.18 tff(9049,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9050,plain,
% 1.97/2.18 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9051,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9050])).
% 1.97/2.18 tff(9052,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9051, 9049])).
% 1.97/2.18 tff(9053,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9054,plain,
% 1.97/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9053, 9052])).
% 1.97/2.18 tff(9055,plain,
% 1.97/2.18 (~b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9054, 192, 2490, 7488, 9048, 9047])).
% 1.97/2.18 tff(9056,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(s(z))))))), z) <=> r(s(s(s(elem!1))), z)),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9057,plain,
% 1.97/2.18 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(s(s(s(z))))))), z)),
% 1.97/2.18 inference(symmetry,[status(thm)],[9056])).
% 1.97/2.18 tff(9058,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(s(z))))))), z)),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[974, 9057])).
% 1.97/2.18 tff(9059,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9060,plain,
% 1.97/2.18 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9061,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9060])).
% 1.97/2.18 tff(9062,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9061, 9059])).
% 1.97/2.18 tff(9063,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9064,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9063, 9062])).
% 1.97/2.18 tff(9065,plain,
% 1.97/2.18 ((~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9064, 77, 504])).
% 1.97/2.18 tff(9066,plain,
% 1.97/2.18 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9065, 9058])).
% 1.97/2.18 tff(9067,plain,
% 1.97/2.18 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[2761, 60, 9066])).
% 1.97/2.18 tff(9068,plain,
% 1.97/2.18 ($false),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9067, 9055, 9046])).
% 1.97/2.18 tff(9069,plain,((~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.18 tff(9070,plain,
% 1.97/2.18 (~r(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9069, 9041, 8977, 9004, 723, 974, 296])).
% 1.97/2.18 tff(9071,plain,
% 1.97/2.18 (b(s(z), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[351, 9070])).
% 1.97/2.18 tff(9072,plain,
% 1.97/2.18 (~b(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[3887, 9071, 9018, 8991])).
% 1.97/2.18 tff(9073,plain,
% 1.97/2.18 (r(s(z), elem!1)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5427, 9072, 9010])).
% 1.97/2.18 tff(9074,plain,
% 1.97/2.18 (r(s(z), s(s(s(s(z)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9073, 9005])).
% 1.97/2.18 tff(9075,plain,
% 1.97/2.18 (~r(s(z), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[625, 77, 295, 9074])).
% 1.97/2.18 tff(9076,plain,
% 1.97/2.18 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[438, 60, 9075])).
% 1.97/2.18 tff(9077,plain,
% 1.97/2.18 (b(s(z), s(s(s(s(s(z))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9076, 609])).
% 1.97/2.18 tff(9078,plain,
% 1.97/2.18 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7577, 192, 9041, 9077, 9004])).
% 1.97/2.18 tff(9079,plain,
% 1.97/2.18 ((s(s(s(s(s(s(s(z))))))) = s(z)) | r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[7219, 60, 9078])).
% 1.97/2.18 tff(9080,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9079, 8997])).
% 1.97/2.18 tff(9081,plain,
% 1.97/2.18 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9080, 8993])).
% 1.97/2.18 tff(9082,plain,
% 1.97/2.18 (~r(z, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[982, 9081, 974])).
% 1.97/2.18 tff(9083,plain,
% 1.97/2.18 (b(z, s(z))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[292, 9082])).
% 1.97/2.18 tff(9084,plain,
% 1.97/2.18 (~b(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4911, 723, 9071, 9017, 9083, 8992])).
% 1.97/2.18 tff(9085,plain,
% 1.97/2.18 (r(s(s(s(s(elem!1)))), z)),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4918, 9084])).
% 1.97/2.18 tff(9086,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9087,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9086])).
% 1.97/2.18 tff(9088,plain,
% 1.97/2.18 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[6783])).
% 1.97/2.18 tff(9089,plain,
% 1.97/2.18 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[6799, 9088])).
% 1.97/2.18 tff(9090,plain,
% 1.97/2.18 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9091,plain,
% 1.97/2.18 ((~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9090])).
% 1.97/2.18 tff(9092,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.97/2.18 tff(9093,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9094,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9095,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9094, 9093])).
% 1.97/2.18 tff(9096,plain,
% 1.97/2.18 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9095, 77, 9092])).
% 1.97/2.18 tff(9097,plain,
% 1.97/2.18 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9096, 9058])).
% 1.97/2.18 tff(9098,plain,
% 1.97/2.18 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9097, 9091])).
% 1.97/2.18 tff(9099,plain,
% 1.97/2.18 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[5001, 9098, 9089])).
% 1.97/2.18 tff(9100,plain,
% 1.97/2.18 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9099, 9087])).
% 1.97/2.18 tff(9101,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9102,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9101])).
% 1.97/2.18 tff(9103,plain,
% 1.97/2.18 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[4425])).
% 1.97/2.18 tff(9104,plain,
% 1.97/2.18 ((~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) <=> (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9103])).
% 1.97/2.18 tff(9105,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9106,plain,
% 1.97/2.18 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9107,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9106])).
% 1.97/2.18 tff(9108,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(transitivity,[status(thm)],[9107, 9105])).
% 1.97/2.18 tff(9109,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9110,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9109, 9108])).
% 1.97/2.18 tff(9111,plain,
% 1.97/2.18 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9110, 77, 9092])).
% 1.97/2.18 tff(9112,plain,
% 1.97/2.18 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9111, 9058])).
% 1.97/2.18 tff(9113,plain,
% 1.97/2.18 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9112, 9104])).
% 1.97/2.18 tff(9114,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[8552, 9113, 6799])).
% 1.97/2.18 tff(9115,plain,
% 1.97/2.18 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9114, 9102])).
% 1.97/2.18 tff(9116,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[2301])).
% 1.97/2.18 tff(9117,plain,
% 1.97/2.18 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(symmetry,[status(thm)],[9116])).
% 1.97/2.18 tff(9118,plain,
% 1.97/2.18 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4956, 4127])).
% 1.97/2.18 tff(9119,plain,
% 1.97/2.18 (~(s(elem!1) = s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4961, 9118])).
% 1.97/2.18 tff(9120,plain,
% 1.97/2.18 (r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[2301])).
% 1.97/2.18 tff(9121,plain,
% 1.97/2.18 ((~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) <=> (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(monotonicity,[status(thm)],[9120])).
% 1.97/2.18 tff(9122,plain,
% 1.97/2.18 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(rewrite,[status(thm)],[])).
% 1.97/2.18 tff(9123,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.97/2.18 inference(quant_inst,[status(thm)],[])).
% 1.97/2.18 tff(9124,plain,
% 1.97/2.18 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9123, 9122])).
% 1.97/2.18 tff(9125,plain,
% 1.97/2.18 (~r(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[9124, 77, 9092, 296])).
% 1.97/2.18 tff(9126,plain,
% 1.97/2.18 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9125, 9121])).
% 1.97/2.18 tff(9127,plain,
% 1.97/2.18 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(unit_resolution,[status(thm)],[4973, 9126, 9119])).
% 1.97/2.18 tff(9128,plain,
% 1.97/2.18 (b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))),
% 1.97/2.18 inference(modus_ponens,[status(thm)],[9127, 9117])).
% 1.97/2.18 tff(9129,plain,
% 1.97/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9130,plain,
% 1.97/2.19 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9131,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9130])).
% 1.97/2.19 tff(9132,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9131, 9129])).
% 1.97/2.19 tff(9133,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9134,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(z)))))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9133, 9132])).
% 1.97/2.19 tff(9135,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9134, 192, 9048, 9128, 9115, 9100])).
% 1.97/2.19 tff(9136,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~(s(elem!1) = s(s(s(s(s(z))))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9137,plain,
% 1.97/2.19 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9136, 9085, 723, 8977, 974, 296])).
% 1.97/2.19 tff(9138,plain,
% 1.97/2.19 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9137])).
% 1.97/2.19 tff(9139,plain,
% 1.97/2.19 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(elem!1))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[4425, 9138])).
% 1.97/2.19 tff(9140,plain,
% 1.97/2.19 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(s(s(s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9139])).
% 1.97/2.19 tff(9141,plain,
% 1.97/2.19 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[7213, 9140, 727, 725])).
% 1.97/2.19 tff(9142,plain,
% 1.97/2.19 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9141])).
% 1.97/2.19 tff(9143,plain,
% 1.97/2.19 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.97/2.19 inference(transitivity,[status(thm)],[741, 9142, 9140, 727])).
% 1.97/2.19 tff(9144,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4133, 9143])).
% 1.97/2.19 tff(9145,plain,((~(s(elem!1) = s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(elem!1), z)) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9146,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9145, 8965, 294, 8963, 8961])).
% 1.97/2.19 tff(9147,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[992, 9146])).
% 1.97/2.19 tff(9148,plain,
% 1.97/2.19 (~(s(s(s(elem!1))) = elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1598, 8961])).
% 1.97/2.19 tff(9149,plain,
% 1.97/2.19 (~b(s(s(s(elem!1))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1330, 9147, 465, 515])).
% 1.97/2.19 tff(9150,plain,
% 1.97/2.19 (r(s(s(s(elem!1))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1313, 9149])).
% 1.97/2.19 tff(9151,plain,
% 1.97/2.19 (r(elem!1, s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[849])).
% 1.97/2.19 tff(9152,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), s(z)) <=> r(elem!1, s(z))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9151])).
% 1.97/2.19 tff(9153,plain,
% 1.97/2.19 (~r(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[302, 8963, 295])).
% 1.97/2.19 tff(9154,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), z)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[526, 9153])).
% 1.97/2.19 tff(9155,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[521, 192, 515, 465, 512, 1745])).
% 1.97/2.19 tff(9156,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9157,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9156, 515, 465, 9154])).
% 1.97/2.19 tff(9158,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[217, 9157])).
% 1.97/2.19 tff(9159,plain,
% 1.97/2.19 (r(elem!1, s(z))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9158, 9152])).
% 1.97/2.19 tff(9160,plain,
% 1.97/2.19 (~r(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2565, 9159, 9150])).
% 1.97/2.19 tff(9161,plain,
% 1.97/2.19 (b(s(s(s(elem!1))), elem!1)),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1628, 9160, 9148])).
% 1.97/2.19 tff(9162,plain,
% 1.97/2.19 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[849])).
% 1.97/2.19 tff(9163,plain,
% 1.97/2.19 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9162, 952])).
% 1.97/2.19 tff(9164,plain,
% 1.97/2.19 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9163])).
% 1.97/2.19 tff(9165,plain,
% 1.97/2.19 ((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9164])).
% 1.97/2.19 tff(9166,plain,
% 1.97/2.19 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[104, 9165])).
% 1.97/2.19 tff(9167,plain,
% 1.97/2.19 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[849])).
% 1.97/2.19 tff(9168,plain,
% 1.97/2.19 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[9167])).
% 1.97/2.19 tff(9169,plain,
% 1.97/2.19 (b(elem!1, s(s(s(z))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[394, 9168])).
% 1.97/2.19 tff(9170,plain,
% 1.97/2.19 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6191, 9169, 221, 440])).
% 1.97/2.19 tff(9171,plain,
% 1.97/2.19 (r(elem!1, s(s(s(s(s(z))))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[2227, 9170, 9166])).
% 1.97/2.19 tff(9172,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[8219, 9171, 9161, 2184, 462, 9147])).
% 1.97/2.19 tff(9173,plain,((~(elem!1 = s(s(s(s(z)))))) | (elem!1 = z) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9174,plain,
% 1.97/2.19 (~(elem!1 = s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9173, 8959, 8944, 2779, 8952, 5227, 465, 8954, 294])).
% 1.97/2.19 tff(9175,plain,
% 1.97/2.19 (~b(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9156, 515, 465, 4804])).
% 1.97/2.19 tff(9176,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[217, 9175])).
% 1.97/2.19 tff(9177,plain,
% 1.97/2.19 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(z))))))),
% 1.97/2.19 inference(symmetry,[status(thm)],[1600])).
% 1.97/2.19 tff(9178,plain,
% 1.97/2.19 (elem!1 = s(s(s(s(z))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[695, 9177, 44])).
% 1.97/2.19 tff(9179,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3528, 9178])).
% 1.97/2.19 tff(9180,plain,((~(s(s(s(s(s(z))))) = s(elem!1))) | (elem!1 = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9181,plain,
% 1.97/2.19 (~(s(s(s(s(s(z))))) = s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9180, 3528])).
% 1.97/2.19 tff(9182,plain,
% 1.97/2.19 (~r(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[4784, 545, 8963])).
% 1.97/2.19 tff(9183,plain,
% 1.97/2.19 (b(s(s(s(s(s(z))))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[597, 9182, 815])).
% 1.97/2.19 tff(9184,plain,
% 1.97/2.19 (r(s(s(s(s(z)))), z) <=> r(s(elem!1), z)),
% 1.97/2.19 inference(symmetry,[status(thm)],[1349])).
% 1.97/2.19 tff(9185,plain,
% 1.97/2.19 ((~r(s(s(s(s(z)))), z)) <=> (~r(s(elem!1), z))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9184])).
% 1.97/2.19 tff(9186,plain,
% 1.97/2.19 (~r(s(elem!1), z)),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[523, 9185])).
% 1.97/2.19 tff(9187,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[545, 9186])).
% 1.97/2.19 tff(9188,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~r(s(elem!1), z)) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9189,plain,
% 1.97/2.19 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9188, 545, 523])).
% 1.97/2.19 tff(9190,plain,
% 1.97/2.19 (~r(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7796, 308, 537])).
% 1.97/2.19 tff(9191,plain,
% 1.97/2.19 (b(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[950, 9190, 115])).
% 1.97/2.19 tff(9192,plain,
% 1.97/2.19 (~b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7841, 9191, 2490, 582])).
% 1.97/2.19 tff(9193,plain,
% 1.97/2.19 (r(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[658, 9192, 639])).
% 1.97/2.19 tff(9194,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7831, 77, 537, 308, 9193])).
% 1.97/2.19 tff(9195,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9196,plain,
% 1.97/2.19 ((~r(s(z), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (s(elem!1) = s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9195, 6957])).
% 1.97/2.19 tff(9197,plain,
% 1.97/2.19 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9196, 9183, 308, 115])).
% 1.97/2.19 tff(9198,plain,
% 1.97/2.19 (b(s(elem!1), s(s(s(s(z)))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[535, 9197, 9189])).
% 1.97/2.19 tff(9199,plain,
% 1.97/2.19 (~b(s(s(s(z))), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[3283, 192, 9198, 9183, 395, 440])).
% 1.97/2.19 tff(9200,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.97/2.19 tff(9201,plain,
% 1.97/2.19 (b(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[427, 9200])).
% 1.97/2.19 tff(9202,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9203,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9204,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9203, 9202])).
% 1.97/2.19 tff(9205,plain,
% 1.97/2.19 (~r(s(s(s(z))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9204, 77, 660, 8372])).
% 1.97/2.19 tff(9206,plain,
% 1.97/2.19 (b(s(s(s(z))), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[920, 9205])).
% 1.97/2.19 tff(9207,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[6983, 192, 2490, 9206, 9201, 221])).
% 1.97/2.19 tff(9208,plain,(r(s(z), s(s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9209,plain,
% 1.97/2.19 (r(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9208, 660, 221, 2490, 8372])).
% 1.97/2.19 tff(9210,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9211,plain,
% 1.97/2.19 (((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9212,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9211])).
% 1.97/2.19 tff(9213,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9212, 9210])).
% 1.97/2.19 tff(9214,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9215,plain,
% 1.97/2.19 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9214, 9213])).
% 1.97/2.19 tff(9216,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9215, 77, 660, 9209, 8372])).
% 1.97/2.19 tff(9217,plain,((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9218,plain,
% 1.97/2.19 (~r(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9217, 8372, 221, 2490])).
% 1.97/2.19 tff(9219,plain,
% 1.97/2.19 (b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[658, 639, 9218])).
% 1.97/2.19 tff(9220,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), 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(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9221,plain,
% 1.97/2.19 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(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(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9222,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(z)))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9221])).
% 1.97/2.19 tff(9223,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, 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(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9222, 9220])).
% 1.97/2.19 tff(9224,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9225,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(z), s(s(s(z)))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9224, 9223])).
% 1.97/2.19 tff(9226,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9225, 192, 953, 582, 2490, 3527, 221])).
% 1.97/2.19 tff(9227,plain,((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9228,plain,
% 1.97/2.19 (~b(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9227, 953, 582, 2490, 221])).
% 1.97/2.19 tff(9229,plain,
% 1.97/2.19 (r(s(z), s(s(s(z))))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[427, 9228])).
% 1.97/2.19 tff(9230,plain,
% 1.97/2.19 (~b(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[7841, 953, 2490, 582])).
% 1.97/2.19 tff(9231,plain,
% 1.97/2.19 (r(s(z), s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[658, 9230, 651])).
% 1.97/2.19 tff(9232,plain,
% 1.97/2.19 ($false),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9215, 77, 9231, 9229, 8372])).
% 1.97/2.19 tff(9233,plain,((~b(s(elem!1), s(z))) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.97/2.19 tff(9234,plain,
% 1.97/2.19 (~b(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9233, 639, 582, 2490, 221, 8372])).
% 1.97/2.19 tff(9235,plain,
% 1.97/2.19 (r(s(elem!1), s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[950, 9234, 115])).
% 1.97/2.19 tff(9236,plain,
% 1.97/2.19 (~r(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[1737, 9235, 545])).
% 1.97/2.19 tff(9237,plain,
% 1.97/2.19 (b(z, s(z))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[292, 9236])).
% 1.97/2.19 tff(9238,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9239,plain,
% 1.97/2.19 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(rewrite,[status(thm)],[])).
% 1.97/2.19 tff(9240,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))))),
% 1.97/2.19 inference(monotonicity,[status(thm)],[9239])).
% 1.97/2.19 tff(9241,plain,
% 1.97/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 1.97/2.19 inference(transitivity,[status(thm)],[9240, 9238])).
% 1.97/2.19 tff(9242,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 1.97/2.19 inference(quant_inst,[status(thm)],[])).
% 1.97/2.19 tff(9243,plain,
% 1.97/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))),
% 1.97/2.19 inference(modus_ponens,[status(thm)],[9242, 9241])).
% 1.97/2.19 tff(9244,plain,
% 1.97/2.19 (~b(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[9243, 192, 869, 1242, 9237, 9219])).
% 1.97/2.19 tff(9245,plain,
% 1.97/2.19 (r(z, s(elem!1))),
% 1.97/2.19 inference(unit_resolution,[status(thm)],[580, 9244])).
% 1.97/2.19 tff(9246,plain,
% 1.97/2.19 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(9247,plain,
% 1.97/2.20 (((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(9248,plain,
% 1.97/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[9247])).
% 1.97/2.20 tff(9249,plain,
% 1.97/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[9248, 9246])).
% 1.97/2.20 tff(9250,plain,
% 1.97/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), z)))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(9251,plain,
% 1.97/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[9250, 9249])).
% 1.97/2.20 tff(9252,plain,
% 1.97/2.20 (~r(s(s(s(z))), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[9251, 77, 9245, 8372])).
% 1.97/2.20 tff(9253,plain,
% 1.97/2.20 (b(s(s(s(z))), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[253, 9252])).
% 1.97/2.20 tff(9254,plain,
% 1.97/2.20 (~r(s(z), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[8348, 115, 2490, 582, 545])).
% 1.97/2.20 tff(9255,plain,
% 1.97/2.20 (b(s(z), z)),
% 1.97/2.20 inference(unit_resolution,[status(thm)],[351, 9254])).
% 1.97/2.20 tff(9256,plain,
% 1.97/2.20 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.20 inference(rewrite,[status(thm)],[])).
% 1.97/2.20 tff(9257,plain,
% 1.97/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 1.97/2.20 inference(monotonicity,[status(thm)],[9256])).
% 1.97/2.20 tff(9258,plain,
% 1.97/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 1.97/2.20 inference(transitivity,[status(thm)],[9257, 930])).
% 1.97/2.20 tff(9259,plain,
% 1.97/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)))),
% 1.97/2.20 inference(quant_inst,[status(thm)],[])).
% 1.97/2.20 tff(9260,plain,
% 1.97/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 1.97/2.20 inference(modus_ponens,[status(thm)],[9259, 9258])).
% 2.04/2.20 tff(9261,plain,
% 2.04/2.20 (~b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9260, 192, 9255, 9237, 9253])).
% 2.04/2.20 tff(9262,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[920, 9261])).
% 2.04/2.20 tff(9263,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[901, 77, 9235, 9262, 8372])).
% 2.04/2.20 tff(9264,plain,((s(elem!1) = s(z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9265,plain,
% 2.04/2.20 ((s(elem!1) = s(z)) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(elem!1), z)) | (~b(s(s(s(s(s(z))))), s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9264, 6957])).
% 2.04/2.20 tff(9266,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9265, 9198, 115, 1242, 221, 545, 9183])).
% 2.04/2.20 tff(9267,plain,
% 2.04/2.20 (s(s(s(z))) = s(elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[906, 60, 9266, 9199])).
% 2.04/2.20 tff(9268,plain,
% 2.04/2.20 (r(s(elem!1), s(s(s(z)))) <=> r(s(elem!1), s(elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9267])).
% 2.04/2.20 tff(9269,plain,
% 2.04/2.20 (r(s(elem!1), s(elem!1)) <=> r(s(elem!1), s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9268])).
% 2.04/2.20 tff(9270,plain,
% 2.04/2.20 ((~r(s(elem!1), s(elem!1))) <=> (~r(s(elem!1), s(s(s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9269])).
% 2.04/2.20 tff(9271,plain,
% 2.04/2.20 ((~![X: $i] : (~r(X, X))) | (~r(s(elem!1), s(elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9272,plain,
% 2.04/2.20 (~r(s(elem!1), s(elem!1))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9271, 1518])).
% 2.04/2.20 tff(9273,plain,
% 2.04/2.20 (~r(s(elem!1), s(s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9272, 9270])).
% 2.04/2.20 tff(9274,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1993, 9189])).
% 2.04/2.20 tff(9275,plain,
% 2.04/2.20 (r(s(elem!1), s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4858, 9266, 2779, 465, 523, 1242, 515, 815, 8963, 221, 545, 9274])).
% 2.04/2.20 tff(9276,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9275, 9273])).
% 2.04/2.20 tff(9277,plain,((~r(s(elem!1), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | r(s(s(s(s(z)))), z) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (s(s(s(s(s(z))))) = s(elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9278,plain,
% 2.04/2.20 (~r(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9277, 9181, 440, 465, 523, 1242, 515, 395, 221, 115, 308])).
% 2.04/2.20 tff(9279,plain,
% 2.04/2.20 (b(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[560, 9278])).
% 2.04/2.20 tff(9280,plain,
% 2.04/2.20 (~b(s(elem!1), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1239, 9279, 465, 515])).
% 2.04/2.20 tff(9281,plain,
% 2.04/2.20 (r(s(elem!1), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[950, 9280, 115])).
% 2.04/2.20 tff(9282,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[782, 77, 537, 668, 67])).
% 2.04/2.20 tff(9283,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(9284,plain,
% 2.04/2.20 (~r(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9283, 9281, 9176])).
% 2.04/2.20 tff(9285,plain,
% 2.04/2.20 (~b(s(elem!1), s(s(s(s(z)))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[7788, 192, 9279, 1242, 4804])).
% 2.04/2.20 tff(9286,plain,
% 2.04/2.20 (s(elem!1) = s(s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[535, 9285, 9284])).
% 2.04/2.20 tff(9287,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9286])).
% 2.04/2.20 tff(9288,plain,
% 2.04/2.20 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9287])).
% 2.04/2.20 tff(9289,plain,
% 2.04/2.20 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9288])).
% 2.04/2.20 tff(9290,plain,
% 2.04/2.20 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9289])).
% 2.04/2.20 tff(9291,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9290])).
% 2.04/2.20 tff(9292,plain,
% 2.04/2.20 (elem!1 = s(s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3339, 9286])).
% 2.04/2.20 tff(9293,plain,
% 2.04/2.20 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9292])).
% 2.04/2.20 tff(9294,plain,
% 2.04/2.20 (s(s(s(z))) = elem!1),
% 2.04/2.20 inference(symmetry,[status(thm)],[9292])).
% 2.04/2.20 tff(9295,plain,
% 2.04/2.20 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9294])).
% 2.04/2.20 tff(9296,plain,
% 2.04/2.20 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9295])).
% 2.04/2.20 tff(9297,plain,
% 2.04/2.20 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5253, 9296])).
% 2.04/2.20 tff(9298,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9288, 9292])).
% 2.04/2.20 tff(9299,plain,
% 2.04/2.20 (r(s(s(s(s(s(s(z)))))), s(s(s(z)))) <=> r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(symmetry,[status(thm)],[9298])).
% 2.04/2.20 tff(9300,plain,
% 2.04/2.20 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) <=> (~r(s(s(s(elem!1))), elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9299])).
% 2.04/2.20 tff(9301,plain,
% 2.04/2.20 (r(s(elem!1), s(s(s(s(s(z)))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9286])).
% 2.04/2.20 tff(9302,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9301])).
% 2.04/2.20 tff(9303,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9304,plain,
% 2.04/2.20 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9305,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9304])).
% 2.04/2.20 tff(9306,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9305, 9303])).
% 2.04/2.20 tff(9307,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9308,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9307, 9306])).
% 2.04/2.20 tff(9309,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9308, 192, 395, 394, 221, 440])).
% 2.04/2.20 tff(9310,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[113, 9309])).
% 2.04/2.20 tff(9311,plain,
% 2.04/2.20 (r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9310, 9302])).
% 2.04/2.20 tff(9312,plain,
% 2.04/2.20 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9295, 1977])).
% 2.04/2.20 tff(9313,plain,
% 2.04/2.20 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9312])).
% 2.04/2.20 tff(9314,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[5253, 9313])).
% 2.04/2.20 tff(9315,plain,
% 2.04/2.20 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9292])).
% 2.04/2.20 tff(9316,plain,
% 2.04/2.20 (r(s(s(s(z))), s(z)) <=> r(elem!1, s(z))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9315])).
% 2.04/2.20 tff(9317,plain,
% 2.04/2.20 (r(elem!1, s(z))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[116, 9316])).
% 2.04/2.20 tff(9318,plain,
% 2.04/2.20 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9286])).
% 2.04/2.20 tff(9319,plain,
% 2.04/2.20 ((s(elem!1) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9318, 3030])).
% 2.04/2.20 tff(9320,plain,
% 2.04/2.20 ((elem!1 = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 2.04/2.20 inference(symmetry,[status(thm)],[9319])).
% 2.04/2.20 tff(9321,plain,
% 2.04/2.20 ((~(elem!1 = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9320])).
% 2.04/2.20 tff(9322,plain,
% 2.04/2.20 (~(s(elem!1) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[3528, 9321])).
% 2.04/2.20 tff(9323,plain,
% 2.04/2.20 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9288])).
% 2.04/2.20 tff(9324,plain,
% 2.04/2.20 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9292, 9323])).
% 2.04/2.20 tff(9325,plain,
% 2.04/2.20 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[9324])).
% 2.04/2.20 tff(9326,plain,
% 2.04/2.20 ((~(s(s(s(z))) = s(s(s(s(s(s(s(z))))))))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9325])).
% 2.04/2.20 tff(9327,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[1969, 9326])).
% 2.04/2.20 tff(9328,plain,
% 2.04/2.20 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[718, 9327])).
% 2.04/2.20 tff(9329,plain,
% 2.04/2.20 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9330,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9329])).
% 2.04/2.20 tff(9331,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9330, 2491])).
% 2.04/2.20 tff(9332,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9333,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9332, 9331])).
% 2.04/2.20 tff(9334,plain,
% 2.04/2.20 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9333, 192, 515, 465, 2490])).
% 2.04/2.20 tff(9335,plain,
% 2.04/2.20 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[269, 60, 266, 9334])).
% 2.04/2.20 tff(9336,plain,
% 2.04/2.20 (~r(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1294, 9335, 795])).
% 2.04/2.20 tff(9337,plain,
% 2.04/2.20 (b(s(elem!1), z)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[560, 9336])).
% 2.04/2.20 tff(9338,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1328, 192, 1005, 515, 465])).
% 2.04/2.20 tff(9339,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1311, 60, 9338, 1307])).
% 2.04/2.20 tff(9340,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9341,plain,
% 2.04/2.20 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9342,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9341])).
% 2.04/2.20 tff(9343,plain,
% 2.04/2.20 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9342, 9340])).
% 2.04/2.20 tff(9344,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9345,plain,
% 2.04/2.20 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[9344, 9343])).
% 2.04/2.20 tff(9346,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[9345, 77, 2554, 9339])).
% 2.04/2.20 tff(9347,plain,
% 2.04/2.20 (b(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2823, 60, 9346, 2807])).
% 2.04/2.20 tff(9348,plain,
% 2.04/2.20 (~b(s(elem!1), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1239, 9337, 515, 465])).
% 2.04/2.20 tff(9349,plain,
% 2.04/2.20 (r(s(elem!1), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[950, 9348, 115])).
% 2.04/2.20 tff(9350,plain,
% 2.04/2.20 (~r(s(elem!1), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3102, 9349, 2554])).
% 2.04/2.20 tff(9351,plain,
% 2.04/2.20 (b(s(elem!1), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3123, 9350, 2795])).
% 2.04/2.20 tff(9352,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9353,plain,
% 2.04/2.20 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(9354,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[9353])).
% 2.04/2.20 tff(9355,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 2.04/2.20 inference(transitivity,[status(thm)],[9354, 9352])).
% 2.04/2.20 tff(9356,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(9357,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9356, 9355])).
% 2.04/2.21 tff(9358,plain,
% 2.04/2.21 (~b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9357, 192, 9351, 1005, 9347, 9337])).
% 2.04/2.21 tff(9359,plain,
% 2.04/2.21 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3228, 77, 9349, 9339])).
% 2.04/2.21 tff(9360,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[3232, 60, 9359, 706, 9358])).
% 2.04/2.21 tff(9361,plain,((~b(s(z), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (elem!1 = s(s(s(elem!1)))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9362,plain,
% 2.04/2.21 ((~b(s(z), z)) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (s(elem!1) = elem!1) | (~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~r(s(elem!1), s(s(s(s(s(z))))))) | (elem!1 = s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9361, 6957])).
% 2.04/2.21 tff(9363,plain,
% 2.04/2.21 (~b(s(s(s(elem!1))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9362, 9328, 465, 9322, 115, 515, 9317, 9314, 9311])).
% 2.04/2.21 tff(9364,plain,
% 2.04/2.21 (r(s(s(s(elem!1))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[992, 9363])).
% 2.04/2.21 tff(9365,assumption,(~r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 2.04/2.21 tff(9366,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), z)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9365, 5068])).
% 2.04/2.21 tff(9367,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[974, 9366])).
% 2.04/2.21 tff(9368,plain,(r(s(s(s(s(s(s(z)))))), z) | (~r(s(s(s(elem!1))), z)) | (~(s(elem!1) = s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9369,plain,
% 2.04/2.21 (r(s(s(s(s(s(s(z)))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9368, 9364, 9286])).
% 2.04/2.21 tff(9370,plain,
% 2.04/2.21 (~b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7102, 192, 1242, 395, 4804])).
% 2.04/2.21 tff(9371,plain,
% 2.04/2.21 (r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[253, 9370])).
% 2.04/2.21 tff(9372,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2597, 77, 9371, 9369])).
% 2.04/2.21 tff(9373,plain,
% 2.04/2.21 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9372, 9300])).
% 2.04/2.21 tff(9374,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1628, 9373, 9297])).
% 2.04/2.21 tff(9375,plain,
% 2.04/2.21 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9374, 9293])).
% 2.04/2.21 tff(9376,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9375, 9291])).
% 2.04/2.21 tff(9377,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9289])).
% 2.04/2.21 tff(9378,plain,
% 2.04/2.21 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[9377])).
% 2.04/2.21 tff(9379,plain,
% 2.04/2.21 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9378])).
% 2.04/2.21 tff(9380,plain,
% 2.04/2.21 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9292])).
% 2.04/2.21 tff(9381,plain,
% 2.04/2.21 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9380])).
% 2.04/2.21 tff(9382,plain,
% 2.04/2.21 (~b(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4615, 9286, 9370])).
% 2.04/2.21 tff(9383,plain,
% 2.04/2.21 (r(elem!1, z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2354, 9382, 2779])).
% 2.04/2.21 tff(9384,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2819, 9364, 9383])).
% 2.04/2.21 tff(9385,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9384, 9381])).
% 2.04/2.21 tff(9386,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9385, 9379])).
% 2.04/2.21 tff(9387,plain,
% 2.04/2.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9388,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9389,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9388, 9387])).
% 2.04/2.21 tff(9390,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9389, 60, 2419])).
% 2.04/2.21 tff(9391,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9390, 9386])).
% 2.04/2.21 tff(9392,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9393,plain,
% 2.04/2.21 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9394,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9393])).
% 2.04/2.21 tff(9395,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9394, 9392])).
% 2.04/2.21 tff(9396,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9397,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9396, 9395])).
% 2.04/2.21 tff(9398,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9397, 192, 221, 9391, 9376])).
% 2.04/2.21 tff(9399,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9400,plain,
% 2.04/2.21 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9401,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9400])).
% 2.04/2.21 tff(9402,plain,
% 2.04/2.21 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9401, 9399])).
% 2.04/2.21 tff(9403,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9404,plain,
% 2.04/2.21 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9403, 9402])).
% 2.04/2.21 tff(9405,plain,
% 2.04/2.21 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9404, 77, 8963, 9369])).
% 2.04/2.21 tff(9406,plain,
% 2.04/2.21 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5120, 60, 9405])).
% 2.04/2.21 tff(9407,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9406, 9398, 5110])).
% 2.04/2.21 tff(9408,plain,((elem!1 = s(s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), z) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9409,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9408, 9174, 465, 115, 8954, 8959, 8946, 8948, 5227, 8952, 8957, 308])).
% 2.04/2.21 tff(9410,plain,
% 2.04/2.21 (b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[920, 9409])).
% 2.04/2.21 tff(9411,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7312, 192, 6957, 8942, 9410, 8952])).
% 2.04/2.21 tff(9412,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9413,plain,
% 2.04/2.21 ((~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (s(elem!1) = s(z)) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9412, 7557])).
% 2.04/2.21 tff(9414,plain,
% 2.04/2.21 (s(elem!1) = s(z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9413, 408, 294, 8813])).
% 2.04/2.21 tff(9415,plain,
% 2.04/2.21 (z = elem!1),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1550, 9414])).
% 2.04/2.21 tff(9416,plain,
% 2.04/2.21 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9415])).
% 2.04/2.21 tff(9417,plain,
% 2.04/2.21 ((s(s(s(s(s(s(s(z))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9416, 8939])).
% 2.04/2.21 tff(9418,plain,
% 2.04/2.21 ((s(s(s(s(s(s(s(z))))))) = z) <=> (s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[9417, 8940])).
% 2.04/2.21 tff(9419,plain,
% 2.04/2.21 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(s(s(s(s(s(s(s(z))))))) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9418])).
% 2.04/2.21 tff(9420,plain,
% 2.04/2.21 (~(s(s(s(s(s(s(s(z))))))) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4083, 9419])).
% 2.04/2.21 tff(9421,plain,
% 2.04/2.21 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7579, 295])).
% 2.04/2.21 tff(9422,plain,
% 2.04/2.21 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7581, 9421])).
% 2.04/2.21 tff(9423,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9415])).
% 2.04/2.21 tff(9424,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7597, 295])).
% 2.04/2.21 tff(9425,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[390, 9424])).
% 2.04/2.21 tff(9426,plain,
% 2.04/2.21 (~b(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6993, 239, 8813])).
% 2.04/2.21 tff(9427,plain,
% 2.04/2.21 (r(s(z), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[351, 9426])).
% 2.04/2.21 tff(9428,plain,
% 2.04/2.21 (~r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7278, 2650, 504])).
% 2.04/2.21 tff(9429,plain,
% 2.04/2.21 (b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[427, 9428])).
% 2.04/2.21 tff(9430,plain,
% 2.04/2.21 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8928, 192, 8813, 6957, 7002])).
% 2.04/2.21 tff(9431,plain,
% 2.04/2.21 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[493, 9430])).
% 2.04/2.21 tff(9432,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[5264, 2650, 9431])).
% 2.04/2.21 tff(9433,plain,
% 2.04/2.21 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[375, 9432])).
% 2.04/2.21 tff(9434,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7004, 9433, 9429, 7002, 221])).
% 2.04/2.21 tff(9435,plain,((~r(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))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9436,plain,
% 2.04/2.21 (~r(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9435, 221, 7002, 9427])).
% 2.04/2.21 tff(9437,plain,
% 2.04/2.21 (b(z, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[237, 9436])).
% 2.04/2.21 tff(9438,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[7088, 9437, 8920, 395])).
% 2.04/2.21 tff(9439,plain,
% 2.04/2.21 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[406, 9438])).
% 2.04/2.21 tff(9440,plain,
% 2.04/2.21 (~r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[8834, 9439])).
% 2.04/2.21 tff(9441,plain,
% 2.04/2.21 (b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[427, 9440])).
% 2.04/2.21 tff(9442,plain,
% 2.04/2.21 (~b(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[2641, 9437, 239, 221])).
% 2.04/2.21 tff(9443,plain,
% 2.04/2.21 (r(s(s(s(z))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[253, 9442])).
% 2.04/2.21 tff(9444,plain,
% 2.04/2.21 (~r(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[509, 9443, 9427])).
% 2.04/2.21 tff(9445,plain,
% 2.04/2.21 (b(s(s(s(z))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[920, 9444])).
% 2.04/2.21 tff(9446,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[6985, 9445, 9441, 221])).
% 2.04/2.21 tff(9447,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(9448,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9447, 8938, 9425, 8922])).
% 2.04/2.21 tff(9449,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[271, 9448])).
% 2.04/2.21 tff(9450,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[302, 9449, 295])).
% 2.04/2.21 tff(9451,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[526, 9450])).
% 2.04/2.21 tff(9452,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9451, 9423])).
% 2.04/2.21 tff(9453,plain,
% 2.04/2.21 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9415])).
% 2.04/2.21 tff(9454,plain,
% 2.04/2.21 (b(elem!1, s(s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[8920, 9453])).
% 2.04/2.21 tff(9455,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9456,plain,
% 2.04/2.21 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9457,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9456])).
% 2.04/2.21 tff(9458,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9457, 9455])).
% 2.04/2.21 tff(9459,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9460,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9459, 9458])).
% 2.04/2.21 tff(9461,plain,
% 2.04/2.21 (~b(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9460, 192, 9454, 9452, 9422])).
% 2.04/2.21 tff(9462,plain,
% 2.04/2.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9463,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(9464,plain,
% 2.04/2.21 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[9463, 9462])).
% 2.04/2.21 tff(9465,plain,
% 2.04/2.21 ((s(s(s(s(s(s(s(z))))))) = elem!1) | b(s(s(s(s(s(s(s(z))))))), elem!1) | r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9464, 60])).
% 2.04/2.21 tff(9466,plain,
% 2.04/2.21 (r(s(s(s(s(s(s(s(z))))))), elem!1)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[9465, 9461, 9420])).
% 2.04/2.21 tff(9467,plain,
% 2.04/2.21 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9415])).
% 2.04/2.21 tff(9468,plain,
% 2.04/2.21 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[9467, 2011])).
% 2.04/2.21 tff(9469,plain,
% 2.04/2.21 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.21 inference(transitivity,[status(thm)],[9468, 5834])).
% 2.04/2.21 tff(9470,plain,
% 2.04/2.21 ((~(s(s(s(z))) = z)) <=> (~(s(s(s(z))) = elem!1))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[9469])).
% 2.04/2.21 tff(9471,plain,
% 2.04/2.21 (~(s(s(s(z))) = elem!1)),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[209, 9470])).
% 2.04/2.21 tff(9472,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9473,plain,
% 2.04/2.21 (((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(9474,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9473])).
% 2.04/2.22 tff(9475,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9474, 9472])).
% 2.04/2.22 tff(9476,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9477,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9476, 9475])).
% 2.04/2.22 tff(9478,plain,
% 2.04/2.22 (~b(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9477, 192, 9454, 9452, 9425])).
% 2.04/2.22 tff(9479,plain,
% 2.04/2.22 (r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2025, 9478, 9471])).
% 2.04/2.22 tff(9480,plain,
% 2.04/2.22 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9481,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9482,plain,
% 2.04/2.22 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), elem!1)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9481, 9480])).
% 2.04/2.22 tff(9483,plain,
% 2.04/2.22 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9482, 77, 9479, 9466])).
% 2.04/2.22 tff(9484,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8834, 408])).
% 2.04/2.22 tff(9485,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[406, 9484])).
% 2.04/2.22 tff(9486,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9487,plain,
% 2.04/2.22 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9488,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9487])).
% 2.04/2.22 tff(9489,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9488, 9486])).
% 2.04/2.22 tff(9490,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9491,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9490, 9489])).
% 2.04/2.22 tff(9492,plain,
% 2.04/2.22 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9491, 192, 9454, 9452, 9425, 9485, 9422])).
% 2.04/2.22 tff(9493,plain,
% 2.04/2.22 ((s(s(s(s(s(s(s(z))))))) = s(s(s(z)))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4440, 60, 9492])).
% 2.04/2.22 tff(9494,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9493, 9483, 4432])).
% 2.04/2.22 tff(9495,plain,((~r(s(z), s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9496,plain,
% 2.04/2.22 (~r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9495, 294])).
% 2.04/2.22 tff(9497,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[427, 9496])).
% 2.04/2.22 tff(9498,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7004, 9497, 8922, 8938])).
% 2.04/2.22 tff(9499,plain,
% 2.04/2.22 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[375, 9498])).
% 2.04/2.22 tff(9500,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5264, 9499, 8930])).
% 2.04/2.22 tff(9501,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[237, 9500])).
% 2.04/2.22 tff(9502,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9503,plain,
% 2.04/2.22 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(9504,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9503])).
% 2.04/2.22 tff(9505,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9504, 9502])).
% 2.04/2.22 tff(9506,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(9507,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X2, X4)) | (~b(X0, X4)) | (~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9506, 9505])).
% 2.04/2.22 tff(9508,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9507, 192, 8920, 8813, 9425, 9497, 9501])).
% 2.04/2.22 tff(9509,plain,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9510,plain,
% 2.04/2.22 ((~r(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4029, 7557])).
% 2.04/2.22 tff(9511,plain,
% 2.04/2.22 (~r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9510, 239, 9509])).
% 2.04/2.22 tff(9512,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[351, 9511, 9426])).
% 2.04/2.22 tff(9513,plain,(~b(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9514,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[271, 9513])).
% 2.04/2.22 tff(9515,plain,
% 2.04/2.22 (~b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8650, 383, 9514])).
% 2.04/2.22 tff(9516,plain,
% 2.04/2.22 (r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[351, 9515])).
% 2.04/2.22 tff(9517,plain,
% 2.04/2.22 (s(elem!1) = s(z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8464, 9516, 9509, 8920])).
% 2.04/2.22 tff(9518,plain,
% 2.04/2.22 ((s(s(s(s(s(z))))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9517])).
% 2.04/2.22 tff(9519,plain,
% 2.04/2.22 ((s(s(s(s(s(z))))) = s(z)) <=> (s(s(s(s(s(z))))) = s(elem!1))),
% 2.04/2.22 inference(symmetry,[status(thm)],[9518])).
% 2.04/2.22 tff(9520,plain,
% 2.04/2.22 ((s(s(s(s(s(z))))) = s(z)) <=> (s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[9519, 747])).
% 2.04/2.22 tff(9521,plain,
% 2.04/2.22 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(elem!1) = s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9520])).
% 2.04/2.22 tff(9522,plain,
% 2.04/2.22 (~(s(elem!1) = s(s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[50, 9521])).
% 2.04/2.22 tff(9523,plain,
% 2.04/2.22 (r(s(elem!1), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5721, 9517, 9516])).
% 2.04/2.22 tff(9524,plain,
% 2.04/2.22 (~r(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1294, 9523, 9514])).
% 2.04/2.22 tff(9525,plain,
% 2.04/2.22 (~r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8622, 383])).
% 2.04/2.22 tff(9526,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[427, 9525])).
% 2.04/2.22 tff(9527,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7652, 383])).
% 2.04/2.22 tff(9528,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[920, 9527])).
% 2.04/2.22 tff(9529,plain,
% 2.04/2.22 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6985, 9528, 9526])).
% 2.04/2.22 tff(9530,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[133, 9529])).
% 2.04/2.22 tff(9531,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5178, 9530, 9514])).
% 2.04/2.22 tff(9532,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[237, 9531])).
% 2.04/2.22 tff(9533,plain,
% 2.04/2.22 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7454, 9532, 8813, 9528, 9526])).
% 2.04/2.22 tff(9534,plain,
% 2.04/2.22 (~b(s(elem!1), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5767, 9533, 9517])).
% 2.04/2.22 tff(9535,plain,
% 2.04/2.22 (s(elem!1) = s(s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[811, 9534, 9524])).
% 2.04/2.22 tff(9536,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[9535, 9522])).
% 2.04/2.22 tff(9537,plain,(~r(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(9538,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[390, 9537])).
% 2.04/2.22 tff(9539,plain,
% 2.04/2.22 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8844, 9538, 9509])).
% 2.04/2.22 tff(9540,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[133, 9539])).
% 2.04/2.22 tff(9541,plain,
% 2.04/2.22 (~r(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[5178, 9540, 9514])).
% 2.04/2.22 tff(9542,plain,
% 2.04/2.22 (b(z, s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[237, 9541])).
% 2.04/2.22 tff(9543,plain,
% 2.04/2.22 (~r(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8850, 9540, 9514])).
% 2.04/2.22 tff(9544,plain,
% 2.04/2.22 (b(s(s(s(z))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[253, 9543])).
% 2.04/2.22 tff(9545,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7088, 9542, 8920, 9538])).
% 2.04/2.22 tff(9546,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[406, 9545])).
% 2.04/2.22 tff(9547,plain,
% 2.04/2.22 (~r(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8834, 9546])).
% 2.04/2.22 tff(9548,plain,
% 2.04/2.22 (b(s(z), s(s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[427, 9547])).
% 2.04/2.22 tff(9549,plain,
% 2.04/2.22 (~b(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7663, 9548, 9544, 9542])).
% 2.04/2.22 tff(9550,plain,
% 2.04/2.22 (r(s(z), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[351, 9549])).
% 2.04/2.22 tff(9551,plain,
% 2.04/2.22 (s(elem!1) = s(z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8464, 9550, 9509, 8920])).
% 2.04/2.22 tff(9552,plain,
% 2.04/2.22 (s(s(elem!1)) = s(s(z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9551])).
% 2.04/2.22 tff(9553,plain,
% 2.04/2.22 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9552])).
% 2.04/2.22 tff(9554,plain,
% 2.04/2.22 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9553])).
% 2.04/2.22 tff(9555,plain,
% 2.04/2.22 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.22 inference(symmetry,[status(thm)],[9554])).
% 2.04/2.22 tff(9556,plain,
% 2.04/2.22 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9555])).
% 2.04/2.22 tff(9557,plain,
% 2.04/2.22 (z = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1550, 9551])).
% 2.04/2.22 tff(9558,plain,
% 2.04/2.22 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9557])).
% 2.04/2.22 tff(9559,plain,
% 2.04/2.22 ((~r(z, s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[9558])).
% 2.04/2.22 tff(9560,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9541, 9559])).
% 2.04/2.22 tff(9561,plain,
% 2.04/2.22 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[9560, 9556])).
% 2.04/2.22 tff(9562,plain,
% 2.04/2.22 (elem!1 = z),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2884, 9557])).
% 2.04/2.22 tff(9563,plain,
% 2.04/2.22 (~b(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8709, 9538, 8920, 9509])).
% 2.04/2.22 tff(9564,plain,
% 2.04/2.22 (r(s(s(s(s(z)))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[526, 9563])).
% 2.04/2.22 tff(9565,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4660, 9550, 9564])).
% 2.04/2.22 tff(9566,plain,
% 2.04/2.22 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8402, 9564, 9514])).
% 2.04/2.22 tff(9567,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[113, 9566])).
% 2.04/2.22 tff(9568,plain,
% 2.04/2.22 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4048, 9567, 8920, 9509])).
% 2.04/2.22 tff(9569,plain,
% 2.04/2.22 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[493, 9568])).
% 2.04/2.22 tff(9570,plain,
% 2.04/2.22 (~r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7010, 9550, 9569])).
% 2.04/2.22 tff(9571,plain,
% 2.04/2.22 (b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[7007, 9570])).
% 2.04/2.22 tff(9572,plain,
% 2.04/2.22 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[217, 9565])).
% 2.04/2.22 tff(9573,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8619, 9572, 8920, 9538, 9509])).
% 2.04/2.22 tff(9574,plain,
% 2.04/2.22 (r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[920, 9573])).
% 2.04/2.22 tff(9575,plain,
% 2.04/2.22 (~b(z, s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[8596, 9574, 8920, 9509, 9544, 9571, 9562, 9565])).
% 2.04/2.22 tff(9576,plain,
% 2.04/2.22 (r(z, s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1021, 9575])).
% 2.04/2.22 tff(9577,plain,
% 2.04/2.22 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[6296, 9576, 9562])).
% 2.04/2.23 tff(9578,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[9577, 9561])).
% 2.04/2.23 % SZS output end Proof
% 2.04/2.23 % E exiting
%------------------------------------------------------------------------------